JP2019106108A - Analysis method of specific substance, and computer program for analysis of specific substance - Google Patents

Abstract

To provide an analysis method of a specific substance or the like excellent in reproducibility of dynamic response due to breakage of a molecular chain.SOLUTION: An analysis method of a specific substance includes the steps of creating an analysis model of a specific substance including a specific substance model to be analyzed ST11, setting a first threshold to distance between at least a pair of particles which belong to a specific substance model and are bound by inter-particle bonding ST12, setting an attractive force interaction between the specific substance models ST13, and making a numerical analysis of the analysis model by performing breakage processing of the inter-particle bonding if the distance between the particles is equal to or more than the first threshold ST14.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a method of analyzing a specific substance and a computer program for analyzing the specific substance, for example, to a method of analyzing a specific substance containing two or more substances and a computer program for analyzing the specific substance.

  Conventionally, a simulation method of a composite material using molecular dynamics has been proposed (see, for example, Patent Document 1). In the simulation method of the composite material described in Patent Document 1, after creating a polymer model and a filler model in a modeling area, the polymer model is bonded to the bonding position on the surface of the filler model. Thereby, in the analysis method of the composite material described in Patent Document 1, it becomes possible to analyze the influence of the bonding state of the polymer particles on the filler surface on the material properties of the composite material.

JP, 2015-064242, A

  By the way, in order to accelerate development of the rubber material which improves the wear resistance performance of a tire, it helps to clarify the mechanism of the destruction of the nano structure accompanying the deformation of the rubber material. By analyzing the fracture of the nano structure of the rubber material before and after deformation, it is possible to accelerate the material development for improving the breaking strength of the filler-filled rubber used in an actual tire.

  In conventional molecular dynamics numerical analysis, it is necessary to break and eliminate interparticle bonds of polymer particles in the rubber material in order to analyze the breakdown of the nanostructures caused by the deformation of the rubber material. However, in the conventional numerical analysis by molecular dynamics, the reproducibility of the mechanical response due to breakage is not always sufficient, and it is difficult to analyze the mechanism of fracture of the nano structure of the rubber material.

  The present invention has been made in view of such circumstances, and it is an object of the present invention to provide a method for analyzing a specific substance excellent in repeatability of mechanical response accompanying breakage of a molecular chain and a computer program for analyzing the specific substance. I assume.

  The method of analyzing a specific substance according to the present invention is a method of analyzing a specific substance by a molecular dynamics method using a computer, and creating a model for analysis of a specific substance including a specific substance model to be analyzed; Setting a first threshold to an interparticle distance of at least a pair of particles belonging to the specific substance model and coupled by interparticle coupling, setting an attractive interaction between the specific substance models, and the interparticle And when the distance is equal to or more than the first threshold value, the processing for breaking the interparticle bonds is performed and the numerical analysis of the analysis model is performed.

  According to the method of analyzing a specific substance according to the present invention, even if the fracture processing is performed, the stretching speed associated with the breakage of the molecular chain of the specific substance is reduced by the attractive interaction set between the specific substance models. Can improve the repeatability of the mechanical response associated with breakage. And since the fracture process can be performed in a pseudo manner, it is possible to numerically analyze the analysis model without the interparticle bonds being eliminated by the fracture. As a result, the analysis method of the specific substance can prevent physical annihilation of the interparticle bond caused by the fracture, so that it is possible to reproduce a pseudo fracture without physically eliminating the interparticle bond. Become.

  It is preferable that the method of analyzing a specific substance of the present invention further includes the step of crosslinking the specific substance model. According to this method, since the analysis method of the specific substance can carry out the numerical analysis of the analysis model in a state in which the specific substance is crosslinked in advance via the crosslinking reaction, it is possible to analyze the influence of the crosslinking of the specific substance on the interparticle bond breakage. It becomes.

  In the analysis method of the specific substance of the present invention, it is preferable to set the attractive interaction to particles of the specific substance model which belong to the molecular chain containing the interparticle bond subjected to the fracture treatment. As a result, it is possible to reduce the area in which the attractive interaction is set in the analysis model, and hence the calculation time can be shortened.

  In the analysis method of the specific substance of the present invention, the attractive interaction is set to particles of the specific substance model in the vicinity including the particles of the specific substance model connected by the fracture-treated interparticle bond. Is preferred. As a result, it is possible to reduce the area in which the attractive interaction is set in the analysis model, and hence the calculation time can be shortened.

  In the method of analyzing a specific substance of the present invention, it is preferable to set the attractive interaction within a predetermined range from the interparticle bonding subjected to the fracture treatment. As a result, it is possible to reduce the area in which the attractive interaction is set in the analysis model, and hence the calculation time can be shortened.

  In the analysis method of the specific substance of the present invention, it is preferable that the setting of the attractive interaction is performed together with the breaking process. As a result, it is possible to reduce the operation load required for setting the attractive interaction while reducing the influence on the reproducibility of the mechanical response.

  In the analysis method of the specific substance of the present invention, it is preferable to set the attractive interaction when the interparticle distance is equal to or more than a second threshold smaller than the first threshold. This makes it possible to prevent the rapid contraction of the molecular chain of the specific substance at the time of the pseudo fracture process, so that the reproducibility of the mechanical response at the time of numerical analysis is further improved.

  In the method of analyzing a specific substance of the present invention, it is preferable to reduce the attractive interaction with the lapse of analysis time after the fracture treatment. Thereby, the calculation load at the time of numerical analysis can be reduced while reducing the influence on the reproducibility of the mechanical response.

  In the specific substance analysis method of the present invention, it is preferable to set the attractive interaction having an intensity distribution between the specific substance models. This makes it possible to reduce the distribution of discontinuous interactions between attractive forces and repulsive forces generated in the analysis model of the specific substance, thereby further improving the reproducibility of the mechanical response at the time of numerical analysis.

  In the analysis method of the specific substance of the present invention, the fracture process is a pseudo fracture process using a fracture bond operation function, and the fracture bond operation function is at least a bond energy and a bond force of the interparticle bond. It is preferred that the one be substantially eliminated. According to this method, the analysis method of the specific substance can accurately reproduce the pseudo cutting of the pair of particles to be analyzed at the time of the numerical analysis of the analysis model, and thus, for example, in the actual composite material such as filler filled rubber. It is possible to reproduce the breakage of the polymer molecule with high accuracy.

  In the method of analyzing a specific substance of the present invention, the specific substance preferably contains a polymer and a filler. By this method, the analysis method of the specific substance can accurately reproduce the analysis result of an actual composite material such as filler-filled rubber, for example.

  The computer program for analyzing a specific substance of the present invention is characterized by making a computer execute the analysis method for the specific substance.

  According to the computer program for analyzing a specific substance of the present invention, even if the fracture processing is performed, the stretching speed associated with the breaking of the molecular chain of the specific substance is reduced by the attractive interaction set between the specific substance models. As a result, the reproducibility of the mechanical response associated with breakage is improved. And since the fracture process can be performed in a pseudo manner, it is possible to numerically analyze the analysis model without the interparticle bonds being eliminated by the fracture. As a result, the analysis method of the specific substance can prevent physical annihilation of the interparticle bond caused by the fracture, so that it is possible to reproduce a pseudo fracture without physically eliminating the interparticle bond. Become.

  According to the present invention, it is possible to realize the analysis method of a specific substance and the computer program for analysis of the specific substance which are excellent in the reproducibility of the mechanical response accompanying the breakage of the molecular chain.

FIG. 1 is a flowchart showing an outline of an example of a method of analyzing a composite material according to an embodiment of the present invention. FIG. 2 is a conceptual view showing an example of an analysis model created by the method of analyzing a composite material according to the embodiment of the present invention. FIG. 3A is an explanatory view of numerical analysis when attractive interaction is set between polymer particles. FIG. 3B is an explanatory view of numerical analysis when attractive interaction is set between polymer particles. FIG. 4A is an explanatory diagram of numerical analysis when repulsive interaction is set between polymer particles. FIG. 4B is an explanatory view of numerical analysis when repulsive interaction is set between polymer particles. FIG. 5 is an explanatory view of an example of setting of attractive interaction. FIG. 6 is an explanatory view of another example of setting of attractive interaction. FIG. 7 is an explanatory view of another example of setting of attractive interaction. FIG. 8A is an explanatory view of attractive interaction having an intensity distribution. FIG. 8B is an explanatory view of an attractive interaction having an intensity distribution. FIG. 9 is a graph showing the relationship between the interparticle distance of a pair of polymer particles and the bonding energy of interparticle bonding. FIG. 10 is a view showing the relationship between the interparticle distance of a pair of polymer particles and the bonding force of interparticle bonding. FIG. 11 is a view showing the relationship between the interparticle distance of the interparticle bonding of a pair of polymer particles and the bonding energy. FIG. 12 is a graph showing the relationship between the interparticle distance of the interparticle bonding of a pair of polymer particles and the bonding energy. FIG. 13 is a view showing the relationship between the interparticle distance of the interparticle bonding of a pair of polymer particles and the bonding energy. FIG. 14A is an explanatory view of a fracture position of interparticle bonding in a modeling area. FIG. 14B is an explanatory view of a fracture position of interparticle bonding in a modeling area. FIG. 14C is an explanatory view of a fracture position of interparticle bonding in a modeling area. FIG. 15 is a view showing an example of the relationship between the distance from the filler model surface and the coordinate distribution of broken coordinates. FIG. 16A is an explanatory diagram of an example of visualization at two analysis times of a first analysis time T1 and a second analysis time T2. FIG. 16B is an explanatory diagram of an example of visualization at two analysis times of the first analysis time T1 and the second analysis time T2. FIG. 17A is an explanatory diagram of an example of visualization at three analysis times of the first analysis time T1 to the third analysis time T3. FIG. 17B is an explanatory diagram of an example of visualization at three analysis times of the first analysis time T1 to the third analysis time T3. FIG. 17C is an explanatory diagram of an example of visualization at three analysis times of the first analysis time T1 to the third analysis time T3. FIG. 18A is an explanatory diagram of an example of visualization at three analysis times of the first analysis time T1 to the third analysis time T3. FIG. 18B is an explanatory diagram of an example of visualization in three analysis times of the first analysis time T1 to the third analysis time T3. FIG. 18C is an explanatory diagram of an example of visualization at three analysis times of the first analysis time T1 to the third analysis time T3. FIG. 19A is an explanatory diagram of an example of aggregating and visualizing two analysis times of a first analysis time T1 and a second analysis time T2. FIG. 19B is an explanatory diagram of an example of aggregating and visualizing two analysis times of a first analysis time T1 and a second analysis time T2. FIG. 20A is an explanatory diagram of an example of aggregating and visualizing two analysis times of a first analysis time T1 and a second analysis time T2. FIG. 20B is an explanatory diagram of an example of aggregating and visualizing two analysis times of a first analysis time T1 and a second analysis time T2. FIG. 21 is a flow diagram schematically showing another example of the method of analyzing a composite material according to the embodiment of the present invention. FIG. 22 is a functional block diagram of an analysis method of a composite material and an analysis apparatus for executing the analysis method of the composite material according to the present embodiment. FIG. 23 is a diagram showing a stress distortion line according to an embodiment of the present invention.

  The present inventor noted that the conventional method of analyzing a composite material using molecular dynamics does not necessarily have sufficient reproducibility of the mechanical response due to breakage. Then, the inventor has found that by setting an attractive interaction between particles constituting the composite material and performing numerical analysis, it is possible to realize an analysis method of a specific substance excellent in reproducibility of mechanical response accompanying breakage. . Furthermore, the present inventor has also found that it is possible to evaluate a broken part of a molecular bond by performing arithmetic processing without physically eliminating the molecular bond, and the present invention has been completed.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. In addition, this invention is not limited to each following embodiment, It can change suitably and can be implemented. In addition, although the case where the specific substance to be analyzed is a composite material containing two or more substances is described below, the present invention is also applicable to the case where the specific substance is a single substance such as a polymer. It is applicable. Moreover, although the composite material demonstrates the example containing a polymer and a filler below, this invention is applicable also to the composite material which contains two or more types of substance. The present invention is also applicable to composite materials containing materials other than fillers and polymers.

  FIG. 1 is a flowchart showing an outline of a method of analyzing a composite material according to the present embodiment. As shown in FIG. 1, the method of analyzing a composite material according to the present embodiment is a method of analyzing a composite material by a molecular dynamics method using a computer. The analysis method of this composite material includes a model for analysis of a composite material including a polymer model (specific material model) modeling a polymer (specific material) and a filler model (specific material model) modeling a filler (specific material). Step ST11 of creating, Step ST12 of setting a first threshold value of inter-particle distance of at least a pair of particles joined by inter-particle bonding, belonging to polymer model or filler model to be analyzed It includes a step ST13 of setting an action, and a step ST14 of performing numerical processing of the analysis model by performing a breaking process when the interparticle distance is equal to or more than a first threshold. The order of steps ST11 to ST14 can be changed as appropriate.

  FIG. 2 is a conceptual view showing an example of the analysis model 1 of the composite material according to the present embodiment. As shown in FIG. 2, the analysis model 1 is modeled, for example, in a model creation area A which is a substantially cubic virtual space having a length L on one side. The model creation area A is a three-dimensional space extending in the X-axis, Y-axis, and Z-axis directions orthogonal to one another. The analysis model 1 includes four filler models 11A, 11B, 11C, and 11D in which a plurality of filler particles 11a are modeled, and four polymer models 21 in which a plurality of polymer particles 21a and bonding chains 21b are modeled. Including. In the example shown in FIG. 2, although the analysis model 1 describes an example in which four filler models 11A, 11B, 11C, and 11D are modeled, the number of filler models to be modeled is not limited. The analysis model 1 may include less than four filler models 11 and may include more than four filler models 11. Further, in FIG. 2, only four polymer models 21 are shown, but in the analysis model 1, a plurality of polymer models 21 exist over the entire region in the model creation area A. Furthermore, in the example illustrated in FIG. 2, the model creation area A is illustrated as an example of a substantially rectangular virtual space, but may be any shape such as a spherical shape, an elliptical shape, a rectangular shape, or a polyhedron shape.

  The filler model 11 is modeled in a state in which a plurality of filler particles 11 a are respectively gathered in a substantially spherical body. In addition, the filler models 11 are arranged at predetermined intervals apart from each other. In addition, the filler model 11 may mutually be connected mutually by the covalent bond in the state which mutually aggregated.

  The filler includes, for example, carbon black, silica, and alumina. The filler particles 11 a are modeled by assembling a plurality of filler atoms. In addition, in the filler particles 11a, a plurality of filler particles 11a are gathered to constitute a filler particle group. The relative position of the filler particles 11a is specified by the bonding chain (not shown) among the plurality of filler particles 11a. The bond chain (not shown) has a function as a spring in which an equilibrium length, which is a bond distance between the filler particles 11a, and a spring constant are defined, and restrains the filler particles 11a. The bonding chain is a bond in which the relative position of the filler particles 11 a and the potential at which a force is generated due to twisting, bending or the like are defined. The filler model 11 is numerical data including the mass, volume, diameter, initial coordinates, and the like of the filler particles 11 a for handling the filler in molecular dynamics. Numerical data of the filler model 11 is input to a computer.

  As a polymer, rubber | gum, resin, an elastomer, etc. are contained, for example. The polymer particles 21a are modeled by assembling atoms of a plurality of polymers. Further, in the polymer particles 21a, a plurality of polymer particles 21a gather to constitute a polymer particle group. In the polymer, a modifier that enhances the affinity to the filler is blended as needed. The modifier includes, for example, a hydroxyl group, a carbonyl group, and a functional group of an atomic group. The polymer model 21 is modeled by packing polymer particles 21 a, which is an assembly of a plurality of polymer atoms and a plurality of polymer atoms, in a modeling area A at a predetermined density. The polymer particles 21a are linked by the connecting chains 21b between the plurality of polymer particles 21a, and the relative position is specified. The bonding chain 21b has a function as a spring in which an equilibrium length, which is a bonding distance between the polymer particles 21a, and a spring constant are defined, and restrains the polymer particles 21a. The bonding chain 21 b is a bond in which the relative position of the polymer particle 21 a and the potential at which a force is generated by twisting or bending are defined. The bonding chains 21b are also bonded as crosslinks (not shown) between polymer models 21 in which a plurality of polymer particles 21a are connected in series. The polymer model 21 is numerical data (including the mass, volume, diameter, initial coordinates, and the like of the polymer particle 21a) for treating the polymer by molecular dynamics. Numerical data of the polymer model 21 is input to a computer.

  In the analysis model 1, various physical quantities are obtained by numerical analysis by the molecular dynamics method. Examples of numerical analysis include motion analysis such as deformation analysis such as extension analysis and shear analysis, and relaxation analysis. The physical quantities acquired in the motion analysis may be values such as displacement obtained as a result of the motion analysis, or may be distortion obtained by executing predetermined arithmetic processing. Among these, deformation analysis is preferable from the viewpoint of being able to analyze the mechanical properties of the compound of the composite material as the motion analysis.

  Next, the analysis method of the composite material according to the present embodiment will be described in detail. In the first step ST11, a composite material including a filler model 11 in which a plurality of filler particles 11a are gathered together and modeled and a polymer model 21 in which a plurality of polymer particles 21a are linked through a linking chain 21b is modeled. An analysis model 1 (see FIG. 2) is created.

  Further, in step ST11, an interaction is set between the created filler model 11 and the polymer model 21. The interaction between the filler model 11 and the polymer model 21 includes, for example, chemical interactions such as attraction and repulsion such as intermolecular forces and hydrogen bonds, and physical interactions such as covalent bonds. . The interaction between the filler model 11 and the polymer model 21 is set as necessary between the filler particles 11a and between the filler particles 11a and the polymer particles 21a, and all the filler particles 11a are not necessarily required. And it is not set to the polymer particle 21a. Moreover, when the polymer model 21 is comprised by several types of polymer particle 21a, you may each set interaction to several types of polymer particle 21a. Further, the interaction between each of the plurality of types of polymer particles 21a and the filler model 11 may be the same or different. For example, the interaction between the polymer particle A and the filler particle 11a and the interaction between the polymer particle B and the filler particle 11a may be set to different interactions.

  Next, in step ST12, a predetermined first threshold value is set for the inter-particle distance of the polymer particles 21a. As the interparticle distance, the length of the connecting chain 21b connecting the polymer particles 21a may be used, or the linear distance between the pair of polymer particles 21a may be used. In the present embodiment, an example in which the predetermined first threshold value is set to the interparticle distance of the pair of polymer particles 21a to be analyzed in the second step ST12 will be described, but the first threshold value of the interparticle distance May be set to the interparticle distance between the pair of filler particles 11a according to the composite material to be analyzed.

  Next, in step ST13, an attractive interaction is set between the polymer particles 21a belonging to the polymer model 21. FIG. 3A and FIG. 3B are explanatory diagrams of numerical analysis in the case where attractive interaction is set between polymer particles 21a. 3A and 3B schematically show a part of the three-dimensional network structure of the plurality of polymer models 21 and show only a part of the polymer particles 21a.

  As shown in FIGS. 3A and 3B, in step ST13, for example, an attractive force X is set between the pair of polymer particles 21a-1 and 21a-2 belonging to the polymer model 21. Thus, even when numerical analysis is performed on the bond chain 21b, which is an interparticle bond between the pair of polymer particles 21a-1 and 21a-2, as the broken bond chain 21bx subjected to the break treatment, the pair of polymers by the attractive force X Particles 21a-1 and 21a-2 are attracted to each other. As a result, since it is possible to prevent the rapid contraction of the polymer model 21 caused by the breaking process of the bonding chain 21b, it is possible to prevent the rapid increase of the interparticle distance between the pair of polymer particles 21a-1 and 21a-2. .

  FIG. 4A and FIG. 4B are explanatory diagrams of numerical analysis in the case of setting repulsive interaction between the polymer particles 21a. 4A and 4B schematically show a part of the three-dimensional network structure of the plurality of polymer models 21 and show only a part of the polymer particles 21a.

  As shown in FIGS. 4A and 4B, when a repulsive force Y is set between the pair of polymer particles 21a-1 and 21a-2, the pair of polymer particles 21a-1 and 21a-2 may be moved away from each other by the repulsive force Y. Do. As a result, when the bond chain 21b, which is an interparticle bond between the pair of polymer particles 21a-1 and 21a-2, is numerically analyzed as the broken bond chain 21bx subjected to the break treatment, the polymer model 21 shrinks rapidly. Thus, the interparticle distance between the pair of polymer particles 21a-1 and 21a-2 rapidly increases.

  As described above, in the step ST13, the setting of attractive interaction can reduce the speed of contraction accompanying a sharp drop in stress acting on the polymer particles 21a before the fracture treatment, so that the analysis model 1 can be used. The reproduction accuracy of the used mechanical response is improved.

  The attractive interaction can be appropriately set as long as the effects of the present invention can be achieved. With regard to the attractive interaction, from the viewpoint of further improving the above-mentioned effects, an attractive interaction which is larger than the repulsion set between the polymer particles 21a and smaller than the attraction set between the filler particles 11a and the polymer particles 21a. It is preferable to set the action. Moreover, when the polymer model 21 is comprised with several types of polymer particle 21a, you may each set attraction interaction in several types of polymer particle 21a. Further, the attractive interaction between each of the plurality of types of polymer particles 21a may be the same or different. For example, an attractive interaction between the polymer particle A and the polymer particle B and an attractive interaction between the polymer particle B and the polymer particle C may be set to be different.

  As shown in FIG. 3A and FIG. 3B, attractive interaction may be set to all or a part between a pair of polymer particles 21a connected by a bonding chain 21b, and a polymer model 21 may be set. It may be set in a certain area of

  FIG. 5 is an explanatory view of an example of setting of attractive interaction. The attractive interaction may be set to the polymer particle 21a of the polymer model 21 belonging to the molecular chain containing the fracture-treated interparticle bond. In the example shown in FIG. 5, an attractive interaction is set to the polymer particle 21a of the region A1 of a certain molecular chain belonging to a specific polymer model 21 including the bonding chain 21b in the analysis model 1. Further, in the example shown in FIG. 5, an attractive interaction may be set to a predetermined range of polymer particles 21 a including a pair of polymer particles 21 a-1 and 21 a-2 connected by a bonding chain 21 b. By these, since area | region A1 to which a gravitation interaction is set in the analysis model 1 can be reduced, calculation time can be shortened.

  6 and 7 are explanatory diagrams of another example of setting of attractive interaction. In the example shown in FIG. 6, the attractive interaction is set to the polymer particle 21a of the range A2 in the vicinity including the bonding chain 21b of the pair of polymer particles 21a-1 and 21a-2. Thereby, as shown in FIG. 7, the polymer particles 21a belonging to the polymer model 21 adjacent to the polymer model 21 to which the pair of polymer particles 21a-1 and 21a-2 belong and the pair of polymer particles 21a-1 and 21a-2 belong There is an attractive interaction between As a result, similarly to FIGS. 3A and 3B, it is possible to prevent a rapid increase in the interparticle distance between the pair of polymer particles 21a-1 and 21a-2 at the time of numerical analysis. Further, as in the example shown in FIG. 5, the region A1 in which the attractive interaction is set in the analysis model 1 can be reduced, so that the calculation time can be shortened.

  In addition, the attractive interaction may be set after the creation of the analysis model 1, or may be set after setting the first threshold value of the distance between the particles of the pair of polymer particles 21a bonded by the bonding chain 21b, You may set with the fracture process of the joint chain 21b of polymer particle 21a. Among these, the attractive interaction is preferably set along with the breaking process of the bonding chain 21b of the polymer particle 21a. As a result, it is possible to reduce the operation load required for setting the attractive interaction while reducing the influence on the reproducibility of the mechanical response.

  In step ST13, the attraction interaction may be set by setting a second threshold value smaller than the first threshold value of the interparticle distance set in step ST12 and becoming equal to or greater than the set second threshold value. Thereby, since the attractive interaction is surely set before the breakage of the bonding chain 21b, the rapid contraction of the polymer model 21 at the time of the breakage treatment can be prevented, and the reproducibility of the mechanical response at the time of numerical analysis is more improves. The second threshold may be smaller than the first threshold, and is preferably 0.95 times or more and less than 1.0 times the first threshold from the viewpoint of reducing calculation processing.

  In step ST13, the attractive interaction may be set to decrease with the lapse of analysis time after the interparticle bond breaking process. In this case, the attractive interaction may be reduced continuously or gradually as the analysis time passes. Thereby, the calculation load at the time of numerical analysis can be reduced while reducing the influence on the reproducibility of the mechanical response.

  Further, in step ST13, an attractive interaction having an intensity distribution may be set. FIG. 8A and FIG. 8B are explanatory drawings of attractive interaction which has intensity distribution. As shown in FIG. 8A, in step ST13, as a result of setting the attraction interaction in the polymer model 21 of the analysis model 1 in which the interaction such as repulsion is set in advance, the repulsion in the analysis model 1 in the model creation area A There is a boundary between the area B1 in which the force acts and the area B2 in which the attraction works. In this case, the interaction between the area B1 and the area B2 is discontinuous, and the calculation efficiency is deteriorated at the time of numerical analysis, and the reproducibility of the mechanical response is also reduced.

  On the other hand, as shown in FIG. 8B, if an area B21 where an attractive force acts weaker than the area B2 is provided in the model preparation area A to set an attractive interaction having an intensity distribution, areas B1, B21 and B2 are set. The interaction changes continuously between By doing this, the difference in the interaction between the polymer particles 21a connected by the break connecting chains 21bx after the breaking process and the polymer particles 21a distant from the polymer particles 21a in bonding number or distance is reduced. be able to. This makes it possible to reduce the distribution of discontinuous interactions between attractive force and repulsive force generated in the analysis model 1 of the composite material, so that the calculation efficiency at the time of numerical analysis becomes better and the reproducibility of the mechanical response is further improved. .

  Next, in step ST14, when the inter-particle distance of the polymer particles 21a is equal to or greater than the first threshold value, the attractive interaction is set using the break coupling operation function that performs the break processing of the inter-particle bonding of the polymer particles 21a. The numerical analysis of the analysis model 1 is performed. The numerical analysis here includes various numerical analysis such as numerical analysis such as temperature change analysis and transformation analysis, deformation analysis such as extension analysis and shear analysis, and motion analysis such as relaxation analysis. In addition, the breaking process may be a breaking process that actually eliminates inter-particle bonding (bonding chain 21b), and may be a pseudo-breaking process that reduces at least one of the bonding energy and the bonding force of the inter-particle bonding. . Hereinafter, the case of the pseudo breaking process will be described.

  Here, the relationship between the bonding energy and the bonding force of the interparticle bonding of the polymer particles 21 a and the interparticle distance will be described. FIG. 9 is a view showing the relationship between the interparticle distance of the pair of polymer particles 21a and the bonding energy of interparticle bonding, and FIG. 10 is a graph showing the interparticle distance of the pair of polymer particles 21a and the interparticle bonding force FIG. In FIG. 9, the ordinate represents the bond energy of interparticle bonding of the pair of polymer particles 21a, and the abscissa represents the interparticle distance of the pair of polymer particles 21a. In FIG. 10, the ordinate represents the bonding force of interparticle bonding of the pair of polymer particles 21a, and the abscissa represents the interparticle distance of the pair of polymer particles 21a.

  As shown in FIG. 9, in the numerical analysis using the analysis model 1, in the pair of polymer model particles 21a bonded between the particles by the bonding chain 21b, the bonding energy of the interparticle bonding is changed by the change of the distance between the particles. Increase or decrease. The bonding energy of the interparticle bond decreases as the distance between the particles of the pair of polymer particles 21a increases and then reaches a minimum (see point P1 in FIG. 9) and then increases as the distance between particles further increases. (See the broken line L1 in FIG. 9).

  Further, as shown in FIG. 10, in the numerical analysis using the analysis model 1, the pair of polymer model particles 21a bonded between the particles by the bonding chain 21b changes the distance between the particles, thereby bonding the particles together. Force increases and decreases. The bonding force of the interparticle bonding increases as the distance between particles of the polymer particles 21a increases, and further increases after passing the inflection point (see the point P2 in FIG. 10) (see the broken line L3 in FIG. 10). ).

  By the way, in the numerical analysis using the general analysis model 1, in order to analyze the breakage of the interparticle bond between the pair of polymer particles 21a, the pair of polymer particles 21a as shown in FIG. 9 and FIG. In order to prevent an increase in the bonding energy and the bonding force of the interparticle bonding between the particles, it is necessary to erase and break the bonding chain 21b or the like when the bonding between particles becomes a certain level or more. For this reason, since the connection relationship of the polymer particles 21a is lost between the pair of polymer particles 21a in which the bonding chains 21b are broken, it is difficult to reproduce and identify the broken interparticle bonding.

  The inventors focused on the relationship between the bonding energy and the bonding force of the interparticle bonding of the pair of polymer particles 21a shown in FIGS. 9 and 10, and the interparticle distance. Then, the inventor conceived of providing a predetermined first threshold value S in the interparticle distance between the pair of polymer particles 21a. Furthermore, when the interparticle distance becomes equal to or greater than the first threshold S, the present invention reduces at least one of the bond energy and the bond strength of the interparticle bond between the polymer particles 21a to analyze the pair of polymers. It has been found that the breakage of interparticle bonding can be reproduced while maintaining the interparticle bonding of the particles 21a.

  In the present embodiment, as shown by the solid line L2 in FIG. 9, when the interparticle distance becomes equal to or more than the predetermined first threshold value S, the bond energy of interparticle coupling between the pair of polymer particles 21a is reduced. Further, as shown by the solid line L4 in FIG. 10, when the interparticle distance becomes equal to or more than the predetermined first threshold value S, the bond strength of interparticle coupling between the pair of polymer particles 21a is reduced. As a result, even if the interparticle distance between the pair of polymer particles 21a becomes long and becomes equal to or more than the first threshold S, the bonding energy and the bonding force of the interparticle bond decrease, so the interparticle bonding becomes even if the first threshold S or more. The numerical analysis of the analysis model 1 can be continued while being maintained. As a result, it is possible to reproduce the break of the interparticle bond while maintaining the interparticle bond between the pair of polymer particles 21a.

  If the fracture process is a pseudo fracture process, a predetermined first threshold value S is set to the interparticle distance of the pair of polymer particles 21a, and if the interparticle distance is equal to or greater than the first threshold value S, the interparticle distance is For the case of less than the first threshold value S, the interparticle coupling is calculated using a fracture coupling operation function that reduces the binding energy and the coupling force of the interparticle coupling. As the said breaking connection calculation function, what is shown to following formula (1) is mentioned, for example. By using this broken bond calculation function, as in the example shown in FIGS. 9 and 10, when the interparticle distance r is less than the predetermined first threshold value S, the interparticle interparticle distance between the pair of polymer particles 21a is obtained. The bonding energy and the bonding force increase or decrease according to the distance r, and when the interparticle distance r is equal to or more than the predetermined first threshold S, the bonding energy and the bonding force become zero. In addition, about a following formula (1), it can change suitably in the range with the effect of this invention. In addition, although the example which reduces binding energy is demonstrated below, also when reducing binding power, it can implement similarly.

  Thus, when the fracture process is a pseudo fracture process, at least one of the bond energy and the bond strength of the interparticle bond decreases in the region where the interparticle distance is equal to or greater than the first threshold S. It is possible to continue the numerical analysis of the analysis model 1 without breaking the As a result, it is possible to prevent the physical disappearance of the interparticle bond due to the breakage, so it is possible to reproduce the pseudo-cut without physically eliminating the interparticle bond. Therefore, it is possible to realize the analysis method of the composite material which makes it possible to identify the fracture point of the fractured interparticle bond at the time of numerical analysis.

  In the example shown in FIG. 9, an example in which the binding energy is made zero at the first threshold S or more has been described, but if the motion analysis of the analysis model 1 can be performed, the binding energy is necessarily reduced to zero. There is no need. The bonding energy at the first threshold S or higher is preferably reduced, for example, to the minimum point P1 or lower of the bonding energy. Similarly, in the example shown in FIG. 10, the example in which the binding force is made zero at the first threshold S or more has been described, but the binding force is necessarily reduced to zero if numerical analysis of the analysis model 1 is possible. There is no need to The bonding strength at the first threshold S or more is preferably reduced to, for example, the inflection point P2 of bonding strength or less, and more preferably reduced to substantially zero, which causes the bonding power to substantially disappear. Here, “substantially zero” means a numerical range substantially close to zero, and includes some numerical ranges between zero and zero.

  In addition, it is preferable to execute the numerical analysis of the analysis model 1 using the break bonding calculation function that sets the bonding energy and bonding force of interparticle bonding to zero at the first threshold S or more as the break bonding calculation function. . As a result, pseudo cutting of a pair of particles to be analyzed at the time of numerical analysis of the analysis model 1 can be reproduced with high accuracy. Therefore, for example, the breakage of polymer molecules in an actual composite material such as filler filled rubber can be performed accurately. It becomes possible to reproduce well.

  In the embodiment described above, an example is described in which the bond energy or the bond strength of the interparticle bond is reduced using one break bond calculating function shown in the above equation (1). The functions may be combined to reduce at least one of binding energy or binding power of interparticle binding. FIG. 11 is a view showing the relationship between the interparticle distance of the interparticle bonding of the pair of polymer particles 21a and the bonding energy. In FIG. 11, the ordinate represents the bond energy of interparticle bonding of the pair of polymer particles 21a, and the abscissa represents the interparticle distance of the pair of polymer particles 21a.

In the example shown in FIG. 11, the break connection calculation function used for the calculation of the interparticle connection is switched between the first break connection calculation function and the second break connection calculation function in accordance with the interparticle distance, and calculation processing is performed. . When the interparticle distance is less than the predetermined first threshold S (see the solid line L5 in FIG. 11), the bond energy of the interparticle bond is calculated using the equation (2) below as a function for calculating the first break bond When the interparticle distance is equal to or greater than a predetermined first threshold value S (see the solid line L6 in FIG. 11), the particles are expressed using the equation (3) below as a function for calculating the second breaking bond. Calculate the bond energy of the bond between them. As described above, by switching and using the first breaking connection calculation function and the second breaking connection calculation function with the first threshold value S as a boundary, the inter-particle distance r can be obtained as in the example shown in FIGS. Is smaller than the predetermined first threshold S, the bonding energy increases or decreases according to the interparticle distance r between the pair of polymer particles 21a, and the interparticle distance r is equal to or larger than the predetermined first threshold S. The binding energy is zero. In addition, about a following formula (2) and a following formula (3), it can change suitably in the range with the effect of this invention.

  In the embodiment described above, an example in which the first threshold value S of the specific numerical value is set to the interparticle distance of the pair of polymer particles 21a has been described, but a predetermined numerical range may be set to the interparticle distance as the first threshold value. You may set as a threshold range which it has. FIG. 12 and FIG. 13 are diagrams showing the relationship between the interparticle distance in the pair of polymer particles 21a and the bonding energy of interparticle bonding. In FIG. 12 and FIG. 13, the vertical axis indicates the bonding energy of interparticle bonding, and the horizontal axis indicates the interparticle distance of the pair of polymer particles 21 a.

  In the example shown in FIG. 12, the threshold value range SR is set in a predetermined numerical value range of the interparticle distance. In this case, as in the examples shown in FIGS. 9 to 11 described above, the binding energy is made to be zero in any of the threshold range SR (see the solid line L7 in FIG. 12). In this case, as shown in FIG. 9, the binding energy is not reduced only at the specific first threshold value S, but the binding energy is reduced at any value within the threshold range SR. It is possible to adjust the probability of occurrence of breakage of As a result, it is possible to accurately reproduce the breakage of interparticle bonds in an actual composite material in which molecular chains are not cut at a specific bond length. The threshold range SR is, for example, preferably set to 1.2 times or more of the equilibrium bond length of the polymer particles 21a, and more preferably to 1.5 times or more. In addition, the binding energy does not necessarily have to be reduced to zero, and the binding energy after reduction may have a constant value or may fluctuate within a predetermined range.

  In the example shown in FIG. 13, in the third step ST13, numerical analysis is performed using a break bonding operation function that reduces at least one of the bond energy and the bond strength of the interparticle bond from the lower limit to the upper limit of the threshold range SR. Run. In this case, for example, as indicated by an alternate long and short dash line L8, a thick broken line L9, and an alternate long and two short dashes line L10 in FIG. 13, a break coupling operation function is used in which the decreasing rate of binding energy within the threshold range SR is arbitrarily adjusted. You may As a result, the binding energy gradually decreases in the range from the lower limit value to the upper limit value of the threshold range SR, so that the occurrence probability of the interparticle bond breakage can be adjusted with high precision, and the molecular chain necessarily has a specific bond length. It is possible to reproduce with high accuracy the breakage of the interparticle bond in the actual composite material in which is not cut. Examples of the fracture coupling calculation function used in the example illustrated in FIG. 13 include a function and an exponential function indicating an n-order curve corresponding to the solid line L8 to the solid line L10.

  Further, in the above-described embodiment, an example is described in which the interparticle coupling is calculated by applying a predetermined breaking bond calculation function when the interparticle distance of the polymer particles 21a is equal to or greater than the first threshold S. The numerical analysis of the analysis model 1 may be performed using a break bonding operation function that reduces the bonding energy and the bonding force of interparticle bonding when the time average value of becomes equal to or greater than the first threshold value. Thus, for example, a break coupling operation function is used to reduce the bonding energy and the bonding force of the interparticle bonding in the pair of polymer particles 21a in which the interparticle distance temporarily becomes equal to or greater than the first threshold by Brownian motion or the like. Operations can be excluded. As a result, it is possible to accurately reproduce the breakage of interparticle bonding in an actual composite material. The first threshold value of the time average value is preferably 1/1000 of the evaluation time interval, and more preferably 1/100.

  By the way, when there are a plurality of pairs of polymer particles 21a connected by interparticle bonding, the distance between the particles of the plurality of pairs of polymer particles 21a sequentially becomes equal to or more than the first threshold S after numerical analysis of the analysis model 1 And at least one of the bonding energy and the bonding force of the interparticle bonding is sequentially reduced. For this reason, when the interparticle distance of the plurality of pairs of polymer particles 21a is equal to or greater than the first threshold S at a specific analysis time after a predetermined analysis time, at least one of the bonding energy and the bonding force of interparticle bonding Even if each of the coordinates of the reduced polymer model 21 is specified, it may not always be possible to sufficiently evaluate each accurate broken position.

  Therefore, in the above embodiment, the coordinates of the interparticle bond at the time when the interparticle distance becomes equal to or more than the first threshold value S may be specified and evaluated as the fracture position. 14A to 14C are explanatory diagrams of broken positions of interparticle bonds in the model creation area A. FIG. 14A shows the state of the first analysis time T1, FIG. 14B shows the state of the second analysis time T2, and FIG. 14C shows the state of the third analysis time T3.

In this embodiment, the binding energy of the interparticle bond and the position of the interparticle bond whose bonding force is reduced are specified for a plurality of analysis times. In the example shown in FIG. 14A, at the first analysis time T1, in the polymer model 21A, the interparticle distance in the vicinity of the filler model 11 becomes equal to or more than the first threshold S, and the broken bond chains 21bx with reduced binding energy or binding force are generated. ing. In the polymer models 21B and 21C present in the vicinity of the filler model 11, the interparticle distance of the polymer particles 21a is less than the first threshold value S, and the bonded chains 21b remain. In the first analysis time T1, it identifies the coordinates of the model polymer 21A as breaking coordinates _{X 1.}

Next, at the second analysis time T2 after the predetermined time has elapsed, in the polymer model 21B, the intergranular distance in the vicinity of the filler model 11 becomes equal to or larger than the first threshold S, and the broken bond chains 21bx with reduced binding energy or binding force It is happening. In the polymer model 21C present in the vicinity of the filler model 11, the interparticle distance of the polymer particles 21a is less than the first threshold value S, and the bonded chains 21b remain. On the other hand, in the polymer model 21A separated from the surface of the filler model 11 by movement, the broken bond chains 21bx in which the bonding energy or the bonding force is reduced are maintained. In the second analysis time T2, to identify the coordinates of the model polymer 21B as a new fracture coordinates X _2, the current coordinates of the model polymer 21A which is already broken tether 21bx generated in the first analysis period T1 as a new fracture coordinates Not specified

Furthermore, in the third analysis time T3 after the predetermined time has elapsed, the polymer model 21C has the interparticle distance in the vicinity of the filler model 11 that is equal to or greater than the first threshold S, and a broken bond chain 21bx with reduced binding energy or binding force is generated. ing. In the polymer models 21A and 21B separated from the surface of the filler model 11 by the movement, the interparticle bonding of the polymer particles 21a becomes equal to or more than the first threshold value S, and the broken bonds 21bx are maintained. In the third analysis time T3, the coordinates of the model polymer 21C newly identified as broken coordinates X _3, the current coordinates of the model polymer 21A which is already broken tether 21bx generated in the first analysis time T1 and the second analysis time T2 The current coordinates of the polymer model 21B in which the broken bond chains 21bx have already been generated are not specified as broken coordinates.

Thus, for example, as shown in FIG. 15, the fracture coordinates X _{1 to} X _{3 in} which the distance between particles becomes equal to or greater than the first threshold S during sequential first analysis time T1 to third analysis time T3 are sequentially identified. As shown, the distance from the surface of the filler model 11 and the coordinate distribution of the broken coordinates are obtained. Accordingly, it is understood that, in the numerical analysis of the analysis model 1 shown in FIGS. 14A to 14C, the coordinate distribution of the broken coordinates X _{1 to} X ₃ increases as the distance from the surface of the filler model 11 decreases. From this result, as shown in FIG. 15, it is possible to evaluate the location where interparticle bonding is likely to be broken, so it is possible to evaluate the relationship between the distance from the surface of the filler model 11 and the breakage probability.

  In the example illustrated in FIGS. 14A to 14C, a representative point may be set for interparticle bonding to specify a fracture position (fracture coordinates). For example, in the example shown in FIG. 14A, the center of gravity (mid point) with the pair of polymer particles 21a in the bonding chain 21b, which is an interparticle bond, or an end point overlapping with the coordinates of the polymer particles 21a, etc. . As a result, since the coordinates of the representative point of the interparticle bond with the increased length can be evaluated as the fracture position, the fracture position can be easily evaluated.

Moreover, in the example shown to FIG. 14A-FIG. 14C, you may visualize the interparticle coupling | bonding in which the distance between particle | grains became more than predetermined value. As a result, since it is possible to visually confirm the broken bond chain 21bx, which is an interparticle bond between a pair of polymer particles 21a broken in a pseudo manner, it is easy to identify the broken portion of the broken interparticle bond at the time of numerical analysis. Become. Similarly, the fracture coordinates X _{1 to} X _{3 in} which the interparticle bond breaks and the broken bond chain 21 bx is generated may be visualized. Thereby, since it is possible to visually evaluate the easily breakable location, evaluation of the easily breakable location becomes easy. Also, the representative points may be visualized. As a result, the representative point is visualized without visualizing the entire length of the interparticle bonding, so that confirmation of the broken interparticle bonding is facilitated. For visualization of inter-particle bonding, for example, the bonding chain 21b other than the broken bonding chain 21bx may be hidden or the transparency of the bonding chain 21b may be increased, and the color and thickness of the broken bonding chain 21bx may be the bonding chain 21b and It may be changed and displayed. This makes it possible to emphasize the broken bonding chain 21bx and to make it possible to easily confirm it visually.

In the above-described embodiment, visualization may be performed at a plurality of analysis times during numerical analysis. 16A and 16B are explanatory diagrams of an example of visualization at two analysis times of the first analysis time T1 and the second analysis time T2, and FIGS. 17A to 17C and 18A to 18C are the first analysis. It is explanatory drawing of the example of visualization in three analysis time of time T1-3rd analysis time T3. 16A to 18C schematically show the broken coordinates X _{1 to} X ₃ in which the distance between the particles of the pair of polymer particles 21a is equal to or more than the first threshold value S in a substantially spherical shape.

In the example shown in FIGS. 16A and 16B, as shown in FIG. 16A, after the breaking coordinates X ₁ in the vicinity of the filler model 11 is visualized generated by the first analysis time T1, as shown in FIG. 16B, the in the second analysis time T2, breaking coordinates X ₁ in accordance with the movement of the filler model 11 is displayed in a state where the relative position is maintained between the filler model 11. That is, breaking the coordinates X ₁ generated by the first analysis time T1 is displayed from the absolute coordinate X ₁₁ of the first analysis time T1 as a new fracture coordinate X ₁ of the relative position is maintained between the filler model 11. Accordingly, even when the analysis time from the first analysis time T1 to the second analysis time T2 is developed, the relative position of the fracture coordinates X ₁ generated around the filler model 11 is displayed is maintained.

In the example shown in FIG 17A~ Figure 17C, as shown in FIG. 17A, it is visualized breaking coordinates _{X 1} in the vicinity of the filler models 11 in the first analysis time T1 is generated. Then, as shown in FIG. 17B, the second analysis time T2, while moving together with the filler model 11 in a state of rupture coordinates X ₁ generated by the first analysis time T1 relative position between the filler model 11 is maintained, The fracture coordinates X ₂ generated at the second analysis time T ₂ are newly visualized in the vicinity of the filler model 11. Furthermore, as shown in FIG. 17C, in the third analysis time T3, breaking coordinate X ₂ generated by the rupture coordinates X ₁ and second analysis time T2 generated in the first analysis time T1 is the relative position between the filler model 11 with move with filler model 11 maintained state, breaking coordinates X ₃ generated in the third analysis time T3 is newly visualized filler models 11 neighborhood. Even when the position of the filler model 11 is changed according to the coordinates at the first analysis time T1 to the third analysis time T3 by visualizing in this manner, fracture coordinates generated around the filler model 11 It becomes possible to maintain the relative coordinates of X _{1 to} X ₃ for display. As a result, it is possible to reproduce the breakage of the interparticle bonding of the polymer model 21 around the filler model 11.

In the example shown to FIG. 18A-FIG. 18C, the position of the filler model 11 in the model preparation area | region A is fixed and displayed. First, as shown in FIG. 18A, it is visualized breaking coordinates X ₁ in the vicinity of the filler models 11 in the first analysis time T1 is generated. Then, as shown in FIG. 18B, the second analysis time T2, in a state where the display position of the break coordinate X ₁ generated by the filler model 11 and the first analysis time T1 is maintained, generated in the second analysis time T2 breaking coordinate X ₂ is newly visible. Furthermore, as shown in FIG. 18C, in the third analysis time T3, filler model 11, the display position of the break coordinate X ₂ generated by the rupture coordinates X ₁ and second analysis time T2 generated in the first analysis time T1 is maintained in a state of being, breaking the coordinates X ₃ generated in the third analysis time T3 is newly visible. As described above, by visualizing with the position of the filler model 11 fixed in the model creation area A, the relative coordinates of the broken coordinates X _{1 to} X ₃ generated around the filler model 11 can be maintained and displayed. It becomes possible. As a result, it is possible to reproduce the breakage of the interparticle bonding of the polymer model 21 around the filler model 11. By these, it is possible to confirm the progress of breakage of interparticle bonding at a plurality of analysis times.

  In the above embodiment, numerical analysis is performed for each of the plurality of polymer models 21 or filler models 11 included in the analysis model 1, and the results of the obtained plurality of numerical analysis are collected and visualized. It may be evaluated. FIG. 19A and FIG. 19B are explanatory diagrams of an example in which two analysis times of the first analysis time T1 and the second analysis time T2 are summarized and visualized. In the present embodiment, the first filler model 11A and the second filler model 11B exist in the model creation area A, and numerical analysis is performed on each of the first filler model 11A and the second filler model 11B. .

As shown in FIG. 19A, at the first analysis time T1, interparticle bond breakage of the polymer model 21 occurs in the vicinity of the first filler model 11A, and one fracture coordinate X ₁ is in the vicinity of the first filler model 11A. It is visualized. Further, as shown in FIG. 19B, in the second analysis time T2, the first filler model 11A and the second filler model 11B move within the model creation area A, respectively. In addition, in the second analysis time T2, breakage of the interparticle bond of one polymer model 21 occurs in the vicinity of the first filler model 11A and in the vicinity of the second filler model 11B, and the breakage occurs in the vicinity of the first filler model 11A. coordinate X ₂ is newly added is visualized breaking coordinates X ₃ in the vicinity of the second filler model 11B is newly visible. As a result, at the second analysis time T2, three fractures of two fracture coordinates X ₁ and X ₂ generated near the first filler model 11A and one fracture coordinate X ₃ generated near the second filler model 11B Coordinates X _{1 to} X ₃ are displayed in an integrated manner.

  As described above, in the present embodiment, since the two first filler models 11A and the second filler models 11B in the analysis model 1 can be collected and displayed in one model creation area A, the analysis result is quick. As well as being obtained, it becomes easy to understand the analysis results.

  In the example shown in FIGS. 19A and 19B, numerical analysis is performed on each of the plurality of polymer models 21 or filler models 11 included in the analysis model 1, and the obtained plurality of numerical analysis results are analyzed. A specific first filler model 11A specified in the model 1 may be aggregated, visualized and evaluated. FIGS. 20A and 20B are explanatory diagrams of an example of aggregating and visualizing two analysis times of the first analysis time T1 and the second analysis time T2.

As shown in FIGS. 20A and 20B, in the present embodiment, the first filler model 11A (not shown in FIGS. 20A and 20B) and the second shown in FIGS. 19A and 19B are included in the model creation area A. There is a representative filler model 11E that summarizes and displays calculation results of the filler model 11B (not shown in FIGS. 20A and 20B). The representative filler model 11E are those that show aggregate break coordinates _X 1 to X ₃ generated in the vicinity of the first filler model 11A and the second filler model 11B shown in FIGS. 19A and 19B. In the example shown in FIGS. 20A and 20B, in the representative filler model 11E, the coordinates in the model creation area A are fixed and displayed.

As shown in FIG. 20A, the first analysis time T1, only the breaking coordinates X ₁ in the vicinity of the first filler model 11A is visualized, breaking coordinates X ₁ generated in the vicinity of the first filler model 11A is representative filler It is displayed at the coordinates corresponding to the model 11E. As shown in FIG. 20B, the second analysis time T2, a new rupture coordinates X ₃ is representative filler models 11E produced in the vicinity of the fracture coordinates X ₂ and the second filler model 11B generated in the vicinity of the first filler model 11A Is added to As a result, the periphery of a representative filler model 11E, broken coordinate X ₁ to X ₃ generated around the entire filler model 11 including the first filler model 11A and the second filler model 11B is displayed aggregate.

  As described above, in the present embodiment, the two first filler models 11A and the second filler models 11B in the analysis model 1 can be aggregated and displayed in the model creation area A as one specific representative filler model 11E. Therefore, analysis results can be obtained quickly and understanding of analysis results is facilitated. As the representative filler model 11E, any filler model 11 included in the analysis model 1 may be specified, and another model such as a new filler model 11 created separately from the analysis model 1 is specified. May be In addition, as the filler model 11 for aggregating information of fracture coordinates into the representative filler model 11E, all filler models 11 in the analysis model 1 may be used, or a plurality of filler model groups specified in the analysis model 1 may be used. . The plurality of filler model groups may be, for example, a dispersion filler model group in which the distance between another filler model 11 and another filler model 11 is separated by a predetermined first threshold value or more. A cohesive filler model group having a distance between the other filler models 11 less than a predetermined first threshold value may be used as a reference.

Further, in the embodiment described above, an example in which analysis results of numerical analysis of fracture coordinates X _{1 to} X ₃ generated around a plurality of filler models 11 included in one analysis model 1 are collectively displayed. However, an ensemble result obtained by projecting an analysis result separately calculated using a plurality of analysis models 1 (for example, ten analysis models) onto an analysis result of one analysis model 1 may be visualized. As a result, since analysis results of a large number of broken coordinates generated around a large number of filler models 11 can be collected and displayed, efficient calculation results can be analyzed.

  In the embodiment described above, as shown in FIG. 21, a step ST21 of creating a model for analysis of a composite material including a polymer model obtained by modeling a polymer and a filler model obtained by modeling a filler, and a polymer model Step ST22 for cross-linking, Step ST23 for setting a first threshold value for the inter-particle distance of at least a pair of particles joined by inter-particle bonding, belonging to a polymer model or filler model to be analyzed A step ST24 of setting an action, and a step ST25 of performing numerical processing of an analysis model by performing breaking processing when the interparticle distance is equal to or more than a first threshold may be included. Thereby, since the analysis method of the composite material can carry out the numerical analysis of the analysis model in a state in which the polymer model is crosslinked in advance through the crosslinking reaction, the influence of the crosslinking of the polymer model on the breakage of interparticle bonds is more accurate. It becomes possible to analyze.

  Next, the analysis method of the composite material and the computer program for analysis of the composite material according to the present embodiment will be described in more detail. FIG. 22 is a functional block diagram of an analysis method of the composite material and a specific substance analysis method according to the present embodiment.

  As shown in FIG. 22, the analysis method of the specific substance according to the present embodiment is realized by the analysis device 50 which is a computer including the processing unit 52 and the storage unit 54. The analysis device 50 is electrically connected to an input / output device 51 provided with an input means 53. The input means 53 processes various physical property values of the polymer and the filler, which are targets for creating a model for analysis of the composite material, the measurement results of the extension test results using the composite material containing the polymer and the filler, and boundary conditions in analysis. Input to the unit 52 or the storage unit 54. As the input unit 53, for example, an input device such as a keyboard or a mouse is used.

  The processing unit 52 includes, for example, a central processing unit (CPU) and a memory. The processing unit 52 reads a computer program from the storage unit 54 and executes it in a memory when executing various processes. The computer program developed in the memory executes various processes. For example, the processing unit 52 appropriately expands data related to various processes stored in advance from the storage unit 54 in an area allocated to itself on the memory as needed, and based on the expanded data, for analysis of a composite material Perform various processes for creating a model and analyzing a composite material using a model for analysis of the composite material.

  The processing unit 52 includes a model generation unit 52a, a condition setting unit 52b, and an analysis unit 52c. The model creating unit 52a is based on the data stored in advance in the storage unit 54, and uses the number of particles, the number of molecules, and the molecular weight of the composite material such as filler and polymer when creating the analysis model 1 of the composite material by molecular dynamics method. Molecular chain length, number of molecular chains, branching, shape, size, reaction time, reaction conditions and arrangement of configuration elements such as target number of molecules, which is the number of molecules contained in the analysis model to be created, etc. Set up the coarse-grained model of. In addition, the model creating unit 52a sets initial conditions of various calculation parameters such as interaction between the filler particles 11a, between the polymer particles 21a, and hydrogen bonding of filler-polymer particles, intermolecular force and the like. In addition, the model creating unit 52a may create a crosslink analysis such as creation of a crosslink by cross linking of the polymer model 21 as needed.

  As calculation parameters for adjusting the interaction between the filler particles 11a and the interaction between the polymer particles 21a, these are adjusted using the Lennard-Jones potential σ and ε represented by the following formula (4). By increasing the upper limit distance (cutoff distance) to calculate the potential, it is possible to adjust the attraction and repulsion that worked up to a long distance. Preferably, the parameters of the interaction between the filler particles 11a and the interaction between the polymer particles 21a are sequentially reduced until the interaction between the filler particles 11a and the interaction between the polymer particles 21a become constant values. By approaching the Lennard-Jones potential σ, ε gradually from the large value to the original value, the particles can be approached at a gentle speed that does not lead the molecule into an unnatural state. In addition, by gradually reducing the cutoff distance, it is possible to adjust the attractive force and the repulsive force within an appropriate range.

  The condition setting unit 52b sets various numerical analysis conditions such as numerical analysis such as temperature change analysis and transformation analysis, deformation analysis such as extension analysis and shear analysis, and motion analysis such as relaxation analysis.

  The analysis unit 52c executes various numerical analysis of the analysis model 1 based on the analysis conditions set by the condition setting unit 52b. In addition, the analysis unit 52 c sets an attractive interaction in the polymer model 21 of the analysis model 1. Further, the analysis unit 52c performs numerical analysis by the molecular dynamics method using the analysis model 1 of the composite material created by the model creation unit 52a, and acquires a physical quantity. Here, the analysis unit 52c executes, as numerical analysis, motion analysis such as extension analysis, deformation analysis such as shear analysis, and relaxation analysis. In addition, the analysis unit 52c acquires a physical quantity such as distortion obtained by executing a predetermined arithmetic process on a value such as displacement obtained as a result of numerical analysis or the obtained value.

  The storage unit 54 is a non-volatile memory which is a read only recording medium such as a hard disk drive, a magneto-optical disk drive, a flash memory and a CD-ROM, and a read and write like RAM (Random Access Memory). Volatile memories, which are possible recording media, may be combined as appropriate.

  The storage unit 54 includes rubber carbon black, data of a filler such as silica and alumina, which is data for creating an analysis model 1 of a composite material to be analyzed through the input means 53, rubber, resin, and Data of a polymer such as an elastomer, a stress-strain curve which is a preset physical quantity history, a method of analyzing a composite material according to the present embodiment, a computer program for realizing a method of analyzing a composite material, and the like are stored. This computer program may be one that can realize the analysis method of the composite material according to the present embodiment by a combination with a computer or a computer program already recorded in a computer system. The “computer system” referred to here includes hardware such as an operating system (OS) and peripheral devices.

  The display unit 55 is, for example, a display device such as a liquid crystal display device. The storage unit 54 may be in another device such as a database server. For example, the analysis device 50 may access the processing unit 52 and the storage unit 54 from the terminal device provided with the input / output device 51 by communication.

  Next, with reference to FIG. 1 again, the analysis method of the composite material according to the present embodiment will be described in more detail.

  First, as shown in FIG. 1, the model creating unit 52a creates a plurality of uncrosslinked polymer models 21 including the polymer particles 21a and the bonding chains 21b in a predetermined model creating area A and a plurality including the filler particles 11a. The analysis model 1 including the filler model 11 is created (step ST11). The uncrosslinked polymer model 21 is, as shown in FIG. 2, formed by connecting a plurality of polymer particles 21a by bonding chains 21b. Here, the model creation unit 52a arranges the uncrosslinked polymer model 21 in the created filler model 11. Next, the model creating unit 52a performs the balancing calculation after setting the initial conditions. In the equilibrium calculation, molecular dynamics calculation is performed at a predetermined temperature, density and pressure, for a predetermined time for various components after initialization to reach an equilibrium state. Then, the model creating unit 52a sets the polymer model 21 and the filler model 11 in the model creating area A where the analysis model of the composite material set in the calculation area is generated after the setting process of the initial conditions and the calculation process of equilibration. Place the composite material model 10 to be included. In addition, the model creating unit 52a may blend a modifier with a modifier such as a hydroxyl group, a carbonyl group, or a functional group of an atomic group that enhances the affinity to the filler, as necessary. In addition, the model creation unit 52a may introduce a crosslink 21e into the created polymer model 21 by crosslink analysis. The model creating unit 52a may, if necessary, add molecular forces such as intermolecular forces and hydrogen bonds, chemical interactions such as repulsion, and physical mutual interactions such as covalent bonds to the analysis model 1 of the composite material. The action may be set.

  Next, various conditions for the condition setting unit 52b to execute crosslink analysis, numerical analysis and motion analysis (simulation) by molecular dynamics method using the analysis model 1 of the composite material generated by the model generation unit 52a are described. Set The condition setting unit 52 b sets various conditions based on the input from the input unit 53 and the information stored in the storage unit 54. As various conditions, position and number of filler model 11 for performing analysis, filler atom, filler atomic group, position and number of filler particles 11a and filler particle group, filler particle number, position and number of molecular chain of polymer, polymer Change the position of atom, polymer atomic group, position and number of polymer particles 21a and polymer particle group, number of polymer particle, position and number of bonding chain 21b, number of bonding chain 21b, stress distortion curve and condition which are physical quantity history set in advance Not including fixed values.

  Next, an interaction is set in the analysis model 1 to execute various numerical analysis such as temperature change analysis and transformation analysis. In the analysis unit 52c, for example, the interaction between the filler particles 11a, the polymer particles 21a, the interaction between the filler particles 11a and the polymer particles 21a, and the bonding between the filler particles 11a and the polymer particles 21a, as necessary. Set the state interaction and so on.

  The analysis unit 52c sets a first threshold value as the interparticle distance of the pair of polymer particles 21a bonded interparticlely by the coupling chain 21b to be analyzed (step ST12). Here, the analysis unit 52c may set a specific first threshold to the interparticle distance as the first threshold, or may set a threshold range having a predetermined numerical range. Next, the analysis unit 52c sets an attractive interaction in the polymer model 21 (step ST13). Here, the analysis unit 52c may set an attractive interaction on the pair of polymer particles 21a bonded by the bonding chain 21b, and may set an attractive interaction on the polymer particles 21a belonging to the molecular chain of the polymer model 21. It is also good. In addition, the analysis unit 52c may set a second threshold for interparticle bonding of the pair of polymer particles 21a, and set an attraction interaction based on the set second threshold. Next, the analysis unit 52c executes various numerical analysis such as motion analysis such as relaxation analysis, extension analysis, shear analysis and deformation analysis by the molecular dynamics method using the analysis model 1 of the composite material (step ST14). . Here, when the distance between the particles of the pair of polymer models 21a to be analyzed becomes equal to or greater than the first threshold, the analysis unit 52c performs break processing of interparticle bonding to perform various numerical analysis of the analysis model 1 Run. In addition, when the distance between particles of the pair of polymer models 21a to be analyzed is less than the first threshold, the analysis unit 52c uses the first fracture coupling calculation function, and the distance between particles is equal to or greater than the first threshold At this time, various numerical analyzes of the analysis model 1 may be performed using a second breaking bond calculation function in which the bonding energy and bonding force of interparticle bonding decrease.

  In addition, the analysis unit 52c acquires various physical quantities such as a nominal strain or the like obtained by calculating motion displacement and nominal stress or motion displacement obtained as a result of motion analysis by numerical analysis. By such numerical analysis and motion analysis, the bond length and polymer particle velocity of the polymer molecule of the whole analysis model 1 changing every analysis time, the velocity between bond points and free end, or physical quantity such as bond length, orientation, etc. Relationship between numerical values representing changes in segment state and strain, relationships between numerical values representing change in segment state such as polymer molecule bond length and polymer particle velocity that change with analysis time, and pressure or analysis time, and analysis time Since it is possible to evaluate the relationship between temperature or analysis time and numerical values that represent segment state changes such as polymer molecule bond length and polymer particle velocity, etc., a more detailed analysis of the local molecular state change of polymer molecules It becomes possible.

  In addition, the analysis unit 52c specifies break coordinates of the polymer model 21 obtained by numerical analysis, and evaluates the specified break coordinates. Here, the analysis unit 52c may visualize and evaluate the fractured interparticle bond, or may visualize and evaluate the fracture coordinates. Furthermore, the analysis unit 52c may aggregate and evaluate the fracture coordinates generated around the plurality of filler models 11, and consolidate the fracture coordinates generated around the plurality of filler models 11 into one representative filler model 11E. May be evaluated. Further, the analysis unit 52c may aggregate and evaluate analysis results separately analyzed using a plurality of analysis models 1. Next, the analysis unit 52c stores the analysis result of the analyzed composite material in the storage unit 54.

(Example)
Next, an example carried out to clarify the effect of the present invention will be described. The present invention is not limited at all by the following examples.

  The present inventors numerically analyze the analysis model 1 using the method of analyzing a composite material according to the above-described embodiment (Example 1) and measure stress distortion using an actual composite material. (Reference Example 1) When the analytical model 1 is numerically analyzed without setting the attractive interaction between the polymer particles 21a (Comparative Example 1), the analytical model 1 is considered without considering the breakage of the interparticle bonding. Were evaluated in comparison with the case where they were numerically analyzed (Comparative Example 2).

  FIG. 23 is a view showing a stress distortion curve according to the present example. As shown in FIG. 23, when the analysis method of the composite material according to the above embodiment is used (Example 1: see solid line L11), the stress distortion curve is measured using an actual composite material (Reference Example 1: As in the case of the dashed-dotted line L12), the stress was maintained substantially constant after the strain increased to a constant value with the stress. On the other hand, when the numerical analysis of the analysis model 1 is performed without setting the attractive interaction (comparative example 1: see the two-dot chain line L13), after the stress rises and the strain rises to a constant value, The result is a significant decrease in stress. In addition, in the case where the fracture of the interparticle bond is not taken into consideration (Comparative Example 2: see the broken line L23), the strain is continuously increased as the stress is increased. The result is that, in Example 1, when the stress and strain increase and the interparticle distance of the polymer particles 21a reaches the first threshold and the bond chains 21b are artificially broken, the polymer model 21 is obtained by attractive interaction. It is considered that the same results as in Reference Example 1 were obtained because the contraction speed of the above was able to be reduced.

  As described above, according to the above embodiment, when the interparticle distance becomes equal to or more than the first threshold value, after setting the attractive interaction on the polymer particle 21a, the fracture process is performed to analyze the analysis model 1 By analysis, it is understood that the analysis method of the composite material which is excellent in the reproducibility of the mechanical response accompanying the breakage can be realized.

DESCRIPTION OF SYMBOLS 1 Model for analysis 10 Composite material model 11, 11A, 11B, 11C, 11D Filler model 11E Representative filler model 11a Filler particle 21, 21A, 21B, 21C Polymer model 21a Polymer particle 21b Connection chain 21bx Breaking connection chain 50 Analysis device 51 Output device 52 processing unit 52a model creation unit 52b condition setting unit 52c analysis unit 53 input unit 54 storage unit 55 display unit A model creation region X ₁ , X ₂ , X ₃ broken coordinates

Claims (12)

A method of analyzing a specific substance by a molecular dynamics method using a computer,
Creating an analysis model of a specific substance including a specific substance model to be analyzed;
Setting a first threshold to an interparticle distance of at least one pair of particles belonging to the specific substance model and coupled by interparticle coupling;
Establishing an attractive interaction between the specific substance models;
And D. a process of breaking the bond between particles and executing numerical analysis of the model for analysis, when the distance between particles is equal to or greater than the first threshold value, and a method of analyzing a specific substance.   The method for analyzing a specific substance according to claim 1, further comprising the step of crosslinking the specific substance model.   The analysis method of the specific substance according to claim 1 or 2, wherein the attractive interaction is set to the particle of the specific substance model belonging to the molecular chain including the interparticle bond subjected to the fracture processing.   The identification according to claim 1 or 2, wherein the attractive interaction is set to the particles of the specific substance model in the vicinity including the particles of the specific substance model connected by the fracture-treated inter-particle bond. Analysis method of substance.   The method for analyzing a specific substance according to claim 1 or 2, wherein the attractive interaction is set within a predetermined range from the interparticle bonding subjected to the fracture treatment.   The method for analyzing a specific substance according to any one of claims 1 to 5, wherein the setting of the attractive interaction is performed together with the breaking process.   The method for analyzing a specific substance according to any one of claims 1 to 6, wherein the attractive interaction is set when the interparticle distance is equal to or greater than a second threshold value smaller than the first threshold value.   The analysis method of the specific substance according to any one of claims 1 to 7, wherein the attractive interaction is decreased with the lapse of analysis time after the breaking process.   The analysis method of the specific substance according to any one of claims 1 to 8, wherein the attractive interaction having an intensity distribution is set between the specific substance models.   The breaking process is a pseudo breaking process using a break bonding calculation function, and the break bonding calculation function is to substantially eliminate at least one of bonding energy and bonding force of the interparticle bonding. The analysis method of the specific substance according to any one of claims 1 to 9.   The analysis method of the specific substance according to any one of claims 1 to 10, wherein the specific substance includes a polymer and a filler.   A computer program for analyzing a specific substance, which causes a computer to execute the method for analyzing a specific substance according to any one of claims 1 to 11.

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