JP2007233859A - Model generating method, simulation method, model generating device, simulation device and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a model generating method for generating a model to obtain a simulation result corresponding to an actual phenomenon, and to provide a simulation method, a model generating device, a simulation device and a computer program. <P>SOLUTION: When simulating that a model of a quartz particle (non-deformable object) comes into contact with a model of rubber material (polymer object) by a coarse-grained molecular dynamics method, a boundary condition of the bottom of the model of rubber material in which a plurality of models of rubber molecules (polymer) with a plurality of coarse-grained units combined are aggregated is set in a wall boundary condition, the inter-center distance r of the coarse-grained units is defined as σ≤r≤2<SP>1/6</SP>σ in the model of a quartz particle in which the plurality of coarse-grained units of a quartz particle are arranged in the shape of a spherical shell to thereby inhibit the entire model of rubber material from being attracted by the model of a quartz particle to float during simulation and the model of rubber molecules from intruding into the model of a quartz particle. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a computer simulation method for behavior of a polymer object such as a rubber material. More specifically, the present invention relates to a model generation method, a simulation method, a model generation device, and a simulation for performing a simulation according to an actual phenomenon. The present invention relates to an apparatus and a computer program.

  The functions such as advance, bend, and stop that are realized by a tire made of rubber are due to the frictional force generated between the tire and the road surface, and the generated frictional force depends on the characteristics of the rubber that is the tire material. It depends. Conventionally, research on rubber for development or design of tires has been performed by an experiment in which a friction coefficient of a test piece of a rubber material actually manufactured is measured. However, in order to develop or design a higher-performance tire, in addition to the rubber material experiment, the characteristics of the rubber material can be determined based on the properties of the rubber molecule by simulation using a computer with a method such as molecular dynamics. Research to make predictions and evaluations has become necessary. Patent Documents 1 and 2 disclose examples of techniques for performing a simulation for obtaining elastic characteristics by deforming a rubber material.

  A rubber molecule is a polymer in which many molecules such as isoprene composed of a plurality of atoms are polymerized in a chain, and a rubber material is expressed as a system in which a large number of polymer rubber molecules are entangled with each other. Since it is not realistic to handle such a large amount of atomic behavior by a computer one by one, it is necessary to perform a simulation after modeling a rubber material so that it can be handled by a computer. As a method of modeling so that a system composed of a large number of atoms can be handled by a computer, there is a coarse graining method in which a set of a plurality of atoms or molecules is handled as a calculation unit. By performing coarse graining, the number of calculation units is greatly reduced, and a system consisting of a large number of atoms can be handled by a computer. Conventionally, a coarse-grained molecular power that represents a system to be simulated as a system in which a large number of coarse-grained units that aggregate a plurality of atoms or molecules are gathered, and performs a simulation by calculating the interaction between the coarse-grained units Science is being used. In the case of rubber molecules in which isoprene is polymerized, polyisoprene in which a predetermined number of isoprene is polymerized in a chain form is used as a coarse-graining unit, and this coarse-grained unit is combined in a plurality of chains to represent rubber molecules. Molecules can be assembled to represent a rubber material. Patent Document 3 discloses an example of a technique for calculating a physical property value of a substance using a coarse graining method.

The characteristics of the rubber material can be examined by simulation using such a coarse-grained molecular dynamics method. For example, when a quartz sphere, which is the main component of gravel existing on the road surface, is pressed into the rubber material, a frictional force generated in the rubber material is simulated, and this occurs when a rubber tire contacts the road surface. It is possible to simulate the phenomenon that occurs. The model of the rubber material is the model as described above, and the model of the quartz sphere is created by arranging a coarse crystal unit of alpha quartz crystals made of a predetermined number of silicon dioxide, and arranging the coarse grain unit in a spherical shape. In order to reduce the number of calculation units, the inside of the model of the quartz sphere is assumed to be hollow. The size of the rubber material model is assumed to be a minimum size imitating a part of the tire, and an increase in the number of calculation units is suppressed. By using such a model to simulate the behavior of a rubber material when a quartz sphere is pressed into the rubber material by coarse-grained molecular dynamics, the tire made of rubber contacts the road surface. It is possible to verify the generated frictional force.
Japanese Patent No. 3660932 Japanese Patent No. 3668238 JP 2004-287812 A

  However, in a simulation using a computer, it is necessary to appropriately design a model in order to obtain a calculation result corresponding to a phenomenon that actually occurs. In the simulation using the above model, the inside of the quartz sphere model is hollow, so when the quartz sphere model contacts the rubber material model, some rubber molecule models penetrate into the quartz sphere model. There is a problem that an unnatural phenomenon occurs, and the obtained simulation result does not correspond to an actual phenomenon. When an alpha quartz coarse-graining unit is filled inside a quartz sphere model, the phenomenon of rubber molecules entering the quartz sphere model can be suppressed, but the number of calculation units increases and the calculation cost increases. There is a problem of increasing the number of people.

  In the simulation using the above-mentioned model, the size of the rubber material model is minimized, and as the quartz sphere model approaches the rubber material model, the entire rubber material model is attracted to the quartz sphere model. An unnatural phenomenon occurs. Since the entire rubber material model is attracted to the quartz sphere model, the entire rubber material model is deformed and compressed, and the density distribution of the rubber material model changes greatly, resulting in simulation results that do not correspond to actual phenomena. There is a risk of being. If the size of the rubber material model is made larger, the occurrence of the phenomenon that the entire rubber material model is attracted to the quartz sphere model can be suppressed, but the number of calculation units increases, leading to an increase in calculation cost. There is a problem.

  The present invention has been made in view of such circumstances, and an object of the present invention is to obtain a simulation result corresponding to an actual phenomenon by appropriately determining the boundary condition of the model of the rubber material. A model generation method, a model generation device, and a computer program.

  Another object of the present invention is to determine the distance between the coarse-graining units constituting the model of a non-deformable object such as a quartz sphere as an appropriate distance, thereby preventing an increase in calculation cost and It is an object of the present invention to provide a model generation method, a model generation apparatus, and a computer program capable of generating a model that can obtain a simulation result corresponding to a phenomenon.

  Furthermore, another object of the present invention is to provide a simulation capable of obtaining a simulation result corresponding to an actual phenomenon by using a model of a rubber material and a quartz sphere generated by using the model generation method of the present invention. A method, a simulation apparatus, and a computer program are provided.

  The model generation method according to the first aspect of the present invention includes a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-grained units representing a set of a plurality of atoms. In order to simulate the behavior of the polymer object when another non-deformed object contacts the surface of the assembled polymer object, a method of generating a model of the polymer object representing the configuration of the polymer object, An upper surface corresponding to the surface of the polymer object, and the polymer object by assembling a plurality of polymer models in which a plurality of polymer coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other A model of a polymer object having a side surface and a bottom surface corresponding to the inside of the model object is generated, and the boundary condition of the side surface of the generated polymer object model is set as a periodic boundary condition. And sets the boundary condition on the wall boundary conditions.

  The model generation method according to the second aspect of the present invention includes a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-grained units representing a set of a plurality of atoms. In a method for generating a model of a non-deformable object representing a configuration of the non-deformable object in order to simulate the behavior of the polymer object when another non-deformable object contacts the surface of the assembled polymer object, A non-deformable object model is generated by arranging a plurality of non-deformable object coarse-graining units representing the structure of a part of the non-deformable object along the shape of the non-deformable object. The distance between the coarse-graining units of the non-deformable object is set to be equal to or less than the distance at which the Leonard Jones potential between the coarse-graining units of the non-deformable object is a minimum value.

According to a third aspect of the present invention, there is provided a model generation method in which a plurality of macromolecules are obtained by a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-grained units representing a set of a plurality of atoms. In a method for generating a model of a non-deformable object representing a configuration of the non-deformable object in order to simulate the behavior of the polymer object when another non-deformable object contacts the surface of the assembled polymer object, A non-deformable object model is generated by arranging a plurality of non-deformable object coarse-graining units representing the structure of a part of the non-deformable object along the shape of the non-deformable object. The center-to-center distance r of the undeformed object coarse-graining unit is set to σ ≦ r ≦ 2 ^1/6 σ, where σ is the center-to-center distance at which the Leonard Jones potential between the non-deformed object coarse-graining units becomes zero. That features To.

  According to a fourth aspect of the present invention, there is provided a model generation method in which a plurality of macromolecules are obtained by a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-grained units representing a set of a plurality of atoms. In order to simulate the behavior of the polymer object when another non-deformable object contacts the surface of the assembled polymer object, a model of the polymer object representing the structure of the polymer object, and the non-deformable object In the method for generating a model of an undeformed object representing the structure of the above, by assembling a plurality of polymer models in which a plurality of polymer coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other, A model of a polymer object having a top surface corresponding to the surface of the polymer object and side and bottom surfaces corresponding to the inside of the polymer object is generated, and the boundary condition of the side surface of the model of the generated polymer object is periodically generated. The boundary condition of the bottom surface of the model of the generated polymer object is set to the wall boundary condition, and the coarse-grained unit of the non-deformable object representing the structure of a part of the non-deformable object is changed to the shape of the non-deformable object. A model of a non-deformable object is generated by arranging a plurality of the non-deformable object models, and the distance between the coarse-grained units of the non-deformable object adjacent to each other in the non-deformed object model It is characterized by being set to be equal to or less than the distance at which the Jones potential becomes a minimum value.

  The model generation method according to a fifth aspect of the invention is characterized in that the coarse-grained unit of the non-deformable object represents a crystal structure of a predetermined mineral.

  The model generation method according to a sixth aspect of the invention is characterized in that the polymer coarse-graining unit represents a polymer compound that is a component of a diene rubber.

A simulation method according to a seventh aspect of the present invention is a method for gathering a plurality of macromolecules by a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-grained units representing a set of a plurality of atoms. In the method for simulating the behavior of the polymer object when another non-deformed object contacts the surface of the polymer object, the height generated by the model generation method according to any one of the first to sixth inventions Using a model of a molecular object and a non-deformable object, the model of the non-deformable object is pressed into the upper surface of the model of the polymer object in the virtual space, and the model of the press-fitted non-deformed object is obtained by coarse-grained molecular dynamics On the other hand, the force generated from the model of the polymer object is calculated.

  According to an eighth aspect of the present invention, there is provided a model generation device that uses a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-grained units representing a set of a plurality of atoms. A model generation device that generates a model of a polymer object representing the configuration of the polymer object in order to simulate the behavior of the polymer object when another non-deformed object contacts the surface of the assembled polymer object A plurality of polymer models in which a plurality of polymer coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other are assembled to form a top surface corresponding to the surface of the polymer object, Means for generating a model of a polymer object having side surfaces and a bottom surface corresponding to the inside of the molecular object, and means for setting the boundary condition of the side surface of the model of the generated polymer object as a periodic boundary condition. Characterized in that it comprises means for setting the boundary condition of the bottom surface of the model of the polymeric object in the wall boundary conditions.

  According to a ninth aspect of the present invention, there is provided a model generation device that uses a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-grained units representing a set of a plurality of atoms. A model generation device that generates a model of a non-deformable object representing the configuration of the non-deformable object in order to simulate the behavior of the polymer object when another non-deformable object contacts the surface of the assembled polymer object A non-deformable object model by arranging a plurality of non-deformable object coarse-graining units representing the structure of a part of the non-deformable object along the shape of the non-deformable object, And a means for setting the distance between the coarse-graining units of the adjacent non-deformable objects in the interior to be equal to or less than the distance at which the Leonard Jones potential between the coarse-graining units of the non-deformable objects is a minimum value. And butterflies.

  According to a tenth aspect of the present invention, there is provided a simulation apparatus in which a plurality of macromolecules are aggregated by a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction that acts between coarse-graining units representing a set of a plurality of atoms. In the simulation apparatus for simulating the behavior of the polymer object when another non-deformable object comes into contact with the surface of the polymer object, generated by the model generation method according to any one of the first to sixth inventions Means for press-fitting a model of a non-deformable object into the upper surface of the model of the polymer object in a virtual space using the model of the polymer object and the non-deformable object, and a non-deformed object press-fitted by the coarse-grained molecular dynamics method And means for calculating a force generated from the model of the polymer object.

  According to an eleventh aspect of the present invention, there is provided a computer program that collects a plurality of macromolecules by a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-graining units representing a set of a plurality of atoms. A computer that generates a model of a polymer object representing a configuration of the polymer object in order to simulate the behavior of the polymer object when another non-deformed object contacts the surface of the polymer object In the program, an upper surface corresponding to the surface of the polymer object is obtained by assembling a plurality of polymer models in which a plurality of polymer coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other. A procedure for generating a model of a polymer object having a side surface and a bottom surface corresponding to the inside of the polymer object, and a computer The method includes a step of setting a boundary condition of a side surface of a child object model as a periodic boundary condition, and a step of causing a computer to set a boundary condition of a bottom surface of a generated polymer object model as a wall boundary condition. .

  According to a twelfth aspect of the present invention, there is provided a computer program that collects a plurality of macromolecules by a coarse-grained molecular dynamics method that calculates the behavior of an object based on an interaction between coarse-graining units representing a set of a plurality of atoms. A computer for generating a model of a non-deformable object representing a configuration of the non-deformable object in order to simulate the behavior of the polymer object when another non-deformable object contacts the surface of the polymer object In the program, the computer causes the computer to generate a model of the non-deformable object by arranging a plurality of coarse-grained units of the non-deformable object representing the structure of a part of the non-deformable object along the shape of the non-deformable object; The distance between the coarse-graining units of the non-deformable objects in the non-deformable object model Lens potential, characterized in that it comprises a procedure for setting the following distance becomes minimum.

  A computer program according to a thirteenth aspect of the invention provides a computer with a plurality of high-level molecular dynamics methods that calculate the behavior of an object based on an interaction between coarse-graining units representing a set of a plurality of atoms. According to any one of the first to sixth inventions, a computer program for simulating the behavior of the polymer object when another non-deformable object contacts the surface of the polymer object assembled with molecules. Using a model of a polymer object and a non-deformable object generated by the model generation method, a procedure for press-fitting the model of the non-deformable object on the upper surface of the model of the polymer object in virtual space, and a coarse-grained molecule in the computer And a procedure for calculating a force generated from the model of the polymer object with respect to the model of the press-fitted non-deformed object by a dynamic method.

  In the first, eighth and eleventh inventions, a polymer object is used to perform a simulation in which a model of a non-deformable object such as quartz particles contacts a model of a polymer object such as a rubber material by a coarse-grained molecular dynamics method. When generating the model of the non-deformable object, the boundary condition of the bottom surface of the model of the polymer object in which a plurality of polymer models combined with a plurality of coarse-grained units is assembled is set as the wall boundary condition. When performing a simulation of contacting the upper surface of the model of the polymer object, it is possible to suppress the entire model of the polymer object from being attracted to the model of the non-deformable object.

In the second, third, ninth and twelfth inventions, in order to perform a simulation in which a model of a non-deformable object such as a quartz particle contacts a model of a polymer object such as a rubber material by the coarse-grained molecular dynamics method When generating a model of a non-deformable object, a plurality of coarse-grained units of the non-deformable object are arranged along the shape of the non-deformable object to generate a model of the non-deformable object, and the distance between the coarse-grained units is determined. The distance between the coarse-grained units is less than the distance at which the Leonard Jones potential becomes a minimum value, that is, the center-to-center distance r of the coarse-grained unit is σ ≦ r ≦ 2 ^{1 /} by setting the ⁶ sigma, when the model of the non-deformed object performs a simulation in contact with the model of the polymeric object, that polymer model from entering the model of the non-deformed object depressive It can be.

  In the fourth aspect of the invention, in order to perform a simulation in which a model of a polymer object such as a rubber material contacts a model of a polymer object such as a rubber material by the coarse-grained molecular dynamics method, the model of the polymer object and the non-deformable object is used. The boundary condition of the bottom surface of a model of a polymer object in which a plurality of polymer models in which a plurality of coarse-graining units are combined is set as the wall boundary condition, and the coarse-grained unit of an undeformed object By generating multiple models of non-deformed objects by arranging them along the shape of the non-deformed object, the distance between the coarse-grained units is set to be less than the distance at which the Leonard Jones potential between the coarse-grained units is minimized. Therefore, when performing a simulation in which the model of the non-deformable object contacts the upper surface of the model of the polymer object, the entire model of the polymer object is drawn to the model of the non-deformable object. The vignetting by floats, and high molecular models in the model of non-deformed object can be prevented from entering.

  In the fifth invention, by using a coarse-graining unit of a non-deformable object representing a crystal structure of a predetermined mineral such as quartz, a model representing a solid substance made of a mineral such as quartz is generated as a model of the non-deformable object. be able to.

  In the sixth aspect of the invention, a model representing a diene rubber can be generated as a model of a polymer object by using a polymer coarse-graining unit representing a polymer compound that is a component of a diene rubber.

  In the seventh, tenth, and thirteenth inventions, the model generated by the model generation method of the present invention is used, and a model of a polymer object such as a rubber material is not deformed by a coarse-grained molecular dynamics method. A simulation is performed in which an object model comes into contact.

  In the first, eighth, and eleventh inventions, when performing a simulation in which the model of the non-deformable object contacts the upper surface of the model of the polymer object, the entire model of the polymer object is attracted to the model of the non-deformable object. As a result, it is possible to suppress an unnatural change in the density distribution of the rubber material and obtain a simulation result corresponding to an actual phenomenon. Further, since the size of the rubber material model is not increased, an increase in calculation cost can be suppressed.

  In the second, third, ninth, and twelfth inventions, when performing a simulation in which the model of the non-deformable object contacts the upper surface of the model of the polymer object, the model of the polymer is included in the model of the non-deformable object. It is possible to suppress the occurrence of an unnatural phenomenon of intrusion and to obtain a simulation result corresponding to the actual phenomenon. In addition, since the coarse-grained unit is not filled in the non-deformable object model, an increase in calculation cost can be suppressed.

  In the fourth invention, when performing a simulation in which the model of the non-deformable object contacts the upper surface of the model of the polymer object, the entire model of the polymer object is attracted to the model of the non-deformable object, and non-deformation It is possible to suppress the occurrence of an unnatural phenomenon that the polymer model enters the object model, and obtain a simulation result corresponding to the actual phenomenon.

  According to the fifth aspect of the invention, a model representing a solid substance made of a mineral such as quartz is generated as a model of the non-deformable object, thereby performing a simulation in which the model of the non-deformable object contacts the upper surface of the model of the polymer object. By doing so, it is possible to obtain a simulation result based on the actual phenomenon that a tire made of a polymer object comes into contact with a road surface on which a solid substance made of mineral such as quartz is present.

  In the sixth invention, the model representing the diene rubber used for the rubber material of the tire is generated as the model of the polymer object, so that the model of the non-deformable object contacts the upper surface of the model of the polymer object. By performing the simulation, it is possible to obtain a simulation result based on the actual phenomenon that the tire formed using the diene rubber contacts the road surface.

  In the seventh, tenth and thirteenth inventions, the simulation is performed by performing a simulation in which the model of the non-deformable object contacts the upper surface of the model of the polymer object using the model generated by the model generation method of the present invention. Since simulation results can be obtained in line with real phenomena where natural phenomena do not occur, the behavior of polymer objects with various compositions or structures can be simulated to facilitate the development of polymer objects with desired performance Thus, the present invention has excellent effects.

Hereinafter, the present invention will be specifically described with reference to the drawings showing embodiments thereof.
FIG. 1 is a block diagram showing an internal functional configuration of a simulation apparatus 1 according to the present invention. The simulation apparatus 1 is configured by using a general-purpose computer such as a personal computer or a server apparatus, and has a configuration that can be executed with the function of the model generation apparatus of the present invention. The simulation apparatus 1 includes a CPU 11 that performs calculation, a RAM 12 that stores information necessary for the calculation, a reading unit 13 such as a CD-ROM drive that reads information from a recording medium 2 such as an optical disk, and a storage unit 14 such as a hard disk. It has. The storage unit 14 includes a computer program 20 of the present invention including a program for the simulation apparatus 1 to perform a simulation of the behavior of the rubber material when the quartz particles are in contact with the surface of the rubber material, and a process according to the computer program 20. A parameter database 21 that records parameters necessary for execution is stored. The CPU 11 causes the reading unit 13 to read the computer program 20 of the present invention from the recording medium 2 and stores the read computer program 20 in the storage unit 14. The computer program 20 is loaded from the storage unit 14 to the RAM 12 as necessary. Based on the loaded computer program 20, the CPU 11 executes processing necessary for the simulation apparatus 1 and the model generation apparatus of the present invention.

  The simulation apparatus 1 also includes an input unit 15 that accepts input of data from the outside and an output unit 16 that outputs data to the outside. The input unit 15 is an interface that receives data transmitted from an accepting device such as a keyboard that accepts data by a user operation or an external device (not shown). The output unit 16 is an interface that transmits a processing result to a display device that displays the processing result, a printer device that outputs the processing result, or an external device (not shown).

  The computer program 20 according to the present invention may be loaded from an external server device (not shown) connected to the simulation apparatus 1 to the simulation apparatus 1 and stored in the storage unit 14. The parameter database 21 stores part or all of the recorded contents in an external server device or storage device (not shown) connected to the simulation apparatus 1, and the recorded contents are loaded into the simulation apparatus 1 as necessary. The form memorize | stored in RAM12 or the memory | storage part 14 may be sufficient.

  The computer program 20 according to the present invention calculates the parameters necessary for performing simulation processing for simulating the behavior of a rubber material when quartz particles come into contact with the surface of the rubber material by the coarse-grained molecular dynamics method. A program for causing the simulation apparatus 1 to execute parameter calculation processing to be performed and model generation processing to generate a model necessary for performing the simulation. In the molecular dynamics method, the potential existing between atoms is calculated, and the behavior of each atom under the calculated potential is calculated. The potential between atoms is determined according to parameters corresponding to the type of atom, the state of the atom, the combination of atoms, and the like, and the parameter database 21 records these already known parameters.

  In the molecular dynamics method, as the potential between atoms, a bonding potential that exists between atoms that are bonded to each other and a non-bond that is a potential that exists between atoms including atoms that are not bonded to each other. Calculate the potential. The bond potential includes so-called bond, angle and torsion potentials. The potential of the bond is a potential that depends on the bond distance between the atoms to be bonded, and the atom performs an oscillating motion in which the bond distance expands and contracts under the bond potential. The potential of the angle depends on the bond angle between the straight line containing the first and second atoms and the straight line containing the second and third atoms in a state where three atoms are bonded in a straight line. And the three atoms perform an oscillating motion in which the bond changes under an angle potential. The torsional potential is a dihedral angle formed by a plane containing the first, second and third atoms and a plane containing the second, third and fourth atoms in a state where four atoms are bonded in a straight chain. The four atoms undergo a variable oscillation motion in which the dihedral angle changes under the torsional potential. The nonbonding potential is a Leonard Jones potential between atoms.

  In the molecular dynamics method, the potential as described above is calculated for each atom included in the system to be calculated, and the motion of each atom under the calculated potential is calculated. Whereas the calculation unit in the molecular dynamics method is an atom, the coarse-grained molecular dynamics method performs the same calculation using a coarse-grained unit in which a plurality of atoms are aggregated as a calculation unit. That is, in the coarse-grained molecular dynamics method, the potential between the coarse-grained units is calculated, and the motion of each coarse-grained unit under the calculated potential is calculated.

  Next, the contents of the model generation method and simulation method executed by the simulation apparatus 1 of the present invention will be described. FIG. 2 is a flowchart showing a procedure of parameter calculation processing performed by the simulation apparatus 1. The CPU 11 executes the following processing according to the computer program 20 loaded into the RAM 12 as necessary. The simulation apparatus 1 accepts a processing start instruction by a user operating the input unit 15 or the like, and the CPU 11 first receives an isoprene monomer that is a monomer of a rubber molecule from the parameter database 21 stored in the storage unit 14. The data of atoms included in is read into the RAM 12 (S101). Next, the CPU 11 generates an isoprene monomer model representing the cis-isoprene monomer by combining the atom model contained in the isoprene monomer with an appropriate other atom model (S102). The CPU 11 outputs an image of the model of each atom contained in the isoprene monomer from the output unit 16, and receives and accepts an instruction for selecting an atom to be combined by operating the input unit 15 by the user. The process of combining the models of each atom may be performed in accordance with the specified instructions. Next, the CPU 11 combines 64 generated isoprene monomer models in a straight chain to generate a coarse-grained unit of rubber molecules representing polyisoprene in which 64 isoprene monomers are bonded (S103).

FIG. 3 is a schematic structural diagram showing the structure of polyisoprene. The polyisoprene is a polymer obtained by polymerizing isoprene CH ₂ ═C (CH ₃ ) CH═CH ₂ , and cis 1,4 polyisoprene is shown in the figure. N in the figure indicates that isoprene monomers having a structure enclosed in parentheses are continuously bonded. The polyisoprene can take a structure other than cis 1,4 polyisoprene, such as a trans isomer structure of the isoprene monomer. A coarse-grained unit representing cis 1,4 polyisoprene is produced. Since cis 1,4 polyisoprene has the same molecular structure as the main component of natural rubber, a model representing natural rubber can be generated by using a coarse-grained unit representing cis 1,4 polyisoprene.

  Next, the CPU 11 reads out the parameters relating to the coarse-grained unit of rubber molecules from the parameter database 21 stored in the storage unit 14 to the RAM 12, and calculates the structure of the coarse-grained unit of rubber molecules by the molecular dynamics method. (S104). Note that the CPU 11 may use a calculation method other than molecular dynamics such as a molecular orbital method in order to optimize the structure. Next, the CPU 11 linearly couples 102 coarse-grained units of rubber molecules to generate a model of rubber molecules in which 102 coarse-grained units are joined (S105). Calculation is performed to optimize the structure of the generated rubber molecule model (S106). Next, the CPU 11 performs a molecular dynamics calculation on the structure-optimized rubber molecule model under a temperature condition of 300K to obtain an equilibrium structure of the rubber molecule model (S107).

  FIG. 4 is a schematic diagram schematically showing a model of rubber molecules. The spheres in the figure represent coarse-grained units representing cis 1,4 polyisoprene, and the coarse-grained units are linked in a straight chain to form a rubber molecule model. The rubber molecule model for which the equilibrium structure has been obtained corresponds to the polymer model according to the present invention.

  Next, the CPU 11 calculates parameters of the coarse-grained potential necessary for calculation of the coarse-grained molecular dynamics method with respect to the rubber molecule model for which the equilibrium structure has been obtained (S108). Here, the CPU 11 calculates the distance between the centroids of the coarse-grained unit, the coupling angle between the centroids of the coarse-grained unit, and the coarse-grained unit from the calculation result of the molecular dynamics method for obtaining the equilibrium structure of the rubber molecule model. Calculate the distribution of dihedral angles between the centroids of rubber, and present between the coarse-grained units of rubber molecules based on the distance between the coarse-grained units, the bond angle and the dihedral angle distribution function obtained by the calculation Calculate the coarse-grained coupling potential parameters for bond, angle and torsion. The CPU 11 also determines the coarse-grained unit of rubber molecules based on the result of averaging the sum of the non-bonding potentials between atoms contained in the two coarse-grained units over all orientations between the two coarse-grained units. Calculate the parameters of the coarse-grained unbonded potential that exist between them.

Next, in order to generate a model of quartz particles, the CPU 11 reads out the data of the crystal structure of alpha quartz from the parameter database 21 stored in the storage unit 14 (S109), and the 81 silicon dioxide models are alpha quartz. By combining them according to the crystal structure, a coarse-grained unit of quartz particles is generated (S110). FIG. 5 is a schematic structural diagram showing a part of the crystal structure of alpha quartz. Alpha quartz is a crystalline phase of silicon dioxide SiO ₂ at room temperature and normal pressure, with four oxygen atoms (O) arranged at the apexes of the tetrahedron and silicon atoms (Si) arranged equidistant from each atom. It has a structured. Alpha quartz particles are the main component of gravel existing on the road surface, and by generating a model representing the alpha quartz particles, a model that matches the actual gravel can be generated.

The CPU 11 then relates to the coarse-grained non-bonding potential between the coarse-grained units of quartz particles and the coarse-grained non-bonded potential between the coarse-grained unit of rubber molecules and the coarse-grained unit of quartz particles. The parameter is calculated (S111). FIG. 6 is a characteristic diagram showing a general non-bonding potential between particles. In the figure, the horizontal axis represents the distance r between the centers of the particles, and the vertical axis represents the value of the non-bonding potential between the particles at each r. The non-bond potential is a Leonard Jones potential. When r is less than or equal to the predetermined parameter σ, the bond potential is 0 or more, and when r> σ, the value is 0 or less, and r = 2 ^1/6 σ is minimal. Takes a value. Therefore, under the non-bonding potential, a large repulsive force is generated between the particles when r ≦ σ, and an attractive force is generated between the particles when r> σ. That is, the parameter σ of the non-bonding potential corresponds to the sum of the radii of adjacent particles, and corresponds to the particle diameter between the same type of particles.

In step S111, the CPU 11 sets the atom as a sphere having a van der Waals (vdw) radius, and sets the radius of a sphere having a volume equal to the sum of the volumes of atoms included in the coarse-grained unit as the vdw radius of the coarse-grained unit. Ask. Further, the CPU 11 determines whether or not to coarse-grain between the coarse-grained units of quartz particles and between the coarse-grained units of rubber molecules and the coarse-grained units of quartz particles based on the obtained vdw radius of the coarse-grained units. The provisional parameter σ of the binding potential is calculated. Further, the CPU 11 calculates the non-bonding potential between the coarse-grained units near r = 2 ^1/6 σ based on the non-bonded potential between atoms included in the two coarse-grained units using the calculated parameter σ. The value of r is calculated so that the value of the non-bonding potential becomes the minimum value. Further, the CPU 11 obtains a parameter of the coarse-grained non-bonded potential based on the calculated minimum value of the non-bonded potential and the value of r from which the minimum value is obtained. At this time, the CPU 11 corrects the parameter σ so that the value of r at which the value of the non-bonding potential becomes the minimum value becomes r = 2 ^1/6 σ.

  Next, the CPU 11 stores the generated coarse-graining unit data and the obtained coarse-graining potential parameter in the RAM 12 or the storage unit 14 (S112), and ends the parameter calculation process.

  FIG. 7 is a flowchart illustrating a procedure of model generation processing performed by the simulation apparatus 1. FIG. 8 is a schematic diagram showing a model to be generated. The CPU 11 executes the following processing according to the computer program 20 loaded into the RAM 12 as necessary. First, the CPU 11 generates a rectangular parallelepiped virtual space for executing a simulation therein (S21). Here, as shown in FIG. 8, the CPU 11 generates a virtual space of 3d × 3d × 4d, where d is the diameter of a quartz particle model to be described later. Next, the CPU 11 generates a rubber material model by arranging 76 models of rubber molecules inside the 3d × 3d × 2d portion that occupies the lower half of the generated virtual space (S22). The hatched portion in FIG. 8 shows a model of the rubber material. Here, as shown in FIG. 8, the CPU 11 generates a rubber material model so that the rubber material model has an upper surface corresponding to the surface of the rubber material in the virtual space. In addition, by arranging 76 rubber molecule models in the 3d × 3d × 2d portion of the virtual space, the rubber material model has a side surface and a bottom surface corresponding to the inside of the rubber material. To be able to. The generated rubber material model corresponds to the model of the polymer object according to the present invention.

  Next, the CPU 11 sets the boundary condition of the side surface of the rubber material model as the periodic boundary condition (S23). Under the periodic boundary condition, the coarse-grained unit of rubber molecules jumping out from the side surface of the virtual space is inserted into the virtual space from the opposite side surface. By setting the periodic boundary condition, a model corresponding to a system in which a part of the rubber material in contact with the road surface is taken out can be generated. Next, the CPU 11 sets the boundary condition of the model of the rubber material with respect to the bottom surface of the virtual space as the wall surface boundary condition (S24). Here, the CPU 11 realizes a wall boundary condition in which an attractive force is generated between the rubber material model and the bottom surface by setting a Leonard Jones potential between the coarse-grained unit of the rubber molecule and the bottom surface of the virtual space. The calculation which calculates | requires the equilibrium structure of the model of a rubber material under the above boundary conditions is performed.

Next, the CPU 11 uses the parameter σ of the coarse-grained non-coupling potential between the coarse-grained units of quartz particles to set the center-to-center distance r between the coarse-grained units of adjacent quartz particles to σ ≦ r ≦ 2 ^{1. / 6} σ and setting a coarse particle unit of 606 quartz particles in a two-layer spherical shell shape so that the diameter d is about 15 nm, a quartz particle model is generated (S25). ). FIG. 9 is a schematic cross-sectional view of a model of quartz particles. The coarse grain unit of quartz particles is arranged in two layers along the shape of the sphere, and the interior of the quartz particle model is hollow. The center-to-center distance r between the coarse-grained units of adjacent quartz particles is σ ≦ r ≦ 2 ^1/6 σ.

  Next, the CPU 11 places the model of the quartz particle generated in the virtual space on the upper surface of the model of the rubber material (S26), and ends the model generation process. The contents of the above parameter calculation process and model generation process correspond to the contents of the model generation method of the present invention.

  FIG. 10 is a flowchart illustrating a procedure of simulation processing performed by the simulation apparatus 1. The CPU 11 executes the following processing according to the computer program 20 loaded into the RAM 12 as necessary. The simulation apparatus 1 receives an instruction to start simulation processing by the user operating the input unit 15 or the like, and the CPU 11 press-fits a model of quartz particles into a model of rubber material (S31). Next, the CPU 11 moves the quartz particle model in the virtual space in accordance with an instruction received by the input unit 15 or a predetermined processing order (S32). At this time, the CPU 11 performs processing such as further press-fitting the quartz particle model, pulling up the quartz particle model, or moving the quartz particle model in a lateral direction while being pressed into the rubber material model.

  Next, the CPU 11 calculates the coarse-grained molecular dynamics under the temperature condition of 300K using the parameters of the coarse-grained potential obtained by the parameter calculation process, thereby causing the rubber accompanying the movement of the quartz particle model. A change in the shape of the material model is obtained, a force generated on the quartz particle model is calculated from the rubber material model in accordance with the change in shape (S33), and the calculation result is stored in the RAM 12 or the storage unit 14 (S34). . Next, the CPU 11 determines whether or not to end the simulation process according to an instruction received by the input unit 15 or a predetermined processing order (S35). If it is determined that the simulation process should not be terminated (S35: NO), the CPU 11 returns the process to step S32 and newly moves the quartz particle model. If it is determined that the simulation process should be terminated (S35: YES), the CPU 11 terminates the process.

In performing the above simulation processing, the center-to-center distance r between the coarse-grained units of adjacent quartz particles is set to σ ≦ r ≦ 2 ^1/6 σ so that the coarse-grained rubber molecules are included in the quartz particle model. It is possible to prevent the intrusion unit from entering. FIG. 11 is a characteristic diagram showing the number of coarse-grained units of rubber molecules that enter the quartz particle model in the simulation process. The horizontal axis in the figure shows the depth at which the quartz particle model is pressed into the rubber material model in the simulation, and the vertical axis is the coarse-grained unit of rubber molecules that penetrates into the quartz particle model according to the press-in depth. Indicates a number. The rhombus marks in the figure indicate the case where r = 2σ, and the number of coarse-grained units of rubber molecules that enter the quartz particle model increases as the press-in depth of the quartz particle model increases. The round mark in the figure indicates the case where r = 2 ^1/6 σ, and the triangular mark indicates the case where r = σ. In the case of r = 2 ^1/6 σ and r = σ, the number of coarse-grained units of rubber molecules entering the quartz particle model is r = 2σ even if the indentation depth of the quartz particle model is increased. Compared to the case, it is much less and almost zero.

  As described above, the present invention suppresses the occurrence of an unnatural phenomenon that rubber molecules enter the quartz sphere when performing a simulation corresponding to the phenomenon in which the quartz sphere contacts the rubber material. It is possible to obtain a simulation result corresponding to this phenomenon. Further, in the present invention, the coarse particle unit of rubber molecules enters the quartz particle model in a state where the quartz particle model is not filled in the quartz particle model and the quartz particle model is hollow. Therefore, it is possible to prevent an increase in calculation cost.

  Further, in performing the simulation processing according to the present invention, the boundary condition of the rubber material model with respect to the bottom surface of the virtual space is set as the wall surface boundary condition, so that the entire rubber material model can be prevented from floating. Conventionally, when the boundary condition of the rubber material model with respect to the bottom surface of the virtual space is the reflection boundary condition, the rubber material model is attracted to the quartz particle model, and the entire rubber material model is lifted, and the bottom surface of the virtual space is There was a gap with the rubber material model. However, in the present invention, since the boundary condition of the rubber material model with respect to the bottom surface of the virtual space is the wall surface boundary condition, even if the rubber material model is attracted to the quartz particle model, As a result, the entire rubber material model will not be lifted.

  Thus, in the present invention, when performing a simulation corresponding to the phenomenon that the quartz sphere contacts the rubber material, the entire rubber material is attracted to the quartz sphere as the quartz sphere approaches the rubber material, and the density of the rubber material is increased. It is possible to suppress a change in distribution unnaturally and obtain a simulation result corresponding to an actual phenomenon. Further, in the present invention, since the entire rubber material can be prevented from being attracted to the quartz sphere without increasing the size of the model of the rubber material, an increase in calculation cost can be suppressed.

  Next, a processing result by the simulation processing according to the present invention will be shown. FIG. 12 is a characteristic diagram showing the result of calculating the force generated when the quartz particle model is pressed into the rubber material model and when the quartz particle model is pulled up. The horizontal axis in the figure indicates the vertical position where the top surface of the rubber material model is 0, and a negative value indicates that the contact portion of the quartz particle model with the rubber material model enters from the top surface of the rubber material model to the inside. Indicates that The vertical axis in the figure indicates the vertical force applied from the rubber material model to the quartz particle model, a positive value indicates that a repulsive force is generated against the quartz particle model, and a negative value indicates quartz. It shows that an adsorption force that adsorbs the particle model is generated. The circles in the figure indicate the force calculated at each position while the quartz particle model is gradually and deeply pressed into the rubber material model from the position of the vertical position 0. Furthermore, the rhombus marks in the figure indicate the force calculated at each position while gradually lifting the model of the rubber material from the deepest part where the quartz particle model is press-fitted into the model of the rubber material.

  As shown in FIG. 12, when a quartz particle model is press-fitted into a rubber material model, a repulsive force is generated from the rubber material model, and repulsion of the rubber material against the road surface is realized. Further, when the quartz particle model is pulled up, an adsorption force having a negative value is generated, and in particular, the adsorption force is generated even at a position where the vertical position of the quartz particle model exceeds zero. Thereby, the adsorption | suction by a rubber material is implement | achieved.

  FIG. 13 is a characteristic diagram showing a result of calculating a force generated when the quartz particle model is moved in the horizontal direction in a state where the quartz particle model is press-fitted into the rubber material model. The horizontal axis in the figure indicates the horizontal position in the model of the rubber material, and the position where the quartz particle model is first press-fitted is zero. The vertical axis in the figure represents the horizontal force applied from the rubber material model to the quartz particle model as an absolute value. The diamond marks in the figure indicate the force calculated at each position while pressing the quartz particle model into the rubber material model and moving the horizontal position in the direction of a positive value. In addition, the triangle marks in the figure indicate the force calculated at each position by moving the quartz particle model in the reverse direction immediately after the movement indicated by the diamond marks is completed. The circles in the figure indicate the forces calculated at each position by moving the quartz particle model in the reverse direction immediately after the movement indicated by the triangles is completed.

  As shown in FIG. 13, an elastic force is generated from the rubber material model to the quartz particle model by pressing the quartz particle model into the rubber material model and moving it. In addition, if the quartz particles are moved in the opposite direction immediately after moving the quartz particles in one direction, the elastic force after reversing the moving direction has a smaller absolute value than the elastic force before reversing the moving direction, It can be seen that the elastic hysteresis peculiar to viscoelastic bodies such as rubber is reproduced. As described above, in the present invention, it is possible to obtain a simulation result corresponding to a phenomenon occurring in an actual rubber material, such as adsorption of quartz particles by the rubber material and occurrence of elastic hysteresis. Therefore, by using the present invention, it is possible to simulate the behavior of rubber materials having various compositions or structures, and promote the development of rubber materials having desired performance.

  Note that the specific contents of the simulation performed in this embodiment are merely examples, and in the present invention, it is possible to perform a simulation in which the configuration and number of coarse-graining units are changed. In the present embodiment, the polymer object to be simulated is polyisoprene, which is the main component of natural rubber. However, in the present invention, the polymer object to be simulated is replaced with a polymer object other than polyisoprene. It may be a molecule. For example, a coarse-grained unit representing a polybutadiene obtained by polymerizing cis-butadiene or a butadiene-styrene copolymer obtained by copolymerizing cis-butadiene and styrene may be used as the polymer coarse-grained unit. Polyisoprene, polybutadiene, and butadiene-styrene copolymer are polymer compounds that are components of diene rubber using a diene monomer as a monomer, and are generally used as a rubber material for tires. By performing a simulation according to the present invention using a coarse-grained unit representing a polymer compound that is a component of these diene rubbers, a real phenomenon that a tire formed using a diene rubber contacts a road surface is realized. An appropriate simulation result can be obtained. In the present invention, the number of monomers contained in the polymer coarse-graining unit, the number of polymer coarse-graining units constituting the polymer model, and the polymer constituting the polymer object model The number of models may be any number suitable for simulation. The polymer model is not limited to a structure in which the coarse-grained units are bonded in a chain, but may include a crosslinked structure.

  In the present embodiment, the non-deformable object to be simulated is a quartz particle having an alpha quartz structure. However, in the present invention, the non-deformable object to be simulated may be another solid substance. Good. For example, as a coarse-graining unit for undeformed objects, silica minerals such as quartz and cristobalite, layered silicate minerals such as mica and clay minerals, carbonate minerals such as limestone, and crystals of predetermined minerals such as iron ore A coarse-grained unit representing the structure may be used. These minerals are components of solid substances existing on the road surface, such as road surface aggregate, pavement material and gravel on the road surface, and according to the present invention using a coarse-grained unit representing the crystal structure of these minerals. By performing the simulation, it is possible to obtain a simulation result based on the actual phenomenon that the tire made of a polymer contacts the road surface on which these solid substances exist. In the present invention, the number of atoms included in the coarse-grained unit of the non-deformable object, the shape of the model of the non-deformable object, the size of the model of the non-deformable object, and the coarse-grain unit constituting the model of the non-deformable object May be arbitrarily determined in order to perform simulation. In the present embodiment, an example in which a quartz particle model is configured by arranging coarse-grained units of quartz particles in a two-layer spherical shell shape is shown, but in the present invention, the shape of an undeformed object is shown. A model of a non-deformable object may be configured by arranging a plurality of coarse-graining units of one layer or three or more layers along.

  In the present embodiment, the rubber material model and the quartz particle model are generated, and the simulation example is performed using the generated model. The model, the model of the non-deformable object, and the parameters necessary for the simulation are stored in the storage unit 14, and the model of the polymer object, the model of the non-deformable object, and the parameters necessary for the simulation are stored in the RAM 12 from the storage unit 14 as necessary. It is also possible to perform a simulation by reading out to. In the present embodiment, the function of the model generation device and the simulation device of the present invention is realized by a single computer. However, the present invention is not limited to this, and the model generation device and the simulation device of the present invention are not limited thereto. It may be realized by using a plurality of computers.

It is a block diagram which shows the function structure inside the simulation apparatus of this invention. It is a flowchart which shows the procedure of the parameter calculation process which a simulation apparatus performs. It is a typical structure figure showing the structure of polyisoprene. It is a schematic diagram which shows the model of a rubber molecule typically. It is a typical structure figure showing a part of crystal structure of alpha quartz. It is a characteristic view which shows the nonbonding potential between general particles. It is a flowchart which shows the procedure of the model production | generation process which a simulation apparatus performs. It is a schematic diagram which shows the model to produce | generate. It is a typical sectional view of a model of quartz particles. It is a flowchart which shows the procedure of the simulation process which a simulation apparatus performs. FIG. 5 is a characteristic diagram showing the number of coarse-grained units of rubber molecules that enter a quartz particle model in a simulation process. It is a characteristic view showing the result of calculating the force generated when the quartz particle model is pressed into the rubber material model and when the quartz particle model is pulled up. It is a characteristic view showing the result of calculating the force generated when the quartz particle model is moved in the horizontal direction with the quartz particle model being pressed into the rubber material model.

Explanation of symbols

1 Simulation device (model generation device)
11 CPU
12 RAM
14 Storage Unit 2 Recording Medium 20 Computer Program 21 Parameter Database

Claims (13)

A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In order to perform a simulation of the behavior of the polymer object when a non-deformed object contacts, a method for generating a model of a polymer object representing the configuration of the polymer object,
An upper surface corresponding to the surface of the polymer object, and the polymer object by assembling a plurality of polymer models in which a plurality of polymer coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other A model of a polymer object having side and bottom surfaces corresponding to the interior of
Set the boundary condition of the side of the model of the generated polymer object to the periodic boundary condition,
A model generation method characterized by setting a boundary condition of a bottom surface of a model of a generated polymer object to a wall boundary condition. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In order to simulate the behavior of the polymer object when the non-deformable object comes into contact, in a method for generating a model of the non-deformable object representing the configuration of the non-deformable object,
Generating a model of the non-deformable object by arranging a plurality of coarse-grained units of the non-deformable object representing the structure of a part of the non-deformable object along the shape of the non-deformable object;
The distance between coarse-graining units of adjacent non-deformable objects in the model of non-deformable objects is set to be equal to or less than the distance at which the Leonard Jones potential between the coarse-grained units of non-deformable objects is minimal. Model generation method. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In order to simulate the behavior of the polymer object when the non-deformable object comes into contact, in a method for generating a model of the non-deformable object representing the configuration of the non-deformable object,
Generating a model of the non-deformable object by arranging a plurality of coarse-grained units of the non-deformable object representing the structure of a part of the non-deformable object along the shape of the non-deformable object;
Σ ≦ r, where σ is the center-to-center distance r between coarse-graining units of non-deformable objects adjacent to each other in the non-deformable object model, and σ ≦ r ≤ 2 ^1/6 σ is set as a model generation method. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In order to simulate the behavior of the polymer object when the non-deformable object comes into contact, a model of the polymer object representing the configuration of the polymer object and a model of the non-deformable object representing the structure of the non-deformable object In the method of generating
An upper surface corresponding to the surface of the polymer object, and the polymer object by assembling a plurality of polymer models in which a plurality of polymer coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other A model of a polymer object having side and bottom surfaces corresponding to the interior of
Set the boundary condition of the side of the model of the generated polymer object to the periodic boundary condition,
Set the boundary condition of the bottom surface of the model of the generated polymer object to the wall boundary condition,
Generating a model of the non-deformable object by arranging a plurality of coarse-grained units of the non-deformable object representing the structure of a part of the non-deformable object along the shape of the non-deformable object;
The distance between coarse-graining units of adjacent non-deformable objects in the model of non-deformable objects is set to be equal to or less than the distance at which the Leonard Jones potential between the coarse-grained units of non-deformable objects is minimal. Model generation method.   The model generation method according to any one of claims 2 to 4, wherein the coarse-graining unit of the non-deformable object represents a crystal structure of a predetermined mineral.   The model generation method according to claim 1, wherein the coarse-graining unit of the polymer represents a polymer compound that is a component of a diene rubber. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In a method of simulating the behavior of the polymer object when a non-deformed object comes into contact,
The model of the non-deformable object is placed on the upper surface of the model of the polymer object in the virtual space using the model of the polymer object and the non-deformable object generated by the model generation method according to claim 1. Press fit,
A simulation method characterized by calculating a force generated from a model of a polymer object against a model of a press-fitted non-deformed object by a coarse-grained molecular dynamics method. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In a model generation device for generating a model of a polymer object representing a configuration of the polymer object, in order to perform a simulation of the behavior of the polymer object when a non-deformable object comes into contact,
An upper surface corresponding to the surface of the polymer object, and the polymer object by assembling a plurality of polymer models in which a plurality of polymer coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other Means for generating a model of a polymer object having side and bottom surfaces corresponding to the interior of
Means for setting the boundary condition of the side surface of the model of the generated polymer object to the periodic boundary condition;
And a means for setting the boundary condition of the bottom surface of the model of the generated polymer object to the wall boundary condition. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In a model generation device for generating a model of a non-deformable object representing a configuration of the non-deformable object in order to perform a simulation of the behavior of the polymer object when the non-deformable object comes into contact,
Means for generating a model of the non-deformable object by arranging a plurality of coarse-grained units of the non-deformable object representing the structure of a part of the non-deformable object along the shape of the non-deformable object;
Means for setting a distance between coarse-graining units of adjacent non-deformable objects in a non-deformable object model to be equal to or less than a distance at which the Leonard Jones potential between the coarse-graining units of non-deformable objects is a minimum value. A model generation device characterized by the above. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In a simulation apparatus for simulating the behavior of the polymer object when a non-deformable object comes into contact,
The model of the non-deformable object is placed on the upper surface of the model of the polymer object in the virtual space using the model of the polymer object and the non-deformable object generated by the model generation method according to claim 1. Means for press-fitting,
A simulation apparatus comprising: means for calculating a force generated from a model of a polymer object with respect to a model of a press-fitted nondeformable object by a coarse-grained molecular dynamics method. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In a computer program for causing a computer to generate a model of a polymer object that represents a configuration of the polymer object, in order to perform a simulation of the behavior of the polymer object when a non-deformable object comes into contact,
By assembling a plurality of polymer models in which a plurality of macroscopic coarse-graining units representing a structure in which a predetermined number of monomers are bonded to each other is collected in a computer, an upper surface corresponding to the surface of the polymer object, and Generating a model of a polymer object having side and bottom surfaces corresponding to the interior of the polymer object;
A procedure for causing the computer to set the boundary condition of the side surface of the model of the generated polymer object as a periodic boundary condition;
A computer program comprising: causing a computer to set a boundary condition of a bottom surface of a model of a generated polymer object as a wall boundary condition. A coarse-grained molecular dynamics method that calculates the behavior of an object based on the interaction between the coarse-grained units representing a set of atoms can be In a computer program for causing a computer to generate a model of an undeformed object representing a configuration of the undeformed object in order to perform a simulation of the behavior of the polymer object when the non-deformed object is in contact,
A step of causing a computer to generate a model of a non-deformable object by arranging a plurality of coarse-grained units of the non-deformable object representing a structure of a part of the non-deformable object along the shape of the non-deformable object;
A procedure for causing a computer to set a distance between coarse-graining units of adjacent non-deformable objects in the model of the non-deformable object to be equal to or less than a distance at which the Leonard Jones potential between the coarse-grained units of the non-deformable object is a minimum value; A computer program comprising: The surface of a polymer object in which multiple polymers are aggregated by a coarse-grained molecular dynamics method that calculates the behavior of the object based on the interaction between the coarse-grained units representing a set of atoms. In a computer program for performing a simulation of the behavior of the polymer object when another non-deformed object comes into contact with
Using a model of a polymer object and a non-deformed object generated by the model generation method according to any one of claims 1 to 6 on a computer, an undeformed object is placed on the upper surface of the model of the polymer object in a virtual space. The procedure to press-fit the model,
A computer program comprising: causing a computer to calculate a force generated from a model of a polymer object with respect to a model of a non-deformed object press-fitted by a coarse-grained molecular dynamics method.

Images