JP2018004604A - Creation method of filler model - Google Patents

Abstract

PROBLEM TO BE SOLVED: To create a filler model capable of improving simulation accuracy in a short time.SOLUTION: There is provided a method for creating a three-dimensional filler model 2. In the creation method, a first step S1 for setting a center part 6 formed of one filler particle model 3, and a second step S2 for setting plural layers U formed of a filler particle model group 8 in which, plural filler particle models 6 are arranged in a concentric spherical state, on the outside of the center part 6, are included. The second step S2 comprises: an arrangement step for arranging the filler particle model 3 forming the M-th layer U; a coupling step for coupling the filler particle model 3 on the (M-1)th layer and the filler particle model 3 on the M-th layer, with at least one coupling chain model 4; and a step for performing a molecule kinetics calculation to the filler particle model 3 on the M-th layer U.SELECTED DRAWING: Figure 4

Description

  The present invention relates to a filler model creation method capable of creating a filler model capable of improving simulation accuracy in a short time.

  In recent years, various simulation methods (numerical calculations) have been proposed for evaluating the properties of a composite material composed of a filler and a polymer material using a computer for the development of rubber compounding. In this type of simulation method, a filler model that models a filler and a polymer model that models a polymer material are input to a computer.

  The filler model is formed in, for example, a three-dimensional substantially spherical shape. The filler model includes a plurality of filler particle models. The polymer model also includes at least one polymer particle model. Then, for example, a mutual potential (for example, Lennard-Jones potential) is defined between the filler particle model and the polymer particle model, and molecular dynamics calculation is performed in a limited space. Related technologies include the following.

JP 2006-64658 A

  In general, the spherical filler model includes a large number of filler particle models, which are randomly arranged according to a random number function or arranged in a lattice pattern.

  When randomly arranged, the filler particle model may be arranged so as to overlap the adjacent filler particle model. Such overlapping of filler particle models causes variations in stress distribution and mutual potential inside the filler model. Due to these variations, the molecular dynamics calculation has a problem that the dynamics calculation becomes unstable and the simulation accuracy is lowered.

  On the other hand, when arranged in the form of a lattice, a regular plane corresponding to the density of the lattice is generated, so there is a problem that the way of interaction with the polymer lattice is different compared to the case of a spherical surface. .

  Moreover, in order to solve the above problems, it is conceivable to manually arrange the filler particle model. However, since it is necessary to arrange many filler particle models, there is a problem that it takes a lot of time. .

  The present invention has been devised in view of the above circumstances, and has as its main object to provide a method capable of creating a filler model that can improve simulation accuracy in a short time.

  The present invention is a method of creating a three-dimensional filler model using a computer, including a plurality of filler particle models and at least one bond chain model connecting the plurality of filler particle models. A first step of setting a central part consisting of a single filler particle model, and a plurality of filler particle models spaced apart from the central filler particle model in a radial direction outside the central part in the computer. A second step of setting a plurality of layers of filler particle model groups arranged in a concentric spherical shape, wherein the second step arranges the filler particle model constituting the Mth layer in the computer. Arranging step, wherein the computer includes a filler particle model of the (M-1) th layer and a filler particle model of the Mth layer. Coupling step of coupling at least one of said binding chain model, as well as the computer, to subject the filler particles model of the M-th layer, characterized in that it comprises a step of calculating molecular dynamics.

In creating of the filler model according to the present invention, the arrangement process, the center point of the filler particles model of the M-th layer is set at a radius R _M of the filler particles model around the central portion Preferably, the method includes a step of determining the number N _M of the filler particle models of the Mth layer by the following formula (1).
here,
N _M : Number of filler particle models of the Mth layer R _M : Radius of the spherical surface of the Mth layer r: Radius of the filler particle model ρ _M : Number density of filler particles of the Mth layer

  In the method for creating a filler model according to the present invention, the second step sets the layers from the third layer of the filler model to the Nth layer arranged on the outermost side in the radial direction. A main setting step, wherein the main setting step includes the step of arranging the Mth layer to be connected to the filler particle model of the M-1st layer through the bond chain model in the arranging step. A determining step of determining the filler particle model, the determining step including a step of selecting one filler particle model of the M-1st layer, a center point of the selected filler particle model, and the center The central axis of the selected filler particle model as a vertex, and the diameter of the filler particle model as the length of the generatrix. Calculating the circumference of the cone, and arranging the filler particle model of the Mth layer on a spherical surface surrounded by the circumference of the cone, and the filler particle model of the Mth layer And connecting to the selected filler particle model of the M-1 th layer.

  In the method for creating the filler model according to the present invention, it is desirable that an angle formed by the central axis and the conical surface of the cone is not less than 0 degrees and less than 60 degrees.

  In the method for creating the filler model according to the present invention, the filler particle model of the Nth layer arranged at the outermost radial direction is connected to the other filler particle model of the Nth layer by the bond chain model. It is desirable to further include the step of carrying out.

  The method for creating a filler model of the present invention includes a first step of setting a central portion made of one filler particle model in a computer. Furthermore, a method for creating a filler model includes a layer composed of a filler particle model group in which a plurality of filler particle models are arranged concentrically at a distance from the filler particle model in the center portion in the radial direction outside the center portion. A second step of setting a plurality is included.

  The second step includes at least one of an arrangement step of arranging a filler particle model constituting the Mth layer, a filler particle model of the (M-1) th layer, and a filler particle model of the Mth layer. A bonding step of connecting with a bond chain model, and a step of calculating molecular dynamics for the filler particle model of the Mth layer.

  In the creation method of the present invention, the filler particle models are arranged in a concentric spherical shape for each layer from the filler particle model in the center, and therefore, it is possible to prevent the filler particle models adjacent in the radial direction of the filler model from overlapping each other. it can.

  Furthermore, in the production method of the present invention, after the filler particle model of the (M-1) th layer and the filler particle model of the Mth layer are connected by a bond chain model, the filler particles of the Mth layer are connected. Since the molecular dynamics calculation is performed on the model, the equilibrium state of the filler particle model of the Mth layer can be calculated. Thereby, the overlap of the filler particle models adjacent in the same layer can be removed.

  As described above, according to the creation method of the present invention, it is possible to effectively prevent the filler particle models from overlapping each other and create the filler model in a short time. In addition, the model obtained by this creation method can suppress, for example, variations in stress distribution and mutual potential inside the filler model, thereby improving simulation accuracy.

It is a perspective view of the computer which performs the creation method of this embodiment. It is a conceptual diagram of a filler model. FIG. 3 is an AA end view of FIG. 2. It is a flowchart of the creation method of this embodiment. It is a conceptual perspective view which shows the center part arrange | positioned in virtual space. It is a flowchart of the 2nd process of this embodiment. It is a flowchart of the initial setting process of this embodiment. It is a flowchart of the arrangement | positioning process of this embodiment. It is a conceptual diagram of the spherical surface of the 2nd layer. It is a conceptual diagram explaining the process of determining the number of the filler particle models of a 2nd layer. It is a conceptual diagram of the filler particle model which comprises a 2nd layer. It is a conceptual diagram which shows the bond chain which connects the filler particle model of a 1st layer, and the filler particle model of a 2nd layer. It is a flowchart of the main setting process of this embodiment. It is a flowchart of the arrangement | positioning process of this embodiment. It is a conceptual diagram explaining the process of determining the number of filler particle models of a 3rd layer. It is a flowchart of the determination process of this embodiment. It is a conceptual diagram of the conical surface which makes the vertex the center point of the filler particle model of a center part. It is a conceptual diagram which shows the pair of the filler particle model of a 2nd layer, and the filler particle model of a 3rd layer. It is a conceptual diagram which shows the bond chain which connects the filler particle model of a 2nd layer, and the filler particle model of a 3rd layer. It is a conceptual diagram which shows the bond chain model which connects the filler particle model of Nth layer, and the other filler particle model 3 of Nth layer.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The filler model creation method of the present embodiment (hereinafter sometimes simply referred to as “creation method”) is a method of creating a filler model in which a filler is modeled using a computer. Examples of the filler include carbon black, silica, or alumina.

  As shown in FIG. 1, the computer 1 includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with an arithmetic processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1, 1a2. Note that a processing procedure (program) for executing the creation method of the present embodiment is stored in the storage device in advance.

  As shown in FIGS. 2 and 3, the filler model 2 of the present embodiment is formed in, for example, a three-dimensional substantially spherical shape having a diameter L1 set to about 5 to 30σ. The filler model 2 includes a plurality of filler particle models 3 and at least one bond chain model 4 that connects the plurality of filler particle models 3. In FIG. 2, the bond chain model 4 is omitted.

  In addition, the filler model 2 includes a central portion 6 composed of one filler particle model 3 and a filler particle model group 8 in which a plurality of filler particle models 3 are arranged concentrically outside the central portion 6. It is out.

  The filler model 2 of the present embodiment includes a plurality of layers composed of a filler particle model group 8 with the filler particle model 3 in the central portion 6 as a first layer (hereinafter sometimes simply referred to as “first layer”) U1. U is provided. The layer U composed of the filler particle model group 8 has a radius from a second layer U2 (hereinafter sometimes simply referred to as “second layer”) adjacent to the filler particle model 3 in the central portion 6 in the radial direction outside. It includes up to the Nth layer (hereinafter, also simply referred to as “Nth layer”) UN arranged on the outermost side in the direction. Each layer U is arranged at a distance in the radial direction from the filler particle model 3 in the central portion 6.

  Each filler particle model 3 is represented by a sphere having a diameter. Such filler particle model 3 is treated as a mass point of the equation of motion in the molecular dynamics calculation. That is, the filler particle model 3 defines parameters such as mass, diameter, charge, or initial coordinates.

  The bond chain model 4 is, for example, a sum of a Lennard-Jones potential (hereinafter sometimes simply referred to as “LJ potential”) P1 represented by the following formula (2) and a FENE potential P2 represented by the following formula (3). It is defined by the set potential (P1 + P2).

Here, each constant and variable are as follows.
r _ij : Distance between each filler particle model r _c : Cut-off distance r ₀ : Full extension length k: Spring constant between each filler particle model ε: LJ potential strength defined between each filler particle model σ: Each It corresponds to the diameter of the filler particle model. Note that the distance r _ij between the filler particle models 3 and 3, the cut-off distance r _c , the extension length r ₀ , and the distance σ on which the LJ potential acts are the respective filler particle models 3. Defined as the distance between the centers 3c and 3c.

LJ potential P1 is as the distance r _ij between filler particles model 3,3 is smaller than the cutoff distance r _c, the value increases. On the other hand, FENE potential P2, the distance r _ij is greater than the cutoff distance r _c, the value increases. Therefore, the bond chain model 4 defines a restoring force that attempts to return the distance r _ij to a position where the LJ potential P1 and the FENE potential P2 are balanced with each other.

Further, in the above formula (3), when the distance r _ij between the filler particle models 3 and 3 becomes the full length r ₀ or more, the FENE potential P2 is set to ∞. Therefore, the bond chain model 4 does not allow the distance r _ij to be longer than the full length r ₀ . Such a bond chain model 4 can be effectively approximated to the behavior of the actual filler model 2 in the molecular dynamics calculation.

Note that the strength ε, elongation length r _0, and particle diameter σ of the LJ potential P1 and the FENE potential P2 can be set as appropriate. These constants are described, for example, in a paper (Kurt Kremer & Gary S. Grest, “Dynamics of entangled linear polymer melts: A molecular-dynamics simulation”, J. Chem Phys. Vol. 92, No. 8, 15 April 1990). Based on this, it is desirable to set as follows.
Strength ε: 1.0
Full length r ₀ : 1.5
Distance σ: 1.0

  The spring constant k is a parameter that determines the rigidity of the filler model 2. For this reason, it is desirable that the spring constant k is set within a range of 10 to 5000 based on the rigidity of the filler to be analyzed. In addition, when the spring constant k is less than 10, the rigidity of the filler model 2 becomes excessively small, and the simulation accuracy may be reduced. On the other hand, even if the spring constant k exceeds 5000, deformation of the filler model 2 is substantially not allowed and the molecular dynamics calculation may become unstable. From such a viewpoint, the spring constant k is more preferably 20 or more, further preferably 25 or more, more preferably 3000 or less, and further preferably 2500 or less.

  Further, the bond chain model 4 may be defined by a bond potential P3 shown in the following formula (4).

Here, the constants and variables are the same as those in the equations (2) and (3) except for the following.
r ₀ : equilibrium length

The bond potential P3 defined by the above formula (4) is a Harmonic type. The Harmonic type is a potential in which a so-called linear spring is defined and a restoring force proportional to the deviation from the equilibrium length r ₀ acts.

In the above equation (4), when the distance r _ij between the filler particle models and the equilibrium length r ₀ are equal, the coupling potential P3 is zero. When the distance r _ij is greater than the equilibrium length r ₀ , the coupling potential P3 increases as the distance r _ij increases. On the other hand, when the distance r _ij is smaller than the equilibrium length r _0, the more the distance r _ij is small, bonding potential P3 increases. Thus, in the coupling potential P3, a restoring force that attempts to return the distance r _ij to the equilibrium length r ₀ is defined. Further, unlike the LJ potential P1 and the FENE potential P2, the upper limit value of the distance r _ij is not limited to the equilibrium length r ₀ .

Note that the value of the equilibrium length r _{0 in} the above equation (4) can be set as appropriate. In this embodiment, it is desirable to set so as to approximate the bond chain model 4 defined by the potential (P1 + P2) set by the sum of the LJ potential P1 and the FENE potential P2.

  Further, the spring constant k in the above equation (4) is a parameter for determining the rigidity of the filler model 2 in the same manner as the spring constant k in the above equation (3). The spring constant k in the above formula (4) is preferably set within the range of 50 to 5000 based on the rigidity of the filler to be analyzed. In addition, when the spring constant k is less than 50, the rigidity of the filler model 2 becomes excessively small, and the simulation accuracy may be reduced. On the other hand, even if the spring constant k exceeds 5000, deformation of the filler model 2 is substantially not allowed and the molecular dynamics calculation may become unstable. From such a viewpoint, the spring constant k is more preferably 300 or more, still more preferably 700 or more, more preferably 3000 or less, and further preferably 2500 or less.

  FIG. 4 shows an example of the processing procedure of the creation method of the present embodiment. In the creation method of the present embodiment, first, as shown in FIG. 5, a central portion 6 composed of one filler particle model 3 is set in the computer 1 (first step S <b> 1). In the first step S1, for example, the central portion 6 is defined in the virtual space 7 having a predetermined volume. Numerical data including the mass, diameter, initial coordinates, and the like of the central portion 6 is stored in the computer 1.

  The virtual space 7 corresponds to a microstructure portion of the rubber polymer to be analyzed, and is defined as a cube, for example. In addition, the length L2 of one side of the virtual space 7 can be set as appropriate. For example, the length L2 of the filler model 2 is twice or more, preferably 10σ or more in this embodiment.

  Next, a plurality of layers composed of filler particle model groups in which a plurality of filler particle models 3 are arranged concentrically on the outside of the central portion 6 are set in the computer 1 (second step S2). FIG. 6 shows an example of the processing procedure of the second step S2 of the present embodiment.

  In the second step S2 of the present embodiment, first, the second layer U2 (shown in FIG. 3) of the filler model 2 is set (initial setting step S21). FIG. 7 illustrates an example of the initial setting step S21 of the present embodiment. In the initial setting step S21 of the present embodiment, first, 2 is set as a constant M as an initial condition (step S211). This constant M is stored in the computer 1.

  Next, the filler particle model 3 constituting the second layer U2 (shown in FIG. 3) is arranged (arrangement step S212). FIG. 8 shows an example of the processing procedure of the arrangement step S212 of the present embodiment.

In disposing step S212, first, as shown in FIG. 9, the spherical T of the second layer U2 radius R ₂ centered on the center point 3g of the filler particles model 3 of the central portion 6 is set (step S61) . The spherical surface T of the second layer U2 is set based on the radius R ₂ obtained from the following equation (5).
R _M = B × (M−1) (5)
Here, the constants and variables are as follows.
B: increment distance radius R _M

In the above equation (5), the radius R _M of the _Mth spherical surface T is set based on a constant incremental distance B. Thereby, the spherical surface T of each layer U is arranged at a certain distance (incremental distance B) from the spherical surface T of the layer U adjacent in the radial direction. The incremental distance B can be set as appropriate, but is preferably set larger than the diameter (radius r (shown in FIG. 10) × 2) of the filler particle model 3. In this step S61, the spherical surface T of the second layer is set based on the radius R _M = incremental distance B. The spherical surface T of the second layer U2 is numerical data including coordinates and is stored in the computer 1.

Next, the number N ₂ of filler particle models 3 in the second layer U2 is determined (step S62). As shown in FIG. 10, in the present embodiment, the number N ₂ is determined using the following formula (1).

here,
N _M : Number of filler particle models of the Mth layer R _M : Radius of the spherical surface of the Mth layer r: Radius of the filler particle model ρ _M : Number density of filler particles of the Mth layer

In the above formula (1), for example, the outer spherical surface 11 whose radius is the sum (R ₂ + r) of the radius R ₂ of the spherical surface T of the second layer U2 and the radius r of the filler particle model 3, and the second layer The maximum number of filler particles 3 that can be arranged in the region 13 between the inner spheres 12 whose radius is the difference (R ₂ −r) between the radius R ₂ of the spherical surface T of U ₂ and the radius r of the filler particle model 3. N ₂ is being sought. Incidentally, if it contains the number N ₂ in the fractional part obtained by the above formula (1) is, the decimal point is truncated desirable. Thus, in step S62, the filler particles model 3 of the second layer U2, it is possible to determine the number N ₂ which can be reliably disposed in the region 13. Such a number N ₂ is stored in the computer 1. Further, the number density ρ _M can be appropriately changed in each layer.

Next, as shown in FIG. 11, the filler particle model 3 constituting the second layer U2 is arranged on the spherical surface T of the second layer U2 (step S63). In this step S63, the filler particle model 3 for the number N ₂ obtained by the above formula (1) is arranged on the spherical surface T of the second layer U2 according to, for example, a random number function. Thereby, the 2nd layer U2 which the filler particle model 3 consists of the filler particle model group 8 arrange | positioned at the radial direction from the center part 6 can be set. Therefore, in step S63, it is possible to prevent the filler particle model 3 of the second layer U2 from being overlapped with the filler particle model 3 of the central portion 6 adjacent in the radial direction.

  In the present embodiment, the center point 3g of the filler particle model 3 of the second layer U2 is disposed on the spherical surface T of the second layer U2. Thereby, in process S63, each filler particle model 3 of 2nd layer U2 can be arrange | positioned in the area | region 13 without making the radial direction vary. In step S63, numerical data including the coordinates of the filler particle model 3 of the second layer U2 is stored in the computer 1.

  Next, as shown in FIG. 12, the computer 1 connects the filler particle model 3 of the first layer U1 and the filler particle model 3 of the second layer U2 with a bond chain model 4 (bonding step S213). . In this bonding step S213, each filler particle model 3 of the second layer U2 is connected to the filler particle model 3 (center portion 6) of the first layer U1 by at least one bond chain model 4 in this embodiment. Has been. Thereby, the filler particle model 3 of the first layer U1 and the filler particle model 3 of the second layer U2 are constrained to each other, and the filler model 2 including the first layer U1 to the second layer U2 is set. In the coupling step S213, numerical data defining the coupled chain model 4 is stored in the computer 1.

  Next, the computer 1 performs molecular force field calculation and molecular dynamics calculation for the filler particle model 3 of the second layer U2 (step S214). In this step S214, the above formula (2) is applied between the filler particle model 3 of the first layer U1 and each filler particle model 3 of the second layer U2 and between the adjacent filler particle models 3 and 3 of the second layer U2. ) LJ potential P1 is set. Further, in step S214, the FENE potential P2 of the above formula (3) is set along the bond chain model 4. Then, molecular dynamics calculation is performed on all filler particle models 3 in the first layer U1 and the second layer U2.

  The molecular force field calculation of this embodiment is performed in order to remove the overlap of the filler particle model 3. In the molecular dynamics calculation of the present embodiment, for example, it is assumed that all filler particle models 3 in the first layer U1 and the second layer U2 arranged in the virtual space 7 for a predetermined time follow classical mechanics. The equation is applied. Then, the movement of all filler particle models 3 in the first layer U1 and the second layer U2 at each time is tracked. Further, when performing molecular dynamics calculation, the particles, volume and temperature in the system are kept constant. Thereby, in step S214, since the equilibrium state of the filler particle model 3 of the second layer U2 can be calculated, the overlap between the filler particle models 3 and 3 adjacent to each other in the same layer can be removed. In step S214, numerical data including the coordinates of the filler particle model 3 of the second layer U2 in the equilibrium state is stored in the computer 1.

As described above, the LJ potential P1 increases as the distance r _ij between the filler particle models 3 and 3 decreases. For this reason, immediately after the arrangement step S212, if the distance between the adjacent filler particle models 3 and 3 is very small, the LJ potential P1 becomes very large and the calculation may be forcibly interrupted.

  Accordingly, in step S214, it is desirable that the parameter σ corresponding to the diameter of the LJ potential P1 is reduced in advance to start the molecular dynamics calculation. As a result, in step S214, it is possible to prevent the interruption of the calculation due to the increase in the LJ potential P1. In step S214, it is desirable that the parameter σ corresponding to the diameter is gradually increased to perform molecular dynamics calculation. Thereby, in process S214, the adjacent filler particle models 3 and 3 can be gradually spaced apart, and the equilibrium state of the filler particle model 3 of the second layer U2 can be efficiently calculated.

  Next, it is determined whether or not the filler particle model 3 of the second layer U2 has been sufficiently relaxed (step S215). In this step S215, when it is determined that the filler particle model 3 of the second layer U2 has been sufficiently relaxed, the next main setting step S22 is performed. On the other hand, when it is determined that the relaxation of the filler particle model 3 of the second layer U2 is insufficient, the unit time is advanced by one (step S216), and step S214 is performed again. Thereby, step S214 can reliably calculate the equilibrium state of the filler particle model 3 of the second layer U2.

  In the initial setting step S21 of the present embodiment, the placement step S212, the combining step S213, and the step S214 have been described independently, but these steps may be performed simultaneously by the computer 1.

  Next, each layer U from the third layer (hereinafter sometimes simply referred to as the third layer) U3 of the filler model 2 to the Nth layer UN is set (main setting step S22). FIG. 13 illustrates an example of the main setting step S22 of the present embodiment.

  In the main setting step S22 of the present embodiment, first, 3 is set as a constant M as an initial condition (step S221). This constant M is stored in the computer 1.

  Next, the filler particle model 3 constituting the Mth layer U (for example, the third layer U3) is arranged on the computer 1 (arrangement step S222). FIG. 14 shows an example of the processing procedure of the arrangement step S222 of the present embodiment.

In the arranging step S222, first, the number N _M of the filler particle models 3 in the Mth layer (for example, the third layer U3) is determined by the above formula (1) (step S71). As shown in FIG. 15, in step S71, as in the initial setting step S21, a region sandwiched between the outer spherical surface 11 having a radius (R ₃ + r) and the inner spherical surface 12 having a radius (R ₃ −r). 13, the maximum number N _{3 at} which the filler particle model 3 of the third layer U3 can be arranged can be obtained. Such a number N ₃ is stored in the computer 1.

Next, the filler particle model 3 of the Mth layer (for example, the third layer U3) connected to the filler particle model 3 per one of the M-1th layer (for example, the second layer U2). The number is determined (step S72). In this step S72, the number NM of the filler particle model 3 of the Mth layer (for example, the third layer U3) is set to the number N _M of the filler particle model 3 of the M−1th layer (for example, the second layer U2). By dividing by the number, the number of filler particle models 3 of the third layer U3 connected to the filler particle model 3 per one of the second layer U2 can be obtained. Such a number is stored in the computer 1.

  Next, the M-th layer (for example, the third layer U3) to be connected to the filler particle model 3 of the M-1th layer (for example, the second layer U2) via the bond chain model 4 The filler particle model 3 is determined (determination step S73). FIG. 16 shows an example of the processing procedure of the determination step S73 of the present embodiment.

  In the determination step S73 of the present embodiment, first, as shown in FIG. 17, one filler particle model 3 is selected in the (M-1) th layer (for example, the second layer U2) (step S81). . Numerical data of the selected filler particle model 3 is stored in the computer 1.

  Next, the circumference 16 of the cone 18 having the apex at the center point 3g of the selected filler particle model 3 of the M-1st layer (for example, the second layer U2) is calculated (step S82). In this step S82, first, a straight line 15L connecting the center point 3g of the selected filler particle model 3 of the (M-1) th layer and the center point 3g of the filler particle model 3 in the central portion 6 is defined. Then, with the straight line 15L as the center axis 15, the center point 3g of the selected filler particle model 3 as the apex, and the diameter (radius r (shown in FIG. 10) × 2) of the filler particle model 3 is the length of the bus The circumference 16 of the cone 18 is calculated. The circumference 16 is numerical data including coordinates, and is stored in the computer 1.

  Next, the filler particle model 3 of the Mth layer (for example, the third layer U3) connected to the filler particle model 3 per one of the M-1th layer (for example, the second layer U2). Based on the number, the filler particle models 3 corresponding to the number are arranged on the spherical surface of the Mth layer surrounded by the circumference 16 (step S83). As shown in FIGS. 17 and 18, the spherical surface 20 of the present embodiment is the surface of the spherical surface T of the Mth layer (for example, the third layer U3) centered on the center point 3g of the filler particle model 3 in the center portion 6. Of these, the region is surrounded by the circumference 16 (that is, outside the circumference 16). In step S83, the filler particle model 3 is arranged so that the center point 3g of the filler particle model 3 of the Mth layer is located on the spherical surface 20.

  Next, the filler particle model 3 existing on the spherical surface 20 of the Mth layer surrounded by the circumference 16 is the selected filler particle model 3 of the M−1th layer (for example, the second layer U2). (Step S84). In this step S84, the filler particle model 3 existing on the spherical surface 20 surrounded by the circumference 16 is used as the filler particle model 3 of the Mth layer (for example, the third layer U3), and the (M−1) th layer. It is determined to be connected to the selected filler particle model 3 (for example, the second layer U2). A pair 19 (for example, coordinate data) of the filler particle model 3 of the third layer U3 and the filler particle model 3 of the second layer U2 determined to be connected is stored in the computer 1. Step S83 and step S84 may be performed simultaneously by the computer 1.

  In addition, among the filler particle models 3 of the third layer U3 existing on the spherical surface 20 surrounded by the circumference 16, the filler particle model 3 whose connection with the other filler particle models 3 of the second layer U2 has already been determined. Are excluded from the scope of consolidation.

  Next, it is determined whether or not all the filler particle models 3 of the M-1st layer (for example, the second layer U2) have been selected (step S85). In this step S85, when it is determined that all the filler particle models 3 have been selected, the next combining step S223 is performed. On the other hand, if it is determined that all the filler particle models 3 have not been selected, one filler particle model 3 that has not yet been selected in the (M-1) th layer (for example, the second layer U2). Selection (step S86), steps S82 to S85 are performed again. Thereby, in determination process S73, as FIG. 18 shows, in all the filler particle models 3 of the 2nd layer U2, the coupling | bonding with the filler particle model 3 of the 3rd layer U3 can be defined.

  Next, the computer 1 combines the filler particle model 3 of the M-1st layer (for example, the second layer U2) and the filler particle model 3 of the Mth layer (for example, the third layer U3), They are linked by at least one bond chain model 4 (bonding step S223). In this coupling step S223, for example, as shown in FIG. 19, based on the pair 19 of the filler particle model 3 of the second layer U2 and the filler particle model 3 of the third layer U3 determined in the determination step S73, A bond chain model 4 is defined between the filler particle models 3 and 3. Thereby, the filler particle model 3 of the second layer U2 and the filler particle model 3 of the third layer U3 are constrained to each other by the bond chain model 4. In the coupling step S223, numerical data defining the coupled chain model 4 is stored in the computer 1.

  Next, the computer 1 performs molecular force field calculation and molecular dynamics calculation for the filler particle model 3 of the Mth layer (for example, the third layer U3) (step S224). In step S224, in addition to the LJ potential P1 and the FENE potential P2 set in the initial setting step S21, further, between the filler particle model 3 of the second layer U2 and each filler particle model 3 of the third layer U3, and The LJ potential P1 of the above formula (2) is set between the filler particle models 3 and 3 adjacent to each other in the third layer U3. In step S224, the FENE potential P2 of the above formula (3) is set along the bond chain model 4. Then, molecular force field calculation and molecular dynamics calculation are performed on all filler particle models 3 of the first layer U1, the second layer U2, and the third layer U3.

  Next, it is determined whether or not the filler particle model 3 of the Mth layer (for example, the third layer U3) has been sufficiently relaxed (step S225). In this step S225, for example, when it is determined that the filler particle model 3 of the third layer U3 is sufficiently relaxed, the next step S226 is performed. On the other hand, when it is determined that the relaxation of the filler particle model 3 of the third layer U3 is insufficient, the unit time is advanced by one (step S227), and step S224 is performed again. Thereby, process S224 can calculate the equilibrium state of the filler particle model 3 of the 3rd layer U3 reliably. In step S224, numerical data including the coordinates of the filler particle model 3 of the third layer U3 in the equilibrium state is stored in the computer 1.

  As described above, in the step S224, as in the initial setting step S21, the equilibrium state of the filler particle model 3 of the Mth layer (for example, the third layer U3) is calculated. The overlap between adjacent filler particle models 3 and 3 can be removed.

  Moreover, in the determination step S73, based on the circumference 16 of the cone 18, the filler particle model 3 of the Mth layer (for example, the third layer U3) and the M-1th layer (for example, the first layer) The connection with the filler particle model 3 of the second layer U2) is determined. Thereby, the filler model 2 can connect the filler particle model 3 homogeneously like the dendrimer which is a structure where the filler particle models 3 and 3 are regularly branched from the center, for example. Therefore, the filler model 2 can effectively suppress variations in the stress distribution and mutual potential inside the filler model 2.

  In order to effectively exhibit such an action, the angle θ1 (shown in FIG. 17) formed by the central axis 15 and the conical surface 18s is preferably 0 ° or more and less than 60 °. When the angle θ1 is 0 degree, the filler particle model 3 of the Mth layer (for example, the third layer U3) and the filler particle model of the M−1th layer (for example, the second layer U2). 3 are arranged on the central axis 15, there is a possibility that the regular branch structure as described above cannot be formed. On the other hand, even if the angle θ1 exceeds 60 degrees, the filler particle models 3 and 3 may be largely separated and a regular branched structure may not be formed. From such a viewpoint, the angle θ1 is more preferably 50 degrees or less, and more preferably 30 degrees or more.

  From the same viewpoint, the filler particle model 3 of the Mth layer (for example, the third layer U3), the filler particle model 3 of the M-1th layer (for example, the second layer U2), and the M-th layer The angle θ2 (shown in FIG. 19) formed by the filler particle model 3 of the second layer (for example, the first layer U1) is preferably 90 degrees or more, more preferably 110 degrees or more.

  Next, it is determined whether or not all the layers from the third layer U3 to the Nth layer NU have been set (step S226). In step S226, when it is determined that all layers are set, the next step S23 is performed. On the other hand, when it is determined that not all layers are set, the constant M is increased by 1 (step S228), and steps S222 to S227 are performed again. Thereby, in main setting process S22, all the layers can be set reliably and the filler model 2 can be created.

  Thus, according to the creation method of the present invention, the filler model 2 can be created in a short time by effectively removing the overlap between the filler particle models 3 and 3. In addition, the model (virtual space 7) obtained by this method can suppress, for example, variations in stress distribution and mutual potential in the filler model 2 in molecular dynamics calculation, thereby improving simulation accuracy. Can be made.

  In the main setting step S22 of the present embodiment, the placement step S222, the combining step S223, and the step S224 have been described independently, but these steps may be performed simultaneously by the computer 1.

  In this embodiment, as shown in FIG. 20, the filler particle model 3 of the Nth layer UN arranged at the outermost radial direction and the other filler particle model 3 of the Nth layer UN are combined into a bond chain model. 4 is desirable (step S23).

As described above, the bond chain model 4 defines a restoring force that attempts to return the distance r _ij to a position where the LJ potential P1 and the FENE potential P2 are balanced with each other. Therefore, since the filler particle model 3 of the Nth layer UN is restrained in a state of maintaining a certain distance from the filler particle model 3 of the other Nth layer UN connected by the bond chain model 4, The outer peripheral surface can be smoothed. Such a filler model 2 can improve the simulation accuracy since the potential can be applied uniformly to a polymer model (not shown) obtained by modeling a polymer material in molecular dynamics calculation.

  Two or more bonding chain models 4 may be arranged between adjacent filler particle models 3 and 3. Thereby, since the bond chain model 4 can restrain the adjacent filler particle models 3 and 3 more firmly, the outer peripheral surface of the filler model 2 can be smoothed more effectively. The bond chain model 4 is a filler particle model of the Nth layer UN arranged within a predetermined distance L3 (for example, 1.0 to 3.0σ) in each filler particle model 3 of the Nth layer UN. It is desirable that the connection is limited to three.

  As mentioned above, although especially preferable embodiment of this invention was explained in full detail, this invention is not limited to embodiment of illustration, It can deform | transform and implement in a various aspect.

  According to the procedure shown in FIG. 4, one filler model (first layer to eleventh layer, total of filler particle models: 5900) was created in the virtual space. In addition, a plurality of polymer models modeling polymer materials are randomly arranged in the virtual space. Furthermore, a molecular potential calculation was performed by defining a mutual potential (Lennard-Jones potential) between the filler model and the polymer model, and an initial model was created (Example 1). In addition, based on the filler model of Example 1, an initial model including a filler model in which filler particle models of the eleventh layer arranged on the outermost radial direction are connected by a bond chain model was also created (implementation) Example 2).

  For comparison, a sphere (radius: 11, 2σ) is defined in the virtual space, and in this sphere, a filler particle model in which the value of the parameter σ of the LJ potential (corresponding to the particle diameter) is 1. (Total: 5900) were randomly arranged, and a filler model was created. In addition, polymer models were randomly arranged in the virtual space. Furthermore, molecular dynamics calculation was performed by defining the above mutual potential between the filler model and the polymer model, and an initial model was created (comparative example).

  Then, the time required to create the filler models of Example 1, Example 2, and Comparative Example was compared. The results are displayed as an index with Example 1 as 100. The smaller the numerical value, the shorter the filler model can be created.

Furthermore, deformation calculation was performed for each model (20 models) of Example 1, Example 2, and Comparative Example at a deformation rate of 0.05σ / τ until the deformation amount reached 5.0σ. And in each model of Example 1, Example 2, and a comparative example, the standard deviation (the number of samples: 20) of the stress when the deformation amount became 2.5σ was determined. The smaller the standard deviation, the higher the simulation accuracy.
The parameters for each potential are as described in the specification, and the common specifications are as follows. Table 1 shows the test results.
Simulation software: Soft material integrated simulator OCTA COGNAC
Virtual space:
Side length L2: 60σ
Filler model:
Potential spring constant k: 1000
Polymer model:
Number: 1890 Polymer chain length N: 100

  As a result of the test, it was confirmed that the filler models of Example 1 and Example 2 can shorten the preparation time as compared with the filler model of the comparative example. It was also confirmed that the models of Example 1 and Example 2 can reduce the standard deviation and improve the simulation accuracy compared to the model of the comparative example. Furthermore, it has confirmed that Example 2 which connected the filler particle model of the 11th layer with the bond chain model can improve a simulation precision compared with Example 1. FIG.

2 Filler model 3 Filler particle model 5 Bond chain model 6 Center

Claims (5)

A method of creating, using a computer, a three-dimensional filler model including a plurality of filler particle models and at least one bond chain model connecting the plurality of filler particle models,
A first step of setting a central portion consisting of one filler particle model in the computer;
A plurality of layers consisting of a group of filler particle models in which a plurality of filler particle models are arranged concentrically at a distance from the filler particle model in the central portion in the radial direction are set on the computer outside the central portion. Including the second step,
The second step is an arrangement step of arranging the filler particle model constituting the Mth layer in the computer.
A combining step in which the computer connects the filler particle model of the (M-1) th layer and the filler particle model of the Mth layer with at least one bond chain model; and
A method for creating a filler model, wherein the computer includes a step of performing molecular dynamics calculation on the filler particle model of the Mth layer. In the arranging step, a center point of the filler particle model of the Mth layer is arranged on a spherical surface of the Mth layer set with a radius R _M centering on the filler particle model of the central portion. And
Wherein the number N _M of the filler particles model of the M-th layer, the method of creating a filler model of claim 1 comprising the step of determining by the following formula (1).

here,
N _M : Number of filler particle models of the Mth layer R _M : Radius of the spherical surface of the Mth layer r: Radius of the filler particle model ρ _M : Number density of filler particles of the Mth layer The second step includes a main setting step of setting each layer from the third layer of the filler model to the Nth layer arranged on the outermost side in the radial direction,
The main setting step determines the filler particle model of the Mth layer to be connected to the filler particle model of the M-1st layer through the bond chain model in the arranging step. Including a decision step to
The determination step includes
Selecting one filler particle model of the M-1 th layer;
A straight line connecting the center point of the selected filler particle model and the center point of the filler particle model in the central portion is a central axis, the center point of the selected filler particle model is the vertex, and the filler particle model Calculating the circumference of a cone whose diameter is the length of the busbar;
The filler particle model of the Mth layer is arranged on a spherical surface surrounded by the circumference of the cone, and the filler particle model of the Mth layer is placed on the M-1th layer. The method for creating a filler model according to claim 2, further comprising a step of determining that the selected filler particle model is connected to the selected filler particle model.   The method for creating a filler model according to claim 3, wherein an angle formed by the central axis and the conical surface of the cone is not less than 0 degrees and less than 60 degrees.   5. The method according to claim 1, further comprising a step of connecting the filler particle model of the Nth layer arranged on the outermost radial direction with another filler particle model of the Nth layer by the bond chain model. How to create a filler model described in Crab.