JP7571535B2 - Polymer material simulation method - Google Patents

Description

The present invention relates to a method for simulating polymeric materials.

The following Patent Document 1 describes a method for simulating polymeric materials. This method includes a step of setting up a polymeric material model that models a polymeric material in a computer, and a deformation step of deforming the polymeric material model.

JP 2018-151212 A

The physical quantities (e.g., viscoelastic properties) of many polymer materials are dependent on temperature and deformation period. Therefore, in the above deformation process, the physical quantities of the polymer material model are usually calculated under deformation conditions that include a predetermined temperature and deformation period. However, there is a problem in that the calculation time increases when the deformation period of the deformation conditions becomes large.

The present invention was devised in consideration of the above-mentioned circumstances, and its main objective is to provide a simulation method that can shorten the calculation time for the physical quantities of polymeric materials.

The present invention is a method for simulating a polymeric material, comprising: a step of inputting a molecular chain model for numerical calculation based on the polymeric material into a computer; and a simulation step in which the computer uses the molecular chain model to calculate the physical quantity of the polymeric material under a first deformation condition including a predetermined first temperature and a first deformation period, the simulation step including: changing the first deformation condition to a second deformation condition including a second temperature and a second deformation period that allows the physical quantity to be calculated under a deformation period shorter than the first deformation period, based on a time-temperature conversion rule that indicates the relationship between the deformation period and temperature in the physical quantity of the polymeric material; and a step of calculating the physical quantity under the first deformation condition as the physical quantity based on the second deformation condition.

In the polymer material simulation method according to the present invention, the computer may further include a conversion rule calculation step for determining the time-temperature conversion rule prior to the simulation step.

In the polymer material simulation method according to the present invention, the conversion rule calculation step may include a step of determining the time-temperature conversion rule in a first range of application based on a plurality of predetermined deformation conditions, and a step of extending the time-temperature conversion rule to a second range of application using deformation conditions different from the plurality of deformation conditions.

In the polymer material simulation method according to the present invention, the physical quantity may include viscoelastic properties.

In the polymer material simulation method according to the present invention, the viscoelastic properties may include a loss tangent.

By adopting the above steps, the polymer material simulation method of the present invention can reduce the calculation time for the physical quantities of the polymer material.

FIG. 1 is a perspective view showing an example of a computer for executing a simulation method for a polymer material. 1 is a flowchart showing an example of a processing procedure of a simulation method for a polymer material. FIG. 2 is a conceptual diagram showing an example of a molecular chain model. FIG. 2 is a conceptual diagram showing an example of a cell in which a molecular chain model is arranged. 1 is a graph showing an example of the relationship between temperature and a conversion factor of a deformation period in the time-temperature conversion rule. 13 is a flowchart showing an example of a processing procedure of a simulation process. 13 is a flowchart showing an example of a processing procedure of a simulation method according to another embodiment of the present invention. 13 is a flowchart showing an example of a processing procedure of a conversion rule calculation step. 1 is a graph showing an example of a plurality of physical quantity curves. 13 is a graph showing an example of a composite curve. 13 is a flowchart showing an example of a processing procedure of a conversion rule calculation step according to another embodiment of the present invention. 1 is a graph showing the relationship between temperature and the deformation period conversion factor when the time-temperature conversion rule is expanded.

Below, one embodiment of the present invention will be described with reference to the drawings. It should be noted that the drawings are intended to enhance understanding of the invention and include exaggerated representations, and that the scales, etc., of the drawings are not strictly consistent.

In the polymer material simulation method of this embodiment (hereinafter sometimes simply referred to as the "simulation method"), the physical quantities of the polymer material are calculated. The physical quantities are not particularly limited, but are preferably those used to evaluate the performance of the polymer material. One example of the physical quantities is the viscoelastic properties of the polymer material. The viscoelastic properties of this embodiment are exemplified by loss tangent tan δ, but may also be, for example, storage modulus G', loss modulus G", or complex modulus E*, or all of these may be calculated.

The polymeric material of this embodiment contains at least one type of molecular chain (polymer). The polymeric material may further contain a filler, a coupling agent, etc. The molecular chain of this embodiment is exemplified by styrene butadiene rubber, but is not particularly limited thereto.

The physical quantities (e.g., viscoelastic properties) of many polymeric materials are dependent on temperature and deformation period. For this reason, it is important to calculate the physical quantities while keeping a predetermined temperature and deformation period (frequency) constant. In the simulation method of this embodiment, the physical quantities are calculated under a first deformation condition that includes a predetermined first temperature and first deformation period.

The first temperature and the first deformation period are not particularly limited, but are desirably set according to the performance to be evaluated. The first temperature and the first deformation period in this embodiment are set based on the scale in the molecular dynamics calculation described below (in this example, the temperature is "T" and the deformation period (time) is "τ"). In this embodiment, for example, the first temperature is set to 1.0 (T) and the first deformation period is set to 10,000 (τ), but are not limited to such an embodiment.

A computer is used for the simulation method of this embodiment. Figure 1 is a perspective view showing an example of a computer for executing the simulation method for polymeric materials.

[computer]
The computer 1 of this embodiment includes a main body 1a, a keyboard 1b, a mouse 1c, and a display device 1d. The main body 1a is provided with, for example, a central processing unit (CPU), a ROM, a working memory, a storage device such as a magnetic disk, and disk drive devices 1a1 and 1a2. Software for executing the simulation method of this embodiment is stored in advance in the storage device.

[Simulation method for polymeric material (first embodiment)]
Next, the simulation method of this embodiment will be described with reference to a flowchart shown in FIG.

[Molecular chain model input process]
In the simulation method of this embodiment, first, a molecular chain model for numerical calculation based on the molecular chain of a polymer material is input to a computer 1 (step S1). Fig. 3 is a conceptual diagram showing an example of the molecular chain model 2.

The molecular chain model 2 in this embodiment is defined as a coarse-grained model (in this embodiment, the Kremer-Grest model) based on the molecular chain of a polymer material (in this example, styrene-butadiene rubber). Note that the molecular chain model 2 may be, for example, an all-atom model or a united atom model, not shown.

The molecular chain model 2 of this embodiment is composed of a plurality of coarse-grained particles 3 and a bond chain model 4 that bonds adjacent coarse-grained particles 3, 3.

The coarse-grained particles 3 in this embodiment are formed by replacing monomers (not shown) in the molecular chain of the polymer material or structural units that form part of the monomers. As a result, multiple (e.g., 10 to 5,000) coarse-grained particles 3 are set in the molecular chain model 2. The coarse-grained particles 3 are treated as mass points in the equation of motion in the molecular dynamics calculations described below. For this reason, parameters such as mass, volume, particle diameter, or charge are defined for the coarse-grained particles 3.

The bond chain model 4 of this embodiment is defined by an interaction potential P1 with a maximum extension length set between the coarse-grained particles 3, 3. The interaction potential P1 of this embodiment can be defined based on the anharmonic potential described in, for example, a patent document (JP Patent Publication No. 2020-086835). The molecular chain model 2 is stored in the computer 1.

[Cell definition process]
Next, in the simulation method of this embodiment, a cell, which is a virtual space corresponding to a part of the polymer material, is input to the computer 1 (step S2). Fig. 4 is a conceptual diagram showing an example of a cell 5 in which a molecular chain model 2 is arranged. In Fig. 4, only a part of the molecular chain model 2 is representatively shown.

The cell 5 in this embodiment has at least one pair of faces 6, 6 facing each other (in this embodiment, three pairs of faces 6, 6 facing each other). The cell 5 in this embodiment is defined as a rectangular parallelepiped or a cube (in this embodiment, a cube).

A periodic boundary condition is defined for each face 6, 6 of the cell 5. The length L1 of each side of the cell 5 can be set appropriately based on the description in, for example, a patent document (JP Patent Publication No. 2020-086835). The cell 5 is stored in the computer 1.

[Molecular chain model arrangement process]
Next, in the simulation method of this embodiment, the computer 1 places a plurality of molecular chain models 2 inside the cell 5 (step S3). In step S3 of this embodiment, the plurality of molecular chain models 2 are randomly placed. The number of molecular chain models 2 can be appropriately set based on, for example, the computational capability of the computer 1, the size of the cell 5, the size of the molecular chain model 2, and the like.

The procedure for placing the molecular chain model 2 is not particularly limited. In step S3 of this embodiment, the molecular chain model 2 is randomly placed inside the cell 5 based on, for example, the DBMC (Density Biased Monte Carlo) method. For the initial placement of such molecular chain models 2, for example, commercially available software (for example, COGNAC included in Soft Material Integrated Simulator (J-OCTA) manufactured by JSOL Co., Ltd.) can be used. The cell 5 in which the molecular chain model 2 is placed is stored in the computer 1.

[Potential definition process]
Next, in the simulation method of this embodiment, an interaction potential P2 in which attractive and repulsive forces act between the molecular chain models 2, 2 arranged in the cell 5 is defined (step S4). The interaction potential P2 of this embodiment is defined between the coarse-grained particles 3, 3 of a pair of molecular chain models 2, 2. The interaction potential P2 can be defined, for example, by the LJ potential described in a patent document (JP 2020-086835 A). These interaction potentials P2 are stored in the computer 1.

[Structural relaxation calculation process]
Next, in the simulation method of this embodiment, the computer 1 calculates structural relaxation of the molecular chain model 2 based on molecular dynamics calculation (step S5). For example, Newton's equation of motion is applied to the cell 5 for a given time, assuming that the coarse-grained particle 3 of the molecular chain model 2 follows classical mechanics. Then, the movement of the coarse-grained particle 3 at each time is expressed as follows: It is tracked at each unit time step.

In the molecular dynamics calculation, the pressure and temperature are kept constant, or the volume and temperature are kept constant, in cell 5. As a result, in step S5, the initial arrangement of the molecular chain model 2 is relaxed to approximate the molecular motion of the actual polymer material. In this embodiment, this is continued until the initial arrangement of the molecular chain model 2 is sufficiently relaxed. As a result, a polymer material model 7 that models the polymer material is created.

For example, the above-mentioned commercially available software can be used to calculate the structural relaxation. The polymer material model 7 is stored in the computer 1.

[Simulation process]
Next, in the simulation method of this embodiment, the computer 1 uses the molecular chain model 2 (polymer material model 7) to calculate the physical quantities of the polymer material under first deformation conditions including the first temperature and the first deformation period (simulation step S6).

The calculation of the physical quantities can be performed as appropriate using the molecular chain model 2 (polymer material model 7). In this embodiment, a shear deformation is applied at a predetermined deformation period to the polymer material model 7, to which a predetermined temperature and strain (initial strain) have been set. Then, the thermal motion of the molecular chain model 2 is calculated based on molecular dynamics calculations. As a result, the physical quantities of the polymer material are calculated based on the predetermined temperature and deformation period. The above-mentioned commercially available software can be used to calculate such physical quantities.

In the calculation of the above physical quantities, the calculation time for the physical quantities increases in proportion to the size of the deformation period. Therefore, if the first deformation period of the first deformation condition is large, the calculation time may be long.

On the other hand, polymeric materials have the property (time-temperature conversion rule) that allows the change in temperature to be converted into a change in deformation period to calculate an equivalent physical quantity. The time-temperature conversion rule shows the relationship between the deformation period and temperature in the physical quantities of polymeric materials. Figure 5 is a graph showing an example of the relationship between temperature and the conversion factor of the deformation period for the time-temperature conversion rule.

The time-temperature conversion law is determined appropriately using the measurement results and calculation results of physical quantities based on multiple predetermined deformation conditions (temperature and deformation period). The multiple deformation conditions include one reference deformation condition (reference temperature and reference deformation period) that serves as the basis for the time-temperature conversion law.

In FIG. 5, the horizontal axis indicates temperature (T), and the vertical axis indicates the logarithm of the conversion factor (shift factor) aT, log(aT). The conversion factor aT represents the magnification of the deformation period at an arbitrary temperature to the reference deformation period. Therefore, the deformation period at an arbitrary temperature can be obtained by multiplying the reference deformation period by the conversion factor aT at the arbitrary temperature.

In FIG. 5, the higher the temperature, the smaller the conversion factor aT (logarithm log(aT)). Therefore, at temperatures higher than the reference temperature, it is possible to calculate a physical quantity equivalent to the reference deformation condition with a deformation period smaller than the reference deformation period (the deformation period multiplied by the conversion factor aT).

Based on such a time-temperature conversion rule, in the simulation step S6 of this embodiment, the first temperature is changed to a different temperature, and a physical quantity equivalent to the first deformation condition is calculated for a deformation period shorter than the first deformation period. It is preferable that the time-temperature conversion rule is input to the computer 1 prior to the simulation step S6. Figure 6 is a flowchart showing an example of the processing procedure of the simulation step S6.

[Simulation process (deformation condition change process)]
In the simulation process S6 of this embodiment, first, based on the time-temperature conversion rule, the first deformation condition is changed to a second deformation condition including a second temperature and a second deformation period that enable calculation of a physical quantity at a deformation period shorter than the first deformation period (process S61).

The second transformation condition is appropriately changed from the first transformation condition as long as the physical quantity can be calculated with a transformation period shorter than the first transformation period. In step S61, first, in the graph shown in FIG. 5, the temperature of the logarithm log(f2) of the conversion factor f2 smaller than the logarithm log(f1) of the conversion factor f1 at the first temperature a1 (1.0(T)) is specified as the second temperature a2 (1.2(T)) of the second transformation condition. Note that, for the logarithm log(f2) of the conversion factor f2, the smallest logarithm of the conversion factor may be selected in the graph shown in FIG. 5 in order to minimize the calculation time.

Next, in step S61 of this embodiment, the ratio f2/f1 between the conversion factor f1 at the first temperature a1 and the conversion factor f2 at the second temperature a2 is calculated. The ratio f2/f1 (0.5/1.0 in this example) indicates the magnification of the magnitude of the second deformation period at the second temperature a2 relative to the magnitude of the first deformation period at the first temperature a1.

Next, in step S61 of this embodiment, the first deformation frequency (in this example, 10,000 (τ)) is multiplied by the ratio f2/f1 (in this example, 0.5/1.0) to obtain a second deformation frequency (in this example, 5,000 (τ)). This second deformation period is shorter than the first deformation period. Therefore, in step S61, the first deformation condition can be changed to a second deformation condition that allows the physical quantity to be calculated in a deformation period shorter than the first deformation period. The second deformation condition is stored in computer 1.

[Simulation process (physical quantity calculation process)]
Next, in the simulation step S6 of this embodiment, the physical quantity under the first deformation condition is calculated as the physical quantity based on the second deformation condition (step S62). In step S62 of this embodiment, first, a second temperature and a strain (initial strain) are set in the polymer material model 7 (shown in FIG. 4). For example, the strain (e.g., 10% initial strain) set at the time of actual measurement of the physical quantity is set as the strain. Next, in step S62, a shear deformation is applied to the polymer material model 7 with a second deformation period.

In step S62 of this embodiment, the thermal motion of the molecular chain model 2 is calculated based on molecular dynamics calculations. Such thermal motion is calculated based on the second deformation conditions, interaction potentials P1 and P2 (shown in Figures 3 and 4, respectively), and an equation of motion. As a result, in step S62, the physical quantities of the polymer material based on the second deformation conditions (second temperature and second deformation conditions) are calculated.

As described above, the second deformation condition is changed from the first deformation condition based on the time-temperature conversion rule. The physical quantities based on the second deformation condition are calculated as equivalent to the physical quantities under the first deformation condition. Furthermore, the second deformation period under the second deformation condition is shorter than the first deformation period under the first deformation condition. Therefore, the simulation method of this embodiment can reduce the calculation time for the physical quantities of the polymer material under the first deformation condition.

In step S62, the physical quantities under the first deformation conditions may be calculated as physical quantities based on the second deformation conditions under a plurality of conditions (parameters) that vary the magnitude of the initial strain set in the polymer material, the arrangement conditions of the molecular chain model 2 in the cell 5, etc. This allows the physical quantities under the first deformation conditions to be calculated in a short time for each condition, making it possible to efficiently perform parameter studies using these calculation results, for example.

[Evaluation process]
Next, in the simulation method of this embodiment, the computer 1 judges whether the physical quantity of the polymer material is good or not (step S7). The judgment of whether the physical quantity is good or not can be performed appropriately. In this embodiment, whether the physical quantity is good or not is judged based on a threshold value set for the physical quantity.

If it is determined in step S7 that the physical quantities are good ("Yes" in step S7), a polymer material (not shown) is manufactured (step S8). On the other hand, if it is determined in step S7 that the physical quantities are not good ("No" in step S7), the conditions of the polymer material are changed (step S9), and steps S1 to S7 are carried out again. In this way, the simulation method of this embodiment can efficiently design and manufacture polymer materials with good physical properties.

[Simulation method for polymeric material (second embodiment)]
In the simulation method of the above embodiment, the first transformation condition is changed to the second transformation condition based on a predetermined time-temperature conversion rule, but the present invention is not limited to such an embodiment. For example, the time-temperature conversion rule may be obtained prior to the simulation step S6. FIG. 7 is a flowchart showing an example of a processing procedure of a simulation method of another embodiment of the present invention. In this embodiment, the same components as those in the above embodiment are given the same reference numerals, and the description may be omitted.

[Conversion rule calculation process]
In the simulation method of this embodiment, prior to the simulation step S6, the computer 1 determines a time-temperature conversion rule (conversion rule calculation step S10). In this embodiment, the molecular chain model 2 (polymer material model 7) shown in Fig. 4 is used to calculate physical quantities based on a plurality of predetermined deformation conditions (temperature and deformation period). Then, based on the calculation results, the time-temperature conversion rule is determined. Fig. 8 is a flowchart showing an example of the processing procedure of the conversion rule calculation step S10.

[Conversion rule calculation process (physical quantity curve acquisition process)]
In the conversion rule calculation step S10 of this embodiment, first, a physical quantity curve showing the relationship between the physical quantity and the deformation period is obtained for each temperature under a plurality of deformation conditions (step S21). The deformation conditions in this embodiment include a first deformation condition (in this example, first temperature: 1.0 (T), deformation period: 10,000) as a reference deformation condition that serves as a basis for the time-temperature conversion rule. It is preferable that the first transformation condition is included. This allows the first transformation condition to be changed to the second transformation condition with high accuracy.

The temperatures for the multiple deformation conditions preferably include the first temperature (reference temperature), a temperature lower than the first temperature, and a temperature higher than the first temperature. This allows physical quantity curves to be obtained at multiple temperatures with the first temperature as the intermediate temperature, making it possible to accurately obtain a time-temperature conversion rule including the first temperature. The temperatures in this embodiment include the first temperature (1.0 (T) in this example), temperatures lower than the first temperature (0.5 (T), 0.8 (T) in this example), and temperatures higher than the first temperature (1.2 (T) in this example).

It is desirable that the deformation periods of the multiple deformation conditions include a first deformation period and a deformation period shorter than the first deformation period. This makes it possible to reliably select a deformation period shorter than the first deformation period. The deformation periods in this embodiment include the first deformation period (in this example, 10,000 (τ)) and deformation periods shorter than the first deformation period (in this example, 1,000 (τ), 100 (τ), and 10 (τ)).

In step S21 of this embodiment, first, the physical quantity of the polymer material is calculated based on multiple deformation conditions that combine the above-mentioned temperature and deformation period. The physical quantity calculated in step S21 is, for example, the loss tangent tan δ, but is not limited to this. The calculation of the physical quantity under each deformation condition is performed using the same procedure as step S62, which calculates the physical quantity based on the second deformation condition described above.

Next, in step S21 of this embodiment, a physical quantity curve showing the relationship between the physical quantity and the deformation period is calculated for each temperature under the multiple deformation conditions using the physical quantities calculated for each of the multiple deformation conditions. FIG. 9 is a graph showing an example of multiple physical quantity curves. The physical quantity curves are stored in computer 1.

[Conversion rule calculation process (movement amount acquisition process)]
Next, in the conversion rule calculation step S10 of this embodiment, the amount of movement of each physical quantity curve on the deformation period is acquired so that one composite curve (master curve) is obtained from each physical quantity curve (step S22). 10 is a graph showing an example of a composite curve.

In step S22, the physical quantity curves for the other temperatures are translated on the axis of the deformation period so as to overlap at least a portion of the physical quantity curve for the first temperature (1.0 (T) in this example), which is the reference temperature shown in FIG. 9. In this embodiment, the physical quantity curves for temperatures lower than the first temperature (0.5 (T) and 0.8 (T) in this example) are translated in the direction in which the deformation period becomes longer (to the right in the figure). Furthermore, in this embodiment, the physical quantity curve for a temperature higher than the first temperature (1.2 (T) in this example) is translated in the direction in which the deformation period becomes shorter (to the left in the figure). As a result, in step S22, one composite curve (master curve) shown in FIG. 10 is obtained.

In step S22 of this embodiment, the amount of movement of each physical quantity curve is obtained by the above-mentioned parallel movement. The amount of movement indicates the magnification of the deformation period of the physical quantity curve after the movement relative to the deformation period of the physical quantity curve before the movement. This amount of movement becomes the conversion factor (shift factor) aT of the time-temperature conversion rule. In this embodiment, for example, the amount of movement (conversion factor) aT of the physical quantity curve with a temperature of 1.2 (T) is 0.5. Note that the physical quantity curve of the first temperature, which is the reference temperature, does not undergo parallel movement, so its amount of movement (conversion factor) aT is 1.0. The amount of movement of each physical quantity curve is stored in computer 1.

[Conversion rule calculation process (time temperature conversion rule acquisition process)]
Next, in the conversion rule calculation step S10 of this embodiment, a time-temperature conversion rule is calculated based on the relationship between the amount of movement of each physical quantity curve and the temperature of each physical quantity curve (step S23). In order to obtain the above, the logarithm log( aT) is plotted. In this way, in step S23, a graph showing the relationship between the temperature and the conversion factor of the deformation period for the time-temperature conversion rule is obtained. The time-temperature conversion rule is stored in the computer 1. .

In this way, the simulation method of this embodiment calculates the time-temperature conversion law regardless of whether the polymer material actually exists, making it possible to efficiently evaluate and develop the performance of unknown polymer materials that do not actually exist.

[Simulation method for polymeric material (third embodiment)]
[Conversion rule calculation process]
In the conversion rule calculation step S10 of the above-mentioned embodiment, the time-temperature conversion rule is obtained based on a plurality of predetermined transformation conditions, but the present invention is not limited to such an embodiment. For example, the time-temperature conversion rule may be extended using a transformation condition different from the plurality of transformation conditions. FIG. 11 is a flowchart showing an example of a processing procedure of the conversion rule calculation step S10 of another embodiment of the present invention. In this embodiment, the same components as those in the above-mentioned embodiment are given the same reference numerals, and the description may be omitted.

[Conversion rule calculation process (first conversion rule calculation process)]
In the conversion rule calculation step S10 of this embodiment, first, a time-temperature conversion rule is calculated in a first application range based on a plurality of predetermined transformation conditions (first conversion rule calculation step S31). The transformation conditions can be appropriately set as long as the time-temperature conversion rule can be obtained. The transformation conditions in this embodiment include the same conditions as those used to obtain the time-temperature conversion rule in the previous embodiment (second embodiment). The deformation conditions (in this example, deformation conditions combining four temperatures and four deformation periods) are adopted. Therefore, in the first conversion rule calculation step S31 of this embodiment, as shown in FIG. A time-temperature conversion rule is obtained with a temperature range of 0.5 to 1.2 (T) as a first application range R1.

The time-temperature conversion rule for the first application range is obtained based on the processing procedure of the conversion rule calculation step S10 shown in FIG. 8. The time-temperature conversion rule for the first application range is stored in the computer 1.

[Conversion rule calculation process (second conversion rule calculation process)]
Next, in the conversion rule calculation step S10 of this embodiment, the time-temperature conversion rule is expanded to a second application range R2 using a transformation condition different from the plurality of transformation conditions (second conversion rule calculation step S32 12 is a graph showing the relationship between temperature and the deformation period conversion factor when the time-temperature conversion rule is expanded.

The deformation conditions used to expand the time-temperature conversion rule are appropriately adopted as long as they are outside the first application range R1 (in this example, the temperature range of 0.5 to 1.2 (T)). In this embodiment, a temperature (e.g., 1.5 (T)) is adopted that is expected to result in a smaller deformation period (i.e., a smaller conversion factor aT) than in the first application range R1, based on the tendency of the time-temperature conversion rule in the first application range.

In the second conversion rule calculation step S32 of this embodiment, the temperature (1.5(T)) of the above deformation condition is extrapolated based on the linear approximation (exponential approximation) of the time-temperature conversion rule in the first application range, and the logarithm log(aT) of the conversion factor aT at that temperature is found. By including such temperature and logarithm log(aT) in the time-temperature conversion rule found in the first application range, the time-temperature conversion rule can be extended to the second application range (in this example, the temperature range of 0.5 to 1.5(T)). The time-temperature conversion rule extended to the second application range R2 is stored in the computer 1.

In this way, in the conversion rule calculation step S10 of this embodiment, the time-temperature conversion rule can be expanded to the second application range R2, so that the second deformation conditions can be changed to allow calculation of physical quantities in a shorter deformation period compared to the time-temperature conversion rule of only the first application range R1 (shown in FIG. 5). Therefore, in the simulation method of this embodiment, the calculation time for the physical quantities of the polymer material under the first deformation conditions can be further shortened.

The above describes in detail a particularly preferred embodiment of the present invention, but the present invention is not limited to the illustrated embodiment and can be modified and implemented in various ways.

Based on the processing procedure in Figure 2, the physical quantities of the polymer material under the first deformation conditions including the first temperature and the first deformation period were calculated (Example and Comparative Example). In the Example and Comparative Example, the physical quantities under the first deformation conditions were calculated under multiple conditions (20 cases) in which the magnitude of the initial strain set in the polymer material and the arrangement conditions of the molecular chain model in the cell were different.

In the example, the first deformation condition was changed to a second deformation condition that can calculate the physical quantity in a deformation period shorter than the first deformation period based on the time-temperature conversion rule in accordance with the processing procedure in Fig. 6. Then, in the example, the physical quantity under the first deformation condition was calculated as the physical quantity based on the second deformation condition in the above 20 cases. Meanwhile, in the comparative example, the physical quantity was calculated based on the first deformation condition in the above 20 cases. The common specifications are as follows.
First transformation condition:
First temperature: 1.0 (T)
First deformation period: 10000 (τ)
Second transformation condition:
Second temperature: 1.2 (T)
Second deformation period: 5000 (τ)
Unit time step Δt: 0.01 (τ)

As a result of the test, the calculation time required to calculate the physical quantities based on the first deformation conditions for the above 20 cases was 10,000,000 steps in the example, whereas it was 20,000,000 steps in the comparative example, twice as long as in the example. Therefore, the example was able to reduce the calculation time for the physical quantities of the polymer material. Furthermore, substantially the same physical quantities were calculated in the example and the comparative example. Therefore, the calculation accuracy of the physical quantities was maintained in the example.

Step S61: Changing the first transformation condition to the second transformation condition. Step S62: Calculating the physical quantity under the first transformation condition as the physical quantity based on the second transformation condition.

Claims (5)

A method for simulating a polymeric material, comprising the steps of:
inputting a molecular chain model for numerical calculation based on the polymer material into a computer;
a simulation step of calculating, by the computer, a physical quantity of the polymer material under a first deformation condition including a predetermined first temperature and a first deformation period, by using the molecular chain model;
The simulation step includes:
changing the first deformation condition to a second deformation condition including a second temperature and a second deformation period that can calculate the physical quantity at a deformation period shorter than the first deformation period based on a time-temperature conversion rule that indicates a relationship between a deformation period and a temperature in the physical quantity of the polymer material;
calculating the physical quantity under the first transformation condition as the physical quantity based on the second transformation condition;
Simulation methods for polymeric materials. The polymer material simulation method according to claim 1, further comprising, prior to the simulation step, a conversion rule calculation step in which the computer determines the time-temperature conversion rule. The conversion rule calculation step includes a step of calculating the time-temperature conversion rule in a first application range based on a plurality of predetermined transformation conditions;
The method for simulating a polymer material according to claim 2 , further comprising the step of: extending the time-temperature conversion rule to a second application range using a deformation condition different from the plurality of deformation conditions. The method for simulating a polymeric material according to any one of claims 1 to 3, wherein the physical quantity includes viscoelastic properties. The method for simulating a polymer material according to claim 4, wherein the viscoelastic properties include a loss tangent.

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