JP7204470B2 - Method, system and program for simulating uniaxial stretching of polymer model - Google Patents

Description

The present invention relates to a method, system and program for simulating uniaxial stretching of a polymer model such as crosslinked rubber.

For example, a uniaxial elongation test is performed on a crosslinked polymer (so-called crosslinked rubber) obtained by adding a crosslinking agent such as sulfur to an unvulcanized rubber to bond (crosslink) the molecules. It is desired that a computer simulation using CAE (Computer Aided Engineering) can also simulate a uniaxial elongation test. It is known that when a crosslinked rubber is uniaxially stretched, if it is pulled with a constant tension, a creep phenomenon occurs and eventually it breaks.

In a molecular simulation, not limited to rubber, a polymer model including a plurality of particles is placed in a three-dimensional calculation area, and a molecular dynamics calculation is performed under analysis conditions of a predetermined pressure and a predetermined temperature according to the environment. The volume of the computational domain is the volume of the polymer. As a means of simulating uniaxial expansion, the computational domain is gradually expanded along the x-axis, and the y- and z-axes of the computational domain are contracted so that the volumes remain constant as the x-axis is expanded. can be considered.

However, in the method of controlling the volume to be constant, it was found that the stress did not become 0 even when the elongation ratio at which the polymer model would start to break was reached, and the break could not be simulated.

As a method for simulating breakage, the method described in Patent Document 1 seems to provide a cutting process for cutting bonds when the distance between bonded particles is greater than a threshold value. However, it is necessary to appropriately set the threshold value, and it is necessary to examine whether the method of cutting according to the distance is appropriate, and there is no mention of whether the creep phenomenon can be reproduced.

As another method for simulating rupture, the method described in US Pat. . However, it is necessary to examine whether it is appropriate to change the Poisson's ratio, and there is no mention of whether the creep phenomenon can be reproduced.

As another method for simulating fracture, the method described in Non-Patent Document 1 seems to extend the x-axis little by little while keeping the y-axis and y-axis sizes of the computational domain fixed. However, it is difficult to say that stretching along the x-axis at a Poisson's ratio of 0 without changing the thickness (y-axis and z-axis) simulates the actual fracture phenomenon of polymers such as rubber. Also, there is no mention of whether the creep phenomenon is reproducible.

JP 2017-97841 A Japanese Patent No. 6405183

2013 K computer industrial use report, Development of high-performance, long-life tires by elucidation of rubber destruction phenomena using large-scale coarse-grained molecular dynamics method, Hiromichi Kishimoto, project number hp120032, Advanced Information Foundation National Institute of Science and Technology

An object of the present invention is to provide a method, system and program for simulating uniaxial elongation of a polymer model that can reproduce the creep phenomenon and breakage of the polymer model.

The method of simulating the uniaxial elongation of the polymer model of the present invention comprises:
A method, performed by one or more processors, comprising:
arranging a macromolecular model having a plurality of particles, in which some particles and other particles are connected by a bond potential, in a three-dimensional computational domain;
performing a molecular dynamics calculation under predetermined analysis conditions including a predetermined pressure and a predetermined temperature in the x-axis, y-axis, and z-axis pressure values acting from the outside on the calculation area;
calculating the cross-sectional area of the calculation region passing through the y-axis and the z-axis;
The pressure values of the y-axis and the z-axis are set as the predetermined pressure, and the pressure value of the x-axis is set to a value obtained by subtracting a value obtained by dividing a constant tension value by the cross-sectional area from the predetermined pressure,
perform a predetermined step molecular dynamics calculation,
The calculation of the cross-sectional area, the update of the x-axis pressure value, and the molecular dynamics calculation of the predetermined step are repeatedly executed.

In this way, by repeatedly executing the calculation of the cross-sectional area of the calculation region passing through the y-axis and z-axis, the update of the pressure value on the x-axis, and the molecular dynamics calculation of a predetermined step, the polymer model is converted to the x-axis It is possible to realize a simulation in which the material is pulled with a constant tension in a direction, and it is possible to reproduce the creep phenomenon and creep rupture.

A diagram showing a system for simulating uniaxial elongation of a polymer model of the present invention. Flowchart of processing performed by the system Diagram showing polymer model and computational domain Diagram showing FENE-LJ and cleavable potential (quartic) Diagram showing changes in calculation area and set pressure value in simulation of creep phenomenon in uniaxial extension A diagram showing the elongation ratio to the elapsed time and the initial state for the example FIG. 10 shows longer-term results for the example.

An embodiment of the present invention will be described below with reference to the drawings.

[System for simulating uniaxial stretching of polymer models]
The system 1 of the present embodiment is configured to simulate uniaxial elongation of a polymer model such as rubber, and reproduce creep and rupture phenomena.

As shown in FIG. 1, the system 1 includes a polymer model acquisition unit 10, a setting unit 11, a model placement unit 12, a molecular dynamics calculation execution unit 13, a cross-sectional area calculation unit 14, and a pressure value setting unit. 15 and. These units 10 to 15 are implemented by cooperation of software and hardware when the processor executes the processing routine shown in FIG. In this embodiment, the processor in one device executes the processing of each unit, but the present invention is not limited to this. For example, it may be distributed using a network so that a plurality of processors execute the processing of each unit. That is, one or more processors perform processing.

The polymer model acquisition unit 10 acquires a polymer model D1 (data) that has a plurality of particles and in which some particles and other particles are bonded with a bond potential. The polymer model acquisition unit 10 may acquire the polymer model D1 from the outside, or may generate the polymer model D1. As shown in FIG. 3, the polymer model D1 of the present embodiment includes a plurality of polymer models 2 in which a plurality of polymer particles 20 are linearly or branched, and a plurality of cross-linking agent particles 3. A polymer model 2 and cross-linking agent particles 3 are bonded. The polymer particles 20 have a non-bonding potential with other particles and have a bonding potential with the polymer particles 20 having a bonding relationship. The cross-linking agent particles 3 have a non-bonding potential with other particles and have a bonding potential with the polymer particles 20 in a bonding relationship. FENE-LJ (Leonard Jones) and WCA (LJ potential with repulsive force only) can be used as the non-bonded potential. As the coupling potential, a severable potential is set so that the potential does not become infinite on the long-distance side. FIG. 4 shows the FENE-LJ and the cleavable potential (denoted as quartic). The horizontal axis indicates the distance r between particles, and the vertical axis indicates the potential [V _bond (r)]. As shown in FIG. 4, the NENE-LJ has an infinite potential on both the short distance side and the long distance side. On the other hand, the severable potential (quartic) becomes infinite on the short distance side, but does not become infinite on the long distance side. It is not very large, so cutting is acceptable. In this embodiment, the cleavable potential is set to both the bond potential between the polymer particles 20 and the bond potential between the crosslinker particles 3 and the polymer particles 20. Not limited. For example, the cleavable potential may be set only to the bond potential between the polymer particles 20 or only to the bond potential between the crosslinker particles 3 and the polymer particles 20 . That is, when there are two or more coupling potentials, at least one coupling potential should be set. Of course, these potentials are only examples, and other settings are possible.

The setting unit 11 sets analysis conditions used for the uniaxial extension simulation of the polymer model D1. Analysis conditions include the predetermined pressure P, the predetermined temperature, the initial shape of the calculation area, the magnitude of the constant tension F, and the like. The predetermined pressure may be atmospheric pressure, and the predetermined temperature may be atmospheric temperature. The computational domain Ar1 is a three-dimensional space in which the polymer model D1 is arranged. The computational region Ar1 is always deformed so as to have the minimum shape in which the macromolecule model D1 inside can be accommodated, unless there are constraints. Therefore, the volume of the computational domain Ar1 means the volume of the polymer model D1. Although the calculation area Ar1 in this embodiment is a rectangular parallelepiped, it is not limited to this, and various shapes can be adopted. In this embodiment, periodic boundary conditions are set for the calculation region Ar1, but the definition of the boundary conditions can be changed.

As shown in FIG. 3, the model placement unit 12 places the polymer model D1 in the initial shape calculation area Ar1. This is done in working memory D2.

The molecular dynamics calculation execution unit 13 executes molecular dynamics calculations under analysis conditions including a predetermined pressure P and a predetermined temperature. Although LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) is used in this embodiment, it is not limited to this. The molecular dynamics calculation execution unit 13 can execute balancing processing. The equilibration process is a process of repeatedly executing molecular dynamics calculations of the polymer model D1 until the energy of the polymer model D1 is minimized at a predetermined pressure and temperature. To minimize is to calculate the behavior of each particle 30 until the energy of the polymer model D1 becomes substantially constant (the energy fluctuation becomes equal to or less than the threshold). This is because it cannot necessarily be said that the molecular dynamics calculation is in a stable state immediately after the arrangement of the polymer model D1 and immediately after the calculation area Ar1, which will be described later, is changed. Specifically, the pressure value Px in the x-axis direction, the pressure value Py in the y-axis direction, and the pressure value Pz in the z-axis direction acting from the outside on the calculation area Ar1 are all the same value, and these pressure values Px, Py, and Pz are equal to the predetermined pressure P.

The cross-sectional area calculator 14 calculates a cross-sectional area S of a calculation area Ar1 passing through the y-axis and the z-axis, as shown in FIG. In the drawing, the cross-sectional area S is indicated by oblique lines.

The pressure value setting unit 15 individually sets the pressure value acting from the outside on the calculation area Ar1 for each of the x-axis, the y-axis, and the z-axis. The pressure value setting unit 15 sets the pressure value Py on the y-axis to a predetermined pressure P. FIG. The pressure value setting unit 15 sets the pressure value Pz on the z-axis to a predetermined pressure P. As shown in FIG. The pressure value setting unit 15 uses the cross-sectional area S calculated by the cross-sectional area calculating unit 14 to set the pressure value Px on the x-axis. Specifically, the x-axis pressure value Px is set to a value obtained by subtracting the value obtained by dividing the constant tension F by the cross-sectional area S from the predetermined pressure P. Expressed as a formula, Px=PF/S. If the pressure values Px, Py, and Pz are set in this way, the external pressure of only Px is (F/S) lower than that of Py and Pz. This means pulling with a constant tension F in the x-axis.

As shown in FIG. 5, the pressure value Px on the x-axis is set to PF/S, the pressure values Py and Pz on the y-axis and z-axis are set to P, and the molecular dynamics calculation execution unit 13 performs molecular dynamics If the calculation is executed, the pressure on the x-axis is weaker than the pressure on the y- and z-axes, so the polymer model D1 in the calculation area Ar1 is pulled by a constant tension F on the x-axis. Then, the macromolecular model D1 in the calculation area Ar1 moves so as to extend along the x-axis, and the macromolecule model D1 moves so as to contract along the y-axis and z-axis, and the calculation area Ar1 follows and deforms. The molecular dynamics calculation execution unit 13 executes a predetermined step molecular dynamics calculation, and the cross-sectional area S also changes due to the deformation of the calculation region Ar1. The cross-sectional area calculation unit 14 calculates the cross-sectional area S, and the pressure value setting unit 15 sets (updates) the pressure value Px based on the latest cross-sectional area S. In this way, the calculation of the cross-sectional area S of the calculation region Ar1 by the cross-sectional area calculation unit 14, the update of the x-axis pressure value Px based on the cross-sectional area S by the pressure value setting unit 15, and the molecular dynamics calculation execution unit 13 A predetermined step of molecular dynamics calculation is repeatedly executed. Then, as shown in FIG. 5, a simulation can be realized in which the polymer model D1 is pulled in the x-axis direction with a constant tension F, and the creep phenomenon and creep rupture can be reproduced. The above repetition ends when a predetermined end condition is satisfied. Predetermined termination conditions include, for example, that the time step for executing the molecular dynamics calculation exceeds a threshold.

[Method for simulating uniaxial elongation of polymer model]
A method of simulating uniaxial stretching of a macromolecule model executed by one or more processors in the system 1 shown in FIG. 1 will be described with reference to FIG.

First, in step ST1, the polymer model acquisition unit 10 obtains a polymer model D1 that has a plurality of particles (2, 3) and that some particles and other particles are coupled by a coupling potential. , obtains a polymer model D1 in which a severable potential that does not become infinite on the long-distance side is set as a bond potential. In the next step ST2, the setting unit 11 sets analysis conditions used for the uniaxial elongation simulation of the polymer model D1. The order of steps ST1 and ST2 is random.

In the next step ST3, the model placement unit 12 places the polymer model D1 in the three-dimensional calculation area Ar1.

In the next step ST4, the molecular dynamics calculation execution unit 13 determines that the pressure values Px, Py, and Pz on the x-axis, y-axis, and z-axis acting from the outside on the calculation area Ar1 are a predetermined pressure P and a predetermined temperature. A molecular dynamics calculation is performed under predetermined analysis conditions including It is preferable to carry out an equilibration process in this process.

In the next step ST5, it is determined whether or not a predetermined termination condition is satisfied, and if it is determined that the predetermined termination condition is not satisfied, the process proceeds to step ST6. If it is determined that the predetermined termination condition is met, the execution of the process is terminated. The predetermined termination condition can be set as appropriate, and includes, for example, that the time step for executing the molecular dynamics calculation exceeds a threshold.

In the next step ST6, the cross-sectional area calculator 14 calculates the cross-sectional area S of the calculation area Ar1 passing through the y-axis and the z-axis.

In the next step ST7, the pressure value setting unit 15 sets the pressure values Py and Pz on the y-axis and z-axis to a predetermined pressure P, and divides the pressure value Px on the x-axis by the cross-sectional area S of the constant tension value F. A value (PF/S) obtained by subtracting the value (F/S) from the predetermined pressure P is set.

In the next step ST8, the molecular dynamics calculation execution unit 13 executes predetermined steps of molecular dynamics calculation.

The results of the simulation method of the present invention will be explained. In FIG. 6, the horizontal axis indicates the elapsed time, and the vertical axis indicates the expansion ratio with respect to the initial state. According to the simulation method of the present invention, it can be seen that the creep phenomenon can be reproduced. FIG. 7 is the result of performing FIG. 6 for a longer time. Finally, it can be seen that crepe rupture occurs.

As described above, the method for simulating the uniaxial elongation of the polymer model of the present embodiment includes:
A method, performed by one or more processors, comprising:
A polymer model D1 having a plurality of particles (polymer particles 20, cross-linking agent particles 3), some of which are bonded to other particles by bonding potentials, is arranged in a three-dimensional calculation area Ar1 (ST3 ),
The pressure values Px, Py, and Pz on the x-axis, y-axis, and z-axis acting from the outside on the calculation area Ar1 are a predetermined pressure P, and the molecular dynamics calculation is performed under predetermined analysis conditions including a predetermined temperature ( ST4),
Calculate the cross-sectional area S of the calculation area Ar1 passing through the y-axis and the z-axis (ST6),
The pressure values Py and Pz on the y-axis and z-axis are set to a predetermined pressure P, and the pressure value Px on the x-axis is obtained by dividing the constant tension F by the cross-sectional area S (F/S), which is subtracted from the predetermined pressure P. Set to the value (PF/S) (ST7),
Predetermined step molecular dynamics calculation is executed (ST8),
Calculation of the cross-sectional area (ST6), updating of the pressure value Px on the x-axis (ST7), and molecular dynamics calculation of predetermined steps (ST8) are repeatedly executed.

The system for simulating the uniaxial elongation of the polymer model of this embodiment includes:
A model arrangement in which a polymer model D1 having a plurality of particles (polymer particles 20, cross-linking agent particles 3) and in which some particles and other particles are coupled by a coupling potential is arranged in a three-dimensional calculation area Ar1. Part 12;
A molecule for which the pressure values Px, Py, and Pz on the x-, y-, and z-axes acting from the outside on the calculation area Ar1 are a predetermined pressure P, and for which a molecular dynamics calculation is performed under predetermined analysis conditions including a predetermined temperature. a dynamics calculation execution unit 13;
a cross-sectional area calculation unit 14 that calculates the cross-sectional area S of the calculation area Ar1 passing through the y-axis and the z-axis;
The pressure values Py and Pz on the y-axis and z-axis are set to a predetermined pressure P, and the pressure value Px on the x-axis is obtained by dividing the constant tension F by the cross-sectional area S (F/S), which is subtracted from the predetermined pressure P. A pressure value setting unit 15 that sets the value (PF/S);
with
Calculation of the cross-sectional area S by the cross-sectional area calculation unit 14, updating of the x-axis pressure value Px by the pressure value setting unit 15, and molecular dynamics calculation of predetermined steps by the molecular dynamics calculation execution unit 13 are repeatedly executed. is configured to

In this way, by repeatedly executing the calculation of the cross-sectional area S of the calculation area Ar1 passing through the y-axis and the z-axis, the update of the pressure value Px on the x-axis, and the molecular dynamics calculation of predetermined steps, the polymer model A simulation in which D1 is pulled in the x-axis direction with a constant tension F can be realized, and the creep phenomenon and creep rupture can be reproduced.

As in the present embodiment, the polymer model D1 has a plurality of polymer models 2 in which a plurality of polymer particles 20 are linearly or branched, and a plurality of cross-linking agent particles 3. It is preferably a crosslinked polymer model to which the crosslinker particles 3 are bonded.

It is a preferred application example of the present invention.

A program according to the present embodiment is a program that causes a computer to execute the above method. By executing this program, it is possible to obtain the effects of the above method.

Although the embodiments of the present invention have been described above with reference to the drawings, it should be considered that the specific configuration is not limited to these embodiments. The scope of the present invention is indicated not only by the description of the above embodiments but also by the scope of claims, and includes all modifications within the scope and meaning equivalent to the scope of claims.

For example, each unit 10 to 15 shown in FIG. 1 is realized by executing a predetermined program by a processor of a computer, but each unit may be configured by a dedicated circuit. In addition, in the present embodiment, the processors in one computer implement the units 10 to 15, but they may be installed in at least one or a plurality of processors in a distributed manner.

It is possible to adopt the structure adopted in each of the above embodiments in any other embodiment. The specific configuration of each part is not limited to the above-described embodiment, and various modifications are possible without departing from the scope of the present invention.

In this embodiment, the polymer model D1 is a model composed of the polymer model 2 and the cross-linking agent particles 3. If so, it is applicable.

12 model placement unit 13 molecular dynamics calculation execution unit 14 cross-sectional area calculation unit 15 pressure value setting unit 2 polymer model 20 polymer particles 3 cross-linking agent particles D1 polymer model Ar1 calculation region

Claims (5)

A method, performed by one or more processors, comprising:
arranging a macromolecular model having a plurality of particles, in which some particles and other particles are connected by a bond potential, in a three-dimensional computational domain;
performing a molecular dynamics calculation under predetermined analysis conditions including a predetermined pressure and a predetermined temperature in the x-axis, y-axis, and z-axis pressure values acting from the outside on the calculation area;
calculating a cross-sectional area of the calculation region passing through a plane normal to the x-axis ;
The pressure values of the y-axis and the z-axis are set to the predetermined pressure, and the pressure value of the x-axis is set to a value obtained by subtracting a value obtained by dividing a constant tension value by the cross-sectional area from the predetermined pressure,
perform a predetermined step molecular dynamics calculation,
A method for simulating uniaxial stretching of a macromolecular model, wherein the calculation of the cross-sectional area, the updating of the x-axis pressure value, and the molecular dynamics calculation of the predetermined steps are repeatedly executed. The polymer model includes a plurality of polymer models in which a plurality of polymer particles are connected in a linear or branched manner, and a plurality of cross-linking agent particles, and the polymer model and the cross-linking agent particles are bonded to form a cross-linking height. 2. The method of claim 1, which is a molecular model. a model placement unit that places a macromolecular model having a plurality of particles, in which some particles are bonded to other particles by a bond potential, in a three-dimensional computational domain;
a molecular dynamics calculation execution unit for executing molecular dynamics calculations under predetermined analysis conditions including a predetermined pressure and a predetermined temperature in the x-axis, y-axis, and z-axis pressure values acting on the calculation area from the outside; ,
a cross-sectional area calculation unit that calculates a cross-sectional area of the calculation region passing through a plane normal to the x-axis ;
Pressure value setting in which the pressure values of the y-axis and the z-axis are set to the predetermined pressure, and the pressure value of the x-axis is set to a value obtained by subtracting a value obtained by dividing a constant tension value by the cross-sectional area from the predetermined pressure. and
Calculation of the cross-sectional area by the cross-sectional area calculation unit, updating of the x-axis pressure value by the pressure value setting unit, and molecular dynamics calculation of predetermined steps by the molecular dynamics calculation execution unit are repeatedly executed. A system that simulates uniaxial stretching of polymer models. The polymer model includes a plurality of polymer models in which a plurality of polymer particles are connected in a linear or branched manner, and a plurality of cross-linking agent particles, and the polymer model and the cross-linking agent particles are bonded to form a cross-linking height. 4. The system of claim 3, which is a molecular model. A program that causes a processor to execute the method according to claim 1 or 2.

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