Elongation breakage determination system of coarse-grained particle model, method, and program

Abstract

To provide an elongation breakage determination technique of a coarse-grained particle model capable of quantitatively determining the time of breakage.SOLUTION: A system includes: a processing execution section 10 that can execute processing of extending a coarse-grained particle model D1 and balancing processing of performing molecular dynamics calculation to the coarse-grained particle model D1; a first coupled length acquisition section 11 that acquires a coupled length group of all coupled pairs in the balancing processing in a state where the processing of extending is not executed as a first coupled length group; a second coupled length acquisition section 12 that acquires a coupled length group of all coupled pairs in the balancing processing after the processing of extending is executed as a second coupled length group; an abnormality degree calculation section 13 that calculates an abnormality degree of coupled length of each coupled pair in the second coupled length group with respect to the first coupled length group; and a determination section 14 that executes determination processing of determining whether or not the coarse-grained particle model D1 is broken on the basis of maximum abnormality degree in a plurality of calculated abnormality degrees.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to a system, method, and program for determining elongation fracture of a coarse-grained particle model. [Background technology]

[0002] Uniaxial extension tests are known to investigate the mechanical properties of rubber. In this test, the relationship between the elongation ratio λ of rubber along one axis and the tensile stress can be measured, and it is widely known as a standard measurement method for understanding rubber elasticity. It is desirable to be able to simulate uniaxial extension tests in computer simulations using CAE (Computer Aided Engineering).

[0003] Patent Documents 1 and 2 refer to the simulation of uniaxial elongation in a molecular simulation using molecular dynamics calculations. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Patent No. 7204470 [Patent Document 2] JP 2019-39774 A Summary of the Invention [Problem to be solved by the invention]

[0005] Patent Documents 1 and 2 state that particle breakage can be achieved by using a so-called severable bond potential, where the potential does not become infinite on the long distance side between particles. However, there is no disclosure of determining the breakage time point using a bond potential where the potential becomes infinite on the long distance side.

[0006] It is possible to perform uniaxial extension simulations at three temperatures, obtain the energy elastic components from the stress at the three temperatures, and determine the time of breakage based on the energy elastic components, but this would be computationally expensive and would not be considered a quantitative method.

[0007] The present disclosure provides a technique for determining elongational fracture of a coarse-grained model, which is capable of quantitatively determining the time point of fracture. [Means for solving the problem]

[0008] The system for determining extension fracture of a coarse-grained particle model disclosed herein includes a process for elongating a coarse-grained particle model including a particle chain formed of bond pairs of coarse-grained particles bonded by an unbreakable bond potential in which the potential on the long-distance side is infinite, and an equilibration process for performing a molecular dynamics calculation on the coarse-grained particle model under analysis conditions including a constant volume condition and a constant temperature condition, and a process for determining the results of all bond pairs in the equilibration process based on a result of the execution of the equilibration process on the coarse-grained particle model on which the elongation process has not been executed. the coarse-grained particle model after the elongation process is performed, the coarse-grained particle model has a first bond length acquisition unit that acquires a bond length group as a first bond length group; a second bond length acquisition unit that acquires a bond length group of all bond pairs in the equilibration process as a second bond length group based on a result of the equilibration process on the coarse-grained particle model after the elongation process is performed; an anomaly calculation unit that calculates an anomaly degree of the bond length of each bond pair in the second bond length group with respect to the first bond length group; and a judgment unit that executes a judgment process to judge whether the coarse-grained particle model has broken or not based on the maximum anomaly degree among the multiple calculated anomalies. [Brief description of the drawings]

[0009] [Figure 1] FIG. 1 is a block diagram showing a system according to an embodiment of the present invention. [Diagram 2] 4 is a flowchart showing a process executed by the system. [Diagram 3] FIG. 1 is a schematic diagram showing a coarse-grained particle model using this embodiment arranged in a virtual space. [Figure 4]Diagram showing the FENE-LJ potential. [Diagram 5] FIG. 13 shows the results of an elongation simulation of a coarse-grained particle model. [Figure 6] FIG. 13 shows the results of an elongation simulation of model A. [Figure 7] A graph of the bond lengths and frequency of occurrence (frequency) of all bond pairs present in the coarse-grained model for Model A. [Figure 8] 13 is a graph showing the transition of the number of executions k of the extension process and the maximum degree of anomaly for models A to C. [Figure 9] FIG. 13 shows the results of an elongation simulation of Model B. [Figure 10] FIG. 13 shows the results of an elongation simulation of Model C. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0010] Hereinafter, an embodiment of the present disclosure will be described with reference to the drawings.

[0011] [System for judging extensional fracture of coarse-grained particle models] The system 1 (apparatus) of this embodiment judges the elongation fracture of the coarse-grained particle model. In this embodiment, the molecular simulation software "LAMMPS" that executes molecular dynamics calculations is used for the elongation simulation of the coarse-grained particle model.

[0012] As shown in FIG. 1, the system 1 has a processing execution unit 10. Each unit constituting the system 1 is realized by software and hardware working together as the processor 1a executes a processing routine shown in FIG. 2 that is prestored in a computer equipped with a processor 1a, a memory 1b, various interfaces, etc. In this embodiment, the processor 1a in one device realizes each unit, but this is not limited to this. For example, the units may be distributed using a network, and multiple processors may execute the processing of each unit. In other words, one or multiple processors execute the processing.

[0013] The memory 1b stores data on a coarse-grained particle model of an elongation target such as rubber. As shown in FIG. 3, the coarse-grained particle model D1 includes one or more particle chains 2. One particle chain 2 is formed by connecting bond pairs of the coarse-grained particles 20. An unbreakable bond potential is set for the bond pairs of the coarse-grained particles 20. An example of the unbreakable bond potential in this embodiment is FENE-LJ (Lenard Jones). As shown in FIG. 4, the unbreakable bond potential is a potential where the potential on the long distance side is infinite. In FIG. 4, the horizontal axis indicates the interparticle distance r, and the vertical axis indicates the potential [Vbond(r)]. Since the potential on the long distance side is infinite, breaking is not allowed. In this embodiment, a process of deleting the bond potential of the bond pair by considering it as a break, or a process of redefining the model is not performed. Note that a non-bonding potential is set between the coarse-grained particles 20 and other particles. As shown in FIG. 3, the coarse-grained particle model D1 is placed in a virtual cubic calculation area Ar1.

[0014] The processing execution unit 10 can execute a process of stretching the coarse-grained particle model D1 arranged in the calculation area Ar1, and an equilibration process of equilibrating the coarse-grained particle model D1. The equilibration process is a process of performing a molecular dynamics calculation on the coarse-grained particle model D1 under analysis conditions including a constant volume condition and a constant temperature condition. In this embodiment, as shown in step ST1 in FIG. 2, the equilibration process is performed on the coarse-grained particle model D1 for an analysis time of 4×10 before executing the stretching process. 6 Next, the stretching process is performed as shown in step ST3 of FIG. 2. The stretching process requires an analysis time of 1×10 6 Next, as shown in step ST4 of Fig. 2, the equilibration process is performed for an analysis time of 6 × 10 6 The stretching process and the balancing process are collectively called an extension process, and the extension process (stretching process and balancing process) is repeated until the desired extension ratio is reached.

[0015] Fig. 5 shows the results of a uniaxial extension simulation of the coarse-grained particle model D1 performed by the processing execution unit 10. As shown in Fig. 5, it can be seen that the coarse-grained particle model D1 is extended along one axis (the vertical axis in Fig. 5). The results of the execution by the processing execution unit 10 can be output to a file or the like for each analysis time, including the coordinate positions of all particles, the size of the calculation area Ar1, and the bond pair relationships of the particles.

[0016] In LAMMPS, the model can be placed in the calculation domain Ar1 with the create_atom command, but coordinate placement is also possible by executing an external program other than LAMMPS. Bond potentials can be set with the bond_style fene command, and non-bonded potentials can be set with the pair_style lj / cut command. Volume and temperature can be specified to be constant with the fix nvt command.

[0017] The extension simulation by the processing execution unit 10 uses an unbreakable bond potential, so the coarse-grained particle model D1 can be extended as much as possible and breakage does not occur. In reality, this causes a calculation error and the program terminates abnormally. Even in a model using an unbreakable bond potential, it is desirable to be able to determine the time when the model breaks.

[0018] As one way of thinking about judging the time of breakage, the stress f generated in the coarse-grained particle model D1 contains an energy elastic component and an entropy elastic component, as shown in the following equation. When the energy elastic component is (∂E / ∂L) T and the entropy elasticity component is (∂f / ∂T) L It is.

number

[0019] It is known that the energy elastic component increases rapidly with an increase in the number of fully stretched bond pairs. Figure 6 shows the results of an elongation simulation of model A of the sample described later, showing the stress and elongation ratio at temperature T = 1.0 [LJ unit]. E indicates the energy elastic component, and S indicates the entropy elastic component. The energy elastic component E rises from an elongation ratio of about 2.59, and this point can be considered as the time of breakage. However, in order to decompose the elongation simulation result (stress) into the energy elastic component and the entropy elastic component, simulation results at at least three temperatures are required. In the example of Figure 6, fitting is performed with a linear function based on the three results of temperatures T = 1.0, 0.8, and 1.2, and the intercept of the linear function is the energy component and the slope is the entropy component. Therefore, calculations at three temperatures are required, which increases the calculation cost. In addition, the time when the energy elastic component rises is judged visually, which is difficult to say that it is a quantitative judgment.

[0020] FIG. 7 is a graph of the bond lengths and the frequency (frequency) of all bond pairs present in the coarse-grained particle model D1 for four cases in which the number of executions of the extension process (stretching process and equilibration process) for the above model A is different. The number of executions of the extension process is indicated by k, and four cases of k=20, 40, 50, and 60 are shown. The horizontal axis indicates the bond length of the bond pair, and the vertical axis indicates the number (frequency) of pairs of that bond length. As shown in FIG. 7, the bond pairs of model A are concentrated around a bond length of 0.95, and the bond lengths are normally distributed in the range from 0.85 to 1.15. When the number of executions of the extension process k becomes 50, pairs with bond lengths longer than 1.15 appear, and when the number of executions of the extension process k becomes 60, the number of pairs with long bond lengths further increases. It is considered that the bond has already broken when the number of executions of the extension process k becomes 50. As the model stretches and breaks, the bond pairs of the unnaturally stretched particles increase. Therefore, it is thought that breakage can be detected by observing the bond lengths and their distribution of the bond pairs that make up the model.

[0021] Therefore, the system 1 includes a first bond length acquisition unit 11, a second bond length acquisition unit 12, an anomaly degree calculation unit 13, and a judgment unit 14. The first bond length acquisition unit 11 acquires, as a first bond length group, a bond length group of all bond pairs within a first predetermined analysis time in the equilibration process for the coarse-grained particle model D1 for which no elongation process has been performed. In this embodiment, the first bond length group is a 4×10 6 Of the steps, the latter 2×10 6 All particle coordinates and bond information of the coarse-grained particle model in the step (first specified analysis time) are output to a file, and the average value of the distance of each bond pair within the first specified analysis time is calculated, and the average value is taken as the bond length x 0,i The first bond length group is x 0,i (i=1~N)=[x 0,1 , …, x 0,N In the first embodiment, in models A to C described below, the number of bond pairs is N=39,800.

[0022] The second bond length acquisition unit 12 acquires, as a second bond length group, a bond length group of all bond pairs within a second predetermined analysis time in the equilibration process after the elongation process. In this embodiment, 6 Of the steps, the latter 2×10 6 All particle coordinates and bond information of the coarse-grained particle model in the step (second specified analysis time) are output to a file, and the average value of the distance of each bond pair within the second specified analysis time is calculated, and the average value is taken as the bond length x k,i The second bond length group is x k,i (k≧1, i=1~N)=[x k,1 , …, x k,N ] can be expressed as:

[0023] The first predetermined analysis time and the second predetermined analysis time may be the same time or may be different times.

[0024] The anomaly calculation unit 13 calculates the bond length x of each bond pair in the second bond length group. k,i The first bond length group [x 0,1, x 0,2 , …, x 0,N ] is calculated. The degree of anomaly can be calculated using a known algorithm for detecting abnormal values ​​or outliers. For example, the degree of anomaly based on the Hotelling theory, the degree of anomaly based on the Gaussian Mixture Model (GMM), and the degree of anomaly based on the KDE (Kernel Density Estimation) can be calculated. In this embodiment, the degree of anomaly based on the Hotelling theory is calculated because the average bond length of the bond pairs in a state not yet broken is accompanied by a normal distribution, but can be changed as appropriate. The degree of anomaly is the number of bond pairs that exist. The maximum degree of anomaly is the maximum value of the multiple degrees of anomaly that exist. The maximum degree of anomaly a(k) based on the Hotelling theory can be calculated by the following formula.

number

[0025] The judgment unit 14 executes a judgment process to judge whether or not the coarse-grained particle model is broken based on the maximum degree of abnormality among the multiple degrees of abnormality calculated by the abnormality degree calculation unit 13. There are various judgment methods, but as a first method, when the elongation process including the balancing process for the coarse-grained particle model D1 on which the elongation process has been executed, the process of calculating the maximum degree of abnormality based on the elongation process, and the judgment process based on the maximum degree of abnormality are repeatedly executed, the coarse-grained particle model may be judged to be broken if the maximum degree of abnormality rises in the judgment process. For example, the elongation process is executed when k=i, the maximum degree of abnormality based on the elongation process is calculated, and the judgment process based on the maximum degree of abnormality is executed. If the judgment process does not judge that the model is broken, the elongation process is next executed with k=(i+1), the maximum degree of abnormality based on the elongation process is calculated, and the judgment process based on the maximum degree of abnormality is executed. FIG. 8 is a graph showing the transition of the number of executions k of the elongation process and the maximum degree of abnormality for models A to C. In Fig. 8, the maximum abnormality degree of model A rises suddenly when k = 48, and based on this, the judgment unit 14 judges that model A has broken down at k = 48. Similarly, in Fig. 8, the maximum abnormality degree of model B rises suddenly when k = 59, and based on this, the judgment unit 14 judges that model B has broken down at k = 59. Similarly, the maximum abnormality degree of model C rises suddenly when k = 66, and based on this, the judgment unit 14 judges that model C has broken down at k = 66.

[0026] As a second method, a threshold value of the maximum degree of abnormality may be set in advance (for example, a threshold value of 50), and the determination unit 14 may determine that the coarse-grained model has broken down when the maximum degree of abnormality exceeds the threshold value. For the degree of abnormality based on the Hotelling theory, the threshold value may be set to 50.

[0027] As a third method, when the maximum anomaly degree increases continuously with the execution of the elongation process including the equilibration process for the coarse-grained particle model D1 that has been subjected to the elongation process, it may be determined that the coarse-grained particle model has broken down. This is because the continuous increase in the maximum anomaly degree every time the elongation process is performed indicates a high possibility of breakage.

[0028] As a fourth method, the determination unit 14 may determine that the coarse-grained particle model has broken down based on the differential value of the maximum degree of abnormality. For example, when the differential value exceeds a predetermined value, the increase in the maximum degree of abnormality is large, so that the possibility of the coarse-grained particle model breaking down is high.

[0029] As described above, it is possible to quantitatively determine whether the coarse-grained particle model has broken down based on the maximum degree of abnormality.

[0030] <Coarse-grained particle model> Models A, B, and C will be briefly described. Specifically, they are models generated by the method described in JP 2022-189529 A. Models A, B, and C all have 40,000 particles, one particle chain has 200 particles, and the model has 200 particle chains. The coarse-grained particle models A, B, and C use the Kremer-Grest model and have the unbonded potential (Unon-bond) of the Kremer-Grest model, the bonded potential (Ubond) of the Kremer-Grest model, and the angular potential (Uangle) representing the interaction between three particles. The unbonded potential can be expressed by formula (1), and the bonded potential can be expressed by formula (2). The angular potential is expressed by formula (3). This formula is just one example.

number

[0031] The parameters for determining the above potentials are K=30.0, R0=1.5, ε=1.0, and σ=1.0, but these can be changed as appropriate. Temperature T=1.0 [LJ unit], pressure P=1.0 [LJ unit]. Models A, B, and C relate to hydrogenated SBR (styrene butadiene rubber).

[0032] Model A has a hydrogenation rate of 0%, and contains 30,543 coarse-grained particles of butadiene and 9,457 coarse-grained particles of styrene. The cross-linked particles are arranged in seven clusters of 64 particles, and the cross-linked particles are bonded (cross-linked) to the butadiene particles. The angular potential parameters are K=3.1 for butadiene and K=6.3 for styrene.

[0033] Model B has a hydrogenation rate of 95%, and contains 1583 coarse-grained particles of butadiene, 28960 coarse-grained particles of styrene, and 9457 coarse-grained particles of styrene. The cross-linked particles are arranged in five clusters of 64, and the cross-linked particles are bonded (cross-linked) to the butadiene particles. The angular potential parameters are K=3.1 for butadiene, K=4.0 for ethylene, and K=6.3 for styrene.

[0034] Model C is the same as Model B, except for the change in K=3.1 for ethylene.

[0035] Figure 9 shows the results of the elongation simulation of sample model B. Figure 10 shows the results of the elongation simulation of sample model C. Figures 9 and 10 are calculated under the same conditions as Figure 6. According to this method, model A is determined to break at k = 48, and the elongation ratio is 1.019^48 = 2.54. This is considered to match because E (energy elastic component) increases from the elongation ratio of 2.54 in Figure 6. Model B is determined to break at k = 59, and the elongation ratio is 1.019^59 = 3.15. This is considered to match because E (energy elastic component) increases from the elongation ratio of 3.15 in Figure 9. Model C is determined to break at k = 66, and the elongation ratio is 1.019^66 = 3.612. This is considered to be consistent with the fact that E (energy elastic component) increases from around the elongation ratio of 3.5 in FIG. Therefore, we believe that we have proposed a method that can quantitatively determine the breakage point of a coarse-grained model during elongation without having to calculate stress.

[0036] The operation of the above-mentioned system for determining elongation fracture of a coarse-grained particle model will be described with reference to Fig. 2. As shown in step ST1 of Fig. 2, an equilibration process is performed on the coarse-grained particle model D1, in which a molecular dynamics calculation is performed under analysis conditions including a constant volume condition and a constant temperature condition. As shown in the next step ST2, the first bond length acquisition unit 11, based on the execution result of the equilibration process on the coarse-grained particle model D1, converts the bond length group of all bond pairs in the equilibration process into a first bond length group [x 0,1 , …, x 0,N]. The first bond length group is used as a reference for calculating the degree of anomaly, which will be described later. In the next step ST3, the processing execution unit 10 executes a process of stretching the coarse-grained particle model D1. Next, as shown in step ST4, the processing execution unit 10 executes an equilibration process in which a molecular dynamics calculation is performed on the stretched coarse-grained particle model D1 under analysis conditions including a constant volume condition and a constant temperature condition. One extension process is performed by executing steps ST3 and ST4. Next, as shown in step ST5, the second bond length acquisition unit 12 acquires the bond length group of all bond pairs in the equilibration process as the second bond length group [x k,1 , …, x k,N Next, as shown in step ST6, the anomaly calculation unit 13 calculates the anomaly degree of the bond length of each bond pair in the second bond length group with respect to the first bond length group. Next, as shown in step ST7, the judgment unit 14 executes a judgment process to judge whether or not the coarse-grained particle model D1 has broken down based on the maximum anomaly degree among the calculated multiple anomaly degrees. The above steps ST3 to ST7 are repeatedly executed until the judgment unit 14 judges that the coarse-grained particle model D1 has broken down.

[0037] [1] As described above, in the present embodiment, the system for determining an extension fracture of a coarse-grained particle model includes a process for extending a coarse-grained particle model D1 including a particle chain 2 formed by bond pairs of coarse-grained particles 20 bonded by an unbreakable bond potential in which the potential on the long-distance side is infinite, and an equilibration process for performing a molecular dynamics calculation on the coarse-grained particle model D1 under analysis conditions including a constant volume condition and a constant temperature condition, and a process for dividing the bond length groups of all bond pairs in the equilibration process into a first bond length group [x 0,1 , …, x 0,N ]; and Based on the results of the equilibration process for the coarse-grained particle model D1 after the stretching process, the bond length group of all bond pairs in the equilibration process is divided into the second bond length group [x k,1 , …, x k,N], and a second bond length acquisition unit 12 that acquires a second bond length group [x k,1 , …, x k,N ], the bond length of each bond pair [x k,i ], the first bond length group [x 0,1 , …, x 0,N ], and a judgment unit 14 that executes a judgment process to judge whether or not the coarse-grained particle model D1 has been broken based on the maximum abnormality degree among the multiple calculated abnormality degrees.

[0038] According to this construction, the second bond length group [x k,1 , …, x k,N ], the bond length of each bond pair [x k,i ], the first bond length group [x 0,1 , …, x 0,N ] is used to determine whether or not the coarse-grained particle model D1 has fractured, making it possible to make a well-founded and quantitative determination.

[0039] [2] In the system for determining elongation fracture of a coarse-grained model described in [1] above, the degree of anomaly may be an anomaly degree based on Hotelling's theory. Since the bond lengths of the unbroken coarse-grained grain model are normally distributed, it is appropriate to calculate the degree of anomaly based on the Hotelling theory, which assumes a normal distribution.

[0040] [3] The elongation fracture determination system for a coarse-grained particle model described in [1] or [2] above may repeatedly execute an elongation process including an elongation process and an equilibration process for the coarse-grained particle model D1 on which the elongation process has been executed, a process for calculating a maximum degree of abnormality based on the elongation process, and a determination process based on the maximum degree of abnormality, and if the maximum degree of abnormality is reached in the determination process, it may be determined that the coarse-grained particle model D1 has fractured. This is an example of a preferable determination process.

[0041] [4] The system for determining whether a coarse-grained model has elongated and broken may be configured to determine that the coarse-grained model D1 has broken when the maximum degree of abnormality exceeds a threshold value in the determination process. This is an example of a preferable determination process.

[0042] [5] The elongation fracture determination system for a coarse-grained particle model described in [1] or [2] above may determine that the coarse-grained particle model D1 has fractured if the maximum abnormality degree increases continuously in association with the execution of an elongation process including an equilibration process for the coarse-grained particle model D1 on which the elongation process has been executed. This is an example of a preferable determination process.

[0043] [6] In the system for determining an elongational fracture of a coarse-grained particle model described in [1] or [2] above, in the determination process, it may be determined that the coarse-grained particle model D1 has fractured based on a differential value of the maximum abnormality degree. This is an example of a preferable determination process.

[0044] [7] As in the present embodiment, the method for determining an extension fracture of a coarse-grained particle model is a method executed by one or more processors, and includes: an equilibration process for performing a molecular dynamics calculation under analysis conditions including a constant volume condition and a constant temperature condition on a coarse-grained particle model D1 that has not been subjected to a process of elongating the coarse-grained particle model D1, the coarse-grained particle model D1 including a particle chain 2 formed by a bond pair of the coarse-grained particles 20 bonded by an unbreakable bond potential in which the potential on the long-distance side is infinite; and a bond length group of all bond pairs in the equilibration process is classified into a first bond length group [x 0,1 , …, x 0,N ], and an equilibration process is performed on the coarse-grained particle model D1 after the stretching process by performing molecular dynamics calculations under analysis conditions including constant volume and constant temperature conditions, and the bond length group of all bond pairs in the equilibration process is obtained as the second bond length group [x k,1 , …, x k,N ] and the second bond length group [xk,1 , …, x k,N ], the bond length of each bond pair [x k,i ], the first bond length group [x 0,1 , …, x 0,N ], and performing a determination process to determine whether or not the coarse-grained particle model has been broken based on a maximum abnormality degree among the calculated multiple abnormality degrees.

[0045] [8] As in the present embodiment, the program performs equilibration processing to perform molecular dynamics calculations under analysis conditions including a constant volume condition and a constant temperature condition for a coarse-grained particle model D1 that has not been subjected to a process of elongating the coarse-grained particle model D1 including a particle chain 2 formed by bond pairs of coarse-grained particles 20 bonded by an unbreakable bond potential in which the potential on the long-distance side is infinite, and then classifies the bond length groups of all bond pairs in the equilibration processing into a first bond length group [x 0,1 , …, x 0,N ], and an equilibration process is performed on the coarse-grained particle model D1 after the stretching process by performing molecular dynamics calculations under analysis conditions including constant volume and constant temperature conditions, and the bond length group of all bond pairs in the equilibration process is obtained as the second bond length group [x k,1 , …, x k,N ] and the second bond length group [x k,1 , …, x k,N ], the bond length of each bond pair [x k,i ], the first bond length group [x 0,1 , …, x 0,N The method may also be configured to have one or more processors perform the following steps: calculate an abnormality degree for ]; and perform a determination process to determine whether the coarse-grained particle model has broken based on the maximum abnormality degree among the calculated multiple abnormality degrees.

[0046] Although the embodiments of the present disclosure have been described above based on the drawings, the specific configurations should not be considered to be limited to these embodiments. The scope of the present disclosure is indicated not only by the description of the above-mentioned embodiments but also by the claims, and further includes all modifications within the meaning and scope equivalent to the claims.

[0047] The structures employed in the above-described embodiments may be employed in any other embodiment. The specific configurations of the components are not limited to the above-described embodiments, and may be modified in various ways without departing from the spirit of the present disclosure.

[0048] (A) In the above embodiment, models A, B, and C are given as examples, but this is merely an example and can be used for any coarse-grained particle model.

[0049] (B) In the above embodiment, the analysis time for each process is an example and can be changed as appropriate.

[0050] For example, the order of execution of each process, such as operations, procedures, steps, and stages, in the devices, systems, programs, and methods shown in the claims, specifications, and drawings, can be arbitrary, as long as the output of a previous process is not used in a subsequent process. Even if the flow in the claims, specifications, and drawings is described using "first," "next," and the like for convenience, this does not mean that it is essential to execute the processes in this order.

[0051] Each unit shown in Fig. 1 is realized by executing a predetermined program on one or more processors, but each unit may be configured with a dedicated memory or a dedicated circuit. In the system 1 of the above embodiment, each unit is implemented in the processor 1a of one computer, but each unit may be distributed and implemented on multiple computers or in the cloud. In other words, the above method may be executed on one or more processors.

[0052] The system 1 includes a processor 1a. For example, the processor 1a can be a central processing unit (CPU), a microprocessor, or other processing unit capable of executing computer-executable instructions. The system 1 also includes a memory 1b for storing data for the system 1. In one example, the memory 1b includes a computer storage medium, including RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, DVD or other optical disk storage, magnetic cassette, magnetic tape, magnetic disk storage or other magnetic storage device, or any other medium that can be used to store desired data and that can be accessed by the system 1. [Explanation of symbols]

[0053] 1: System 1a: Processor 2: Particle chain 10: Decompression processing execution unit 11:First bond length acquisition part 12:Second bond length acquisition part 13: Abnormality calculation part 14: Judgment section 20: Coarse-grained particles a(k): Maximum abnormality D1: Coarse grained model T :Temperature

Claims

1. a process for extending a coarse-grained particle model including a particle chain formed by a bond pair of coarse-grained particles bonded by an unbreakable bond potential in which the potential on the long-distance side is infinite; and an equilibration process for performing a molecular dynamics calculation on the coarse-grained particle model under analysis conditions including a constant volume condition and a constant temperature condition; a first bond length acquisition unit that acquires, based on a result of the equilibration process performed on the coarse-grained particle model on which the elongation process has not been performed, a bond length group of all bond pairs in the equilibration process as a first bond length group; a second bond length acquisition unit that acquires, based on a result of the equilibration process performed on the coarse-grained particle model after the elongation process is performed, a bond length group of all bond pairs in the equilibration process as a second bond length group; an anomaly calculation unit that calculates an anomaly degree of a bond length of each bond pair in the second bond length group with respect to the first bond length group; a determination unit that performs a determination process for determining whether or not the coarse-grained particle model is broken based on a maximum abnormality degree among the calculated multiple abnormality degrees; A system for determining elongation fracture of a coarse-grained particle model comprising:

2. The system for determining elongation fracture of a coarse-grained model according to claim 1 , wherein the degree of anomaly is an degree of anomaly based on Hotelling's theory.

3. Repeating the elongation process, an elongation process including the balancing process for the coarse-grained particle model on which the elongation process has been executed, a process of calculating the maximum degree of abnormality based on the elongation process, and a determination process based on the maximum degree of abnormality; 3 . The system for determining an elongation fracture of a coarse-grained model according to claim 1 , wherein, in the determination process, it is determined that the coarse-grained model has fractured when the maximum abnormality degree rises.

4. 3 . The system for determining an elongation fracture of a coarse-grained model according to claim 1 , wherein the determination process determines that the coarse-grained model has fractured when the maximum degree of abnormality exceeds a threshold value. 4 .

5. The elongation fracture determination system for a coarse-grained particle model as described in claim 1 or 2, wherein in the determination process, if the maximum abnormality degree increases continuously with the execution of the elongation process including the equilibration process on the coarse-grained particle model on which the elongation process has been executed, the coarse-grained particle model is determined to have fractured.

6. The system for determining an elongation fracture of a coarse-grained model according to claim 1 or 2, wherein in the determination process, it is determined that the coarse-grained particle model has fractured based on a differential value of the maximum abnormality degree.

7. A method executed by one or more processors, comprising: performing an equilibration process for performing a molecular dynamics calculation under analysis conditions including a constant volume condition and a constant temperature condition on a coarse-grained particle model that has not been subjected to a process of extending the coarse-grained particle model including a particle chain formed by bond pairs of coarse-grained particles bonded by an unbreakable bond potential in which the potential on the long-distance side is infinite, and acquiring a bond length group of all bond pairs in the equilibration process as a first bond length group; performing an equilibration process for performing a molecular dynamics calculation on the coarse-grained particle model after performing the stretching process under analysis conditions including a constant volume condition and a constant temperature condition, and acquiring a bond length group of all bond pairs in the equilibration process as a second bond length group; Calculating an anomaly of the bond length of each bond pair in the second bond length group with respect to the first bond length group; executing a determination process for determining whether or not the coarse-grained particle model is broken based on a maximum abnormality degree among the calculated multiple abnormality degrees; A method for determining elongation fracture of a coarse-grained particle model, comprising:

8. performing an equilibration process for performing a molecular dynamics calculation under analysis conditions including a constant volume condition and a constant temperature condition on a coarse-grained particle model that has not been subjected to a process of extending the coarse-grained particle model including a particle chain formed by bond pairs of coarse-grained particles bonded by an unbreakable bond potential in which the potential on the long-distance side is infinite, and acquiring a bond length group of all bond pairs in the equilibration process as a first bond length group; performing an equilibration process for performing a molecular dynamics calculation on the coarse-grained particle model after performing the stretching process under analysis conditions including a constant volume condition and a constant temperature condition, and acquiring a bond length group of all bond pairs in the equilibration process as a second bond length group; Calculating an anomaly of the bond length of each bond pair in the second bond length group with respect to the first bond length group; executing a determination process for determining whether or not the coarse-grained particle model is broken based on a maximum abnormality degree among the calculated multiple abnormality degrees; A program for causing one or more processors to execute the above.

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