Polymer model simulation method and simulation program

Abstract

To provide a new method for obtaining stress distribution in a polymer model.SOLUTION: In a polymer model simulation method, a computer executes simulation that includes the movement of each particle by a molecular dynamics method using a polymer model containing a plurality of particles. The polymer model simulation method includes dividing a simulation region into a plurality of sections, identifying the particles included in each of the sections in at least any of a plurality of steps from a start to an end of the simulation to calculate, for each section, an average value of von Mises stress of the particles included in the section as a stress average value.SELECTED DRAWING: Figure 4

Description

Technical Field

[0001] The present invention relates to a method for simulating a polymer model and a simulation program.

Background Art

[0002] For example, a method for simulating a polymer model by the molecular dynamics method as described in Patent Document 1 and Patent Document 2 is known. In the simulation method by the molecular dynamics method, the time-series change in the position of each particle can be obtained by solving the equation of motion for each particle constituting the polymer model. Furthermore, the motion of each particle can be observed by visualizing each particle.

Prior Art Documents

Patent Documents

[0003]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[0004] By the way, when simulating a test or phenomenon in which stress concentration occurs, such as a crack propagation test of a polymer material, it is required to obtain the stress distribution in the polymer model. However, conventionally, a method for successfully obtaining the stress distribution has not been established.

[0005] Therefore, an object of the present invention is to provide a new method for obtaining the stress distribution in a polymer model.

Means for Solving the Problems

[0006] The present invention includes the embodiments shown below.

[0007] [1] In a method for simulating a polymer model, a computer performs a simulation including the movement of each of a plurality of particles in the polymer model by the molecular dynamics method. The simulation region is divided into a plurality of compartments. At least in any one of a plurality of steps from the start to the end of the simulation, the particles contained in each of the compartments are specified, and for each compartment, the average value of the von Mises stress of the particles contained in that compartment is calculated as the stress average value. A method for simulating a polymer model.

[0008] [2] In each of a plurality of steps from the start to the end of the simulation, the stress average value is calculated for each of the compartments. The method for simulating a polymer model according to [1].

[0009] [3] The simulation is a simulation of the polymer model in which a crack is formed. For a portion including the tip of the crack and spanning a plurality of the compartments, each of the compartments is colored according to the magnitude of the stress average value. The method for simulating a polymer model according to [1] or [2].

[0010] [4] The shape of the compartment is a cube, and the plurality of particles included in the polymer model are set as spheres all having the same diameter or as a plurality of types of spheres having different diameters in terms of size and shape. The length of the side of the cube is 2 to 3 times the diameter of the most numerous spheres. The method for simulating a polymer model according to any one of [1] to [3].

[0011] [5] A program for simulating a polymer model that causes the computer to execute the method according to any one of [1] to [4]. [Advantages of the Invention]

[0012] According to the above embodiment, the stress distribution in the polymer model can be obtained. [Brief Description of the Drawings]

[0013]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Mode for Carrying Out the Invention

[0014] The embodiments will be described with reference to the drawings. Note that the embodiments described below are merely examples, and those appropriately modified without departing from the gist of the present invention are included in the scope of the present invention.

[0015] First, the overall configuration of the simulation device 10 that executes the method of the present embodiment will be described. The simulation device 10 is realized by a computer including a processing device, a storage device, an input device, a display device, etc. As the storage device, RAM (Random Access Memory), ROM (Read Only Memory), HDD (Hard Disk Drive), etc. are provided. Further, the processing device is composed of a CPU (Central Processing Unit), etc.

[0016] As shown in FIG. 1, the simulation device 10 includes a model creation unit 11, a setting unit 12, an analysis unit 13, and a visualization unit 14. Each of these units is realized by the cooperation of software and hardware when the processing device reads and executes a program stored in the storage device. In this embodiment, it is assumed that one computer executes the processing of each unit, but a plurality of computers connected via a network may function as the simulation device 10.

[0017] Various data necessary for this embodiment are stored in the above storage device. The input device includes a keyboard, a mouse, etc., and is appropriately used in scenes such as creating a polymer model 30 and setting conditions, which will be described later. The display device is, for example, a liquid crystal display, and the simulation results, etc. are displayed.

[0018] Next, each of the model creation unit 11, the setting unit 12, the analysis unit 13, and the visualization unit 14 will be described. The simulation device 10 of this embodiment executes a simulation of the crack propagation when an initial crack 22 is introduced into a rubber sample 20 held and extended by upper and lower jigs 21 as shown in FIG. 2, and visualizes the distribution of the von Mises stress at at least some steps during the simulation.

[0019] The model creation unit 11 generates or acquires a polymer model 30 from the outside. The polymer model 30 is a model of a rubber member, specifically, the rubber sample 20 used in the crack propagation test, and is a three-dimensional model.

[0020] Figure 3 shows an enlarged view of a part of the polymer model 30. As shown in Figure 3, the polymer model 30 includes a plurality of polymer models 33 and a plurality of crosslinking agent particles 32 (black circles in Figure 3). Each polymer model 33 is formed by a plurality of polymer particles 31 (white circles in Figure 3) connected linearly or branchedly. The crosslinking agent particles 32 bond the polymer models 33 together. A non-bonding potential is set between each particle and other particles. Also, a bonding potential is set between the bonded particles. In addition, each particle is numbered so that the movement of the particles can be tracked.

[0021] All the polymer particles 31 are set as spheres of the same diameter. Also, all the crosslinking agent particles 32 are set as spheres of the same diameter. The diameter of the polymer particles 31 and the diameter of the crosslinking agent particles 32 may be the same or different.

[0022] The type of rubber of the rubber sample 20 that is the basis of the polymer model 30 is, for example, styrene-butadiene rubber or butadiene rubber. When the polymer model 30 is a model of styrene-butadiene rubber, it can be considered that the polymer model 33 corresponds to the molecular chain of styrene-butadiene rubber and the crosslinking agent particles 32 correspond to one or more sulfur atoms. Also, when the polymer model 30 is a model of butadiene rubber, it can be considered that the polymer model 33 corresponds to the molecular chain of butadiene rubber and the crosslinking agent particles 32 correspond to one or more sulfur atoms.

[0023] Also, the model creation unit 11 executes an equilibration process for the polymer model 30. The equilibration process is a process of repeatedly performing molecular dynamics calculations of the polymer model 30 until the energy of the polymer model 30 is minimized. After the polymer model 30 is placed in the simulation region described later or after the polymer model 30 is stretched as described below, since the polymer model 30 is not in an equilibrium state, the equilibration process is used to bring the polymer model 30 to an equilibrium state.

[0024] Further, the model creation unit 11 extends the polymer model 30, which is a model of the rubber sample 20, or forms an initial crack 34 (see FIG. 6) in the polymer model 30. As shown in FIG. 2, the crack propagation test simulated in this embodiment is a test in which the upper and lower portions of the rubber sample 20 are constrained by the jigs 21 to extend the rubber sample 20 in the vertical direction, and in this state, an initial crack 22 extending in the left-right direction is formed at the central position in the vertical direction of the rubber sample 20 and the initial crack 22 is propagated. To simulate this crack propagation test, the model creation unit 11 extends the polymer model 30 that reproduces the rubber sample 20 in the vertical direction and forms an initial crack 34 in the polymer model 30. The initial crack 34 can be formed by removing the particles at the location where the crack is to be introduced.

[0025] The setting unit 12 sets the conditions necessary for the simulation. In this embodiment, a simulation with a constant temperature and a constant volume is executed. Therefore, the setting unit 12 sets, as conditions, a predetermined temperature and the shape (including the volume) of the simulation region that is three-dimensional. The entire polymer model 30 is arranged in the set simulation region. In the crack propagation test, since the positions of the upper and lower jigs 21 do not change and the range of the rubber sample 20 also does not change, the shape of the simulation region does not change.

[0026] Further, the setting unit 12 sets the step interval (time interval) and the total number of steps (total number of steps) of the simulation. The simulation in this embodiment is executed by dividing the period from start to end into the steps set at this time.

[0027] Further, the setting unit 12 divides the simulation region into a plurality of sections of the same size for visualization described later. Each section is set as a cube. The size of the section is set to a size that can include the centers of gravity of a plurality of particles inside.

[0028] When the diameters of the polymer particles 31 and the crosslinking agent particles 32 are the same, the length of one side of each compartment is preferably 2 to 3 times the diameter d of the sphere representing those particles. When the diameters of the polymer particles 31 and the crosslinking agent particles 32 are different, the length of one side of each compartment is preferably 2 to 3 times the diameter d of the sphere with the largest number as if they had the same diameter (that is, the sphere representing the polymer particles 31).

[0029] The analysis unit 13 performs a molecular dynamics calculation on the polymer model 30 in which the initial crack 34 is formed. Thereby, a simulation including the movement of each particle constituting the polymer model 30 is executed.

[0030] In addition, the analysis unit 13 calculates the von Mises stress of all particles for each step during the simulation, identifies the particles included in each compartment, and calculates the average value of the von Mises stress of all particles included in each compartment in each compartment. The average value of the von Mises stress of all particles included in one compartment calculated at this time is defined as the stress average value.

[0031] Here, a specific method for calculating the stress average value will be described with reference to FIGS. 4(a) and (b). FIG. 4(a) is a diagram depicting the compartment of the coordinate xyz at step t1, and FIG. 4(b) is a diagram depicting the same compartment at the next step t2. Assume that there are a plurality of polymer particles 31 in this compartment at both step t1 and step t2.

[0032] At step t1, the analysis unit 13 calculates the von Mises stress of each particle in the entire polymer model 30. Next, the analysis unit 13 identifies the particles included in each compartment at step t1. For example, in the case of FIG. 4(a), the analysis unit 13 identifies the polymer particles 31 numbered 2 to 6 as the particles included in the compartment of the coordinate xyz (the square frame in the figure). Here, for particles on the boundary of a plurality of compartments such as the polymer particle 31 numbered 2, they are assumed to be included in the compartment where the center of gravity of the particle is located. The analysis unit 13 also identifies the particles included in other compartments for each compartment.

[0033] Next, the analysis unit 13 calculates, for each section, the average value of the von Mises stresses of all the particles included in that section as the stress average value. For example, in the case of FIG. 4(a), there are five polymer particles 31 numbered 2 to 6 in the section. In this case, if the von Mises stress of each polymer particle 31 is σ i (where i is the particle number), the stress average value σ(x, y, z; t1) is calculated by the following equation.

[0034] [Equation]

[0035] The analysis unit 13 calculates the stress average value by the same equation as Equation 1 for other sections as well.

[0036] In the next step t2, the analysis unit 13 calculates again the von Mises stress of each particle in the entire polymer model 30, identifies the particles included in each section, and calculates the average value of the von Mises stresses of all the particles included in that section as the stress average value. In FIG. 4(b), there are four polymer particles 31 numbered 3 to 6 in the section. In this case, if the von Mises stress of each polymer particle 31 is σ i (where i is the particle number), the stress average value σ(x, y, z; t2) is calculated by the following equation.

[0037] [Equation]

[0038] The analysis unit 13 calculates the stress average value in the same way for other sections as well.

[0039] The analysis unit 13 performs such calculations for all sections at all steps from the start to the end of the simulation. Thereby, the distribution of the stress average value in the polymer model 30 at each step is obtained.

[0040] The visualization unit 14 generates an image and a video that visualize the distribution of the stress average value by either of the following two methods.

[0041] In the first method, the visualization unit 14 generates an image that visualizes the distribution of the stress average value for each step during the simulation. Specifically, the visualization unit 14 colors each section in the simulation region according to the magnitude of the stress average value, and generates an image in which the distribution of the stress average value is represented as a color distribution. Such an image is generated for each step during the simulation. Further, the visualization unit 14 generates a video that continuously plays back the generated images of each step.

[0042] In the second method, the visualization unit 14 calculates the average value for a plurality of consecutive steps for the stress average value of each section. At this time, the average value for a plurality of consecutive steps for the stress average value in one section to be calculated is defined as the time zone average value. The average value (i.e., the time zone average value) σ(x, y, z) of the stress average value from the m-th step to the m + n-th step in the section of coordinates xyz is based on the stress average value σ(x, y, z; t j at the j-th step t j ) of that section, and is calculated by the following formula.

[0043]

Equation

[0044] The visualization unit 14 calculates the time zone average value by the same formula as Equation 3 for other sections. Then, the visualization unit 14 colors each section according to the magnitude of the time zone average value calculated from the formula of Equation 3, thereby generating an image in which the distribution of the time zone average value is represented as a color distribution.

[0045] Such an image based on the time zone average value is generated for all time zones (step ranges consisting of a plurality of consecutive steps) from the start to the end of the simulation. For example, when generating an image from the time zone average values of n consecutive steps, and the total number of steps from the start to the end of the simulation is N, N / n images are generated. Further, the visualization unit 14 generates a video that continuously plays back the generated plurality of images. The number of n above is determined in consideration of the ease of understanding of crack propagation when made into a video, the presence or absence of noise when n is small, the weight of the video, and other circumstances.

[0046] Note that it can be said that the images and videos in which each section is colored according to the magnitude of the time zone average value are also a kind of the images and videos in which each section is colored according to the magnitude of the stress average value.

[0047] In this way, images and videos are generated by either of the above two methods. The range of the generated images and videos may be the entire simulation area, or may be a part of the polymer model 30. The range of the images and videos preferably includes at least the tip of the crack and is a portion that spans a plurality of sections.

[0048] Next, the simulation method of the present embodiment will be described. The simulation device 10 including the above-described respective units executes the simulation method of the present embodiment according to the flowchart shown in FIG. 5.

[0049] First, the simulation device 10 generates or acquires a polymer model 30 as shown in FIG. 3 (S1 in FIG. 5). Next, the simulation device 10 sets a predetermined temperature and the shape of the simulation area as simulation conditions (S2 in FIG. 5). The polymer model 30 is arranged in this simulation area. Further, the simulation device 10 sets the step interval and the total number of steps of the simulation (S3 in FIG. 5). Next, the simulation device 10 executes an equilibration process of the polymer model 30 (S4 in FIG. 5).

[0050] Next, the simulation device 10 extends the polymer model 30 in the vertical direction (S5 in FIG. 5), and after the extension, executes the equilibration process again (S6 in FIG. 5). Next, the simulation device 10 divides the simulation region into a plurality of compartments (S7 in FIG. 5). Next, the simulation device 10 forms an initial crack 34 in the polymer model 30 (S8 in FIG. 5).

[0051] Next, the simulation device 10 executes a molecular dynamics calculation for one step (S9 in FIG. 5). As a result, each particle moves, and the von Mises stress of each particle also changes. Next, the simulation device 10 identifies all the particles within each compartment (S10 in FIG. 5). Next, the simulation device 10 calculates, in each compartment, the average value of the von Mises stress of all the particles within that compartment as the stress average value (S11 in FIG. 5).

[0052] Next, the simulation device 10 checks whether the molecular dynamics calculation for the total number of steps has ended (S12 in FIG. 5). If not (No in S12 in FIG. 5), it executes the molecular dynamics calculation for the next one step (S9 in FIG. 5). Thereafter, until the molecular dynamics calculation for the total number of steps ends, the molecular dynamics calculation and the calculation of the stress average value are repeated.

[0053] And when the molecular dynamics calculation for the total number of steps ends (Yes in S12 in FIG. 5), an image and a video colored according to the magnitude of the stress average value are generated and output (S13 in FIG. 5).

[0054] Note that the order of S1 to S13 in FIG. 5 can be appropriately interchanged within the range where simulation is possible.

[0055] The effects of this embodiment will be described. In this embodiment, the simulation region is divided into a plurality of sections, and at least one of a plurality of steps from the start to the end of the simulation, the particles included in each section are specified, and for each section, the average value of the von Mises stress of the particles included in that section is calculated as the stress average value. Thereby, the stress distribution in the polymer model 30 can be obtained in the form of the distribution of the stress average value for each section.

[0056] Based on the stress distribution obtained in this way, the stress concentration points can be identified. If the stress concentration points can be identified, for example, it becomes possible to observe in detail the movement of the particles at that location and lead to the development of a polymer material that relaxes the stress concentration.

[0057] Also, not only in one step, but in each of a plurality of steps from the start to the end of the simulation, the particles included in each section are specified, and for each section, the average value of the von Mises stress of the particles included in that section is calculated as the stress average value. Therefore, the time-series change of the stress distribution can be confirmed. Also, the time-series change of the stress distribution can be generated as a video.

[0058] Further, the simulation is a simulation of the polymer model 30 in which cracks are formed, and in order to obtain the stress average value for a portion spanning a plurality of sections including the crack tip, the stress distribution near the crack tip where stress concentration is likely to occur can be confirmed. Also, since each section is colored and displayed according to the magnitude of the stress average value, the stress distribution can be visually confirmed.

[0059] Also, as described above, the particles included in the polymer model 30 are set as spheres all having the same diameter in terms of size and shape, or are set as a plurality of types of spheres having different diameters. In either case, if the length of one side of each section is 2 to 3 times the diameter d of the most numerous spheres, an appropriate number of particles will be included in one section, and images and videos of stress distributions that are neither too coarse nor too fine can be generated. Here, the diameter d of the most numerous spheres means the diameter when all the particles included in the polymer model 30 are set as spheres having the same diameter, and means the diameter of the most numerous spheres when a plurality of particles included in the polymer model 30 are set as a plurality of types of spheres having different diameters.

[0060] As an example, the above simulation method was actually executed. In this example, the total number of steps was set to 10,000, and the average value (time-zone average value) of the stress average values of each section was calculated every 100 steps to generate an image. When calculating the stress average value, the length of one side of each section was set to 2d. Also, the vertical and horizontal lengths of the generated image were each set to 120d. Here, d is the diameter of the particles. In the generated image, coloring was performed so that the brighter the stress average value (time-zone average value), the greater it is.

[0061] FIG. 6 is an overall image of the polymer model 30 immediately after the start of the simulation, and FIGS. 7(a) and (b) are images with vertical and horizontal lengths of 120d each, generated by the above simulation method. FIG. 7(a) is an image showing the distribution of the stress average value near the tip of the initial crack 34 immediately after the start of the simulation. The initial crack 34 enters in the direction indicated by the arrow in FIG. 7(a). FIG. 7(b) is an image showing the distribution of the stress average value near the tip of the crack after a predetermined time has elapsed since the start of the simulation. In FIG. 7(b), the darkest part on the left side and at the vertical center is the crack.

[0062] In Fig. 7(a) immediately after the start of the simulation, the initial crack 34 had not spread, and a stress distribution in the vertical direction was observed across the entire image. On the other hand, in Fig. 7(b) after a predetermined time had elapsed, the crack had spread, and stress concentration was observed near the tip of the crack. Thus, in the embodiment, it was possible to obtain the stress distributions immediately after the start of the simulation and after a predetermined time had elapsed, and to confirm the stress concentration near the tip of the crack after a predetermined time had elapsed.

[0063] Also, using the same polymer model 30 as in the embodiment, the simulation method of the comparative example was executed. Specifically, without dividing the simulation region into sections, each particle was colored according to the magnitude of the von Mises stress and visualized as it was. As a result, images and videos were generated in which it was difficult to identify stress concentration locations.

[0064] Various changes can be made to the simulation method described above. For example, the simulation method of the above embodiment is applicable to simulations of various tests (such as tensile tests) in which stress concentration occurs, in addition to crack propagation tests. Also, the simulation method of the above embodiment is applicable to various polymer models containing a plurality of particles.

Description of Reference Numerals

[0065] 10…Simulation device, 11…Model creation unit, 12…Setting unit, 13…Analysis unit, 14…Visualization unit, 20…Rubber sample, 21…Fixture, 22…Initial crack, 30…Polymer model, 31…Polymer particle, 32…Crosslinking agent particle, 33…Polymer model, 34…Initial crack

Claims

1. In a method for simulating a polymer model, a computer performs a simulation including the movement of each of the particles using a polymer model containing a plurality of particles by the molecular dynamics method, divide the simulation region into a plurality of compartments, identify the particles contained in each of the compartments at at least any one of a plurality of steps from the start to the end of the simulation, and calculate, for each compartment, the average value of the von Mises stress of the particles contained in that compartment as the stress average value. A method for simulating a polymer model.

2. Calculate the stress average value for each compartment at each of a plurality of steps from the start to the end of the simulation. The method for simulating a polymer model according to Claim 1.

3. The simulation is a simulation of the polymer model in which a crack is formed, For a portion including the tip of the crack and spanning a plurality of the compartments, color each of the compartments according to the magnitude of the stress average value. The method for simulating a polymer model according to Claim 1 or 2.

4. The shape of the compartment is a cube, The plurality of particles contained in the polymer model are set as spheres all having the same diameter or as a plurality of types of spheres having different diameters in terms of size and shape, The method for simulating a polymer model according to Claim 1 or 2, wherein the length of the side of the cube is 2 to 3 times the diameter of the sphere having the largest number.

5. A program for simulating a polymer model that causes the computer to execute the method according to Claim 1 or 2.

Images