Physical experiment simulation system

Abstract

The invention provides a physical experiment simulation system, and relates to the technical field of material mechanics tests, the physical experiment simulation system is based on an actual stress-strain curve, a simulation test piece three-dimensional model with a gap is established, cells are divided, a typical plane is selected, a groove cell, a slope bottom cell, a stretching cell and a gap cell are divided, and the physical experiment simulation system is obtained. The method comprises the following steps of: performing accurate simulation analysis on each position conveniently, directly simulating a real stretching effect in a stretching cell, acquiring radial stress at a groove cell according to a rotation trend generated by an intermolecular acting force, judging whether a notch cell and a slope bottom cell which serve as stress concentration points are in an elastic deformation stage or not through a vonMises yield criterion, and judging whether the notch cell and the slope bottom cell are in an elastic deformation stage or not. And the deformation condition of each cell caused by the influence of the stress is visualized, and the process and the result of the abnormal test result caused by the gap are intuitively displayed.

Description

Technical Field

[0001] This invention relates to the field of materials mechanics testing technology, specifically a physical experiment simulation system. Background Technology

[0002] Tensile testing is an important test for exploring the physical properties of materials. It is a skill that everyone in the industry must master and an important part of the curriculum. Teaching should not only teach how to use the test, but also teach students to make basic judgments about the test process and results under various conditions. In tensile testing, the problem that has a significant impact on the test results is the presence of defects in the specimen, such as cutting grooves, roughness that does not meet requirements, scratches, and notches. However, if the results of each condition are obtained through field testing, the workload is large and time-consuming, which is not conducive to the teaching process. Therefore, it is necessary to visually demonstrate the impact and changes of such conditions.

[0003] Existing physical simulation systems typically rely on numerical methods such as finite element analysis to study the stress-strain response of materials during tensile processes. These systems are based on constitutive models and stress-strain curves of the material, employing simplified assumptions for simulation. However, current techniques often use macroscopic models, neglecting the specific influence of factors such as local notches, geometry, and load distribution within the material on material deformation. In these simulations, the stress concentration effect in notch or crack regions and the non-uniformity of the deformation process are often difficult to accurately simulate, leading to an inability to accurately predict local fracture and failure of the material.

[0004] The prior art, document CN113420391A, discloses a method for obtaining high-precision hardening model parameters of materials under complex stress states. The method includes: S1, obtaining the force-displacement curve of the material under uniaxial tensile stress; S2, calculating the engineering stress-engineering strain curve; S3, calculating the true stress-true strain curve; S4, calculating the effective stress-strain curve; S5, fitting and extrapolating the effective stress-strain curve to obtain the extrapolated stress-strain curve; S6, adjusting the shape of the fitted curve; S7, establishing numerical models for material samples under different stress states and comparing the force-displacement curves from experimental and simulation results; S8, returning to S6, optimizing the weighting coefficients until the benchmarking results in S7 meet the requirements.

[0005] The publicly available documents demonstrate how to obtain better material parameters through simulation, but they do not disclose the possibility of inaccurate test results due to notches in the specimens during the experiment, nor do they show the experimental process that produces such inaccurate results.

[0006] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0007] The purpose of this invention is to provide a physical experiment simulation system to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides the following technical solution: A physical experiment simulation system, specifically comprising: Data construction module: used to obtain stress-strain curves and elastic modulus of material specimens, construct a three-dimensional model of a simulated specimen with a notch, and divide the parallel segments of the simulated specimen into multiple cells and establish an orthogonal coordinate system. Based on the bevel and the coordinates of the bevel, a typical plane is selected, and the cells in the typical plane are divided into bevel cells, slope bottom cells, tension cells and notch cells. The stretching cell simulation module is used to perform unilateral stretching simulation on the simulated specimen. It sets the stretching step size for each step and performs the stretching simulation of the simulated specimen step by step according to the set step size. After each stretching step, the total stress of the simulated specimen is obtained according to the elastic modulus and stress-strain curve. The axial side length change and axial stress of the stretching cell are obtained according to the total stress and stress-strain curve. Bevel cell simulation module: After each stretching step, it forms an equivalent distance based on the distance between each bevel cell and the notch cell, obtains the axial stress of each bevel cell based on the equivalent distance and the axial stress of the stretching cell, and obtains the radial stress based on the torque generated by the axial stress of each bevel cell. Slope bottom cell simulation module: After each stretching step, it obtains the axial stress of each slope bottom cell based on the total stress and the number of cells in the slope bottom cell plane, determines the side length change of the slope bottom cell based on the stress-strain curve of the axial stress gauge, and obtains the equivalent stress of the notch cell based on the radial stress of the notch cell and the von Mises yield criterion, so as to determine whether the notch cell and each slope bottom cell are in the elastic deformation stage after each stretching step. Plastic Deformation Positioning Module: Used to determine the elastic deformation state of all slope bottom cells and form the judgment condition for the simulated specimen to reach plastic deformation, and record the total step length and total stress when plastic deformation is reached.

[0009] Furthermore, the specimen was subjected to an actual tensile test to obtain its stress-strain curve, and the elastic modulus and yield strength of the elastic deformation stage in the stress-strain curve were obtained.

[0010] Furthermore, a model of the simulated specimen is constructed. The material of the simulated specimen is set to be the same as that of the specimen in the actual experiment. The parallel sections of the simulated specimen are provided with bevels. The simulated specimen is then meshed, and the meshing logic is as follows: The parallel segment of the simulated specimen is divided into multiple closely connected cubes, each cube being a cell. The side length of the cube is less than the bevel length. The bevel is filled in to form a complete cube where it is not long enough. The bottom of the bevel is located at the center of one of the cubes. The cell corresponding to the bottom of the bevel is marked as the gap cell. An orthogonal coordinate system is established along the axial direction. The X-axis of the coordinate system coincides with the axis of the simulated specimen, and the positive direction of the X-axis is towards one of the directions of the axis of the model specimen. The positive direction of the Y-axis is perpendicular to the axis and points to the centroid of the bevel. Point O is the intersection of the X-axis and the Y-axis. The positive direction of the Z-axis is selected to be perpendicular to one of the directions of the XOY plane.

[0011] Furthermore, the cells within the XOY plane are selected as the typical plane, and the cells within the classic plane are divided according to the following logic: The cells immediately adjacent to the bevel in the typical plane are marked as bevel cells, the column of cells parallel to the Y-axis where the bottom of the slope is located is marked as bottom cells, and the remaining cells are marked as stretch cells.

[0012] Furthermore, the tensile step length is set: one end of the simulated specimen is fixed, the other end is marked as the tensile end and a tensile force is applied, the parallel section is set as the strain region, and the clamping section and the transition arc region do not generate strain, but only transmit force. Set the stretching step size so that the stretching end moves by one step each time, and calculate the total stress applied to the parallel segment. The logic for calculating the total stress of the parallel segment is as follows: The total stress is obtained by multiplying the elastic modulus by the step size and then by the number of moves.

[0013] Furthermore, the cell is stretched according to the stress-strain curve. The stretching logic is as follows: change the side length of the cell parallel to the axis, obtain the stress at the current moment, obtain the stretch amount corresponding to the stress by referring to the stress-strain curve, and change the side length of the cell parallel to the axis in the unstressed state by adding the stretch amount, while the other side lengths remain unchanged. The marked stretch cell is only subjected to stress in the axial direction, and the stress magnitude is equal to the total stress magnitude; there is no stress in the radial direction.

[0014] Furthermore, each bevel cell is projected onto the Y-axis, and the distance of each projection from the notch cell is marked as the equivalent distance of the bevel cell. Each bevel cell is stretched, and the stretching process of each bevel cell is the same as that of its adjacent stretched cells. The marked bevel cell is subjected to stress not only in the axial direction but also in the radial direction, as follows: The axial stress is calculated based on the equivalent distance of each bevel cell, as follows: Set the bevel element adjacent to the notch cell to have the same axial stress as the tension cell, and set a gradient value so that the axial stress of each bevel cell decreases by the gradient value as the equivalent distance increases. The radial stress is obtained based on the equivalent distance and axial stress of each bevel element, as follows: Each bevel cell is tightly bound to a stretching cell. There is a molecular force between the two cells, which ensures that the two cells do not slip when the bevel cell is subjected to axial force. The direction of this anti-slipping force is opposite to the axial stress, and the point of application is located outside the cell. It generates a torque on the center of the bevel cell. The value of this torque is obtained. The radial force is obtained by multiplying half the side length of the bevel cell parallel to the X-axis by half the radial force and making the product equal to the value of the torque.

[0015] Further, select a plane in the parallel segment that does not contain the bevel region and is parallel to the YOZ plane. Obtain the number of cells in this plane and mark it as the nominal number. Obtain the number of cells in the YOX plane where the bevel cells are located and mark it as the variation number. Calculate the axial stress of the bevel cells using the nominal number, the variation number, and the axial stress of the tension cells. The logic is as follows: Multiply the axial stress of the stretch cell by the nominal quantity to obtain the product, divide the product by the variation quantity to obtain the quotient, which is the axial stress of the bevel cell. In the calibration bevel cells, only the notched cells have radial force, while the others only have axial force. During the stretching process, the side length of the bottom bevel cells is changed, with the following logic: Obtain the axial stress of the bottom cell, and obtain the elongation under the axial stress according to the stress-strain curve. Add the elongation to the side of the bottom cell that is parallel to the X-axis when it is not subjected to axial force to obtain the changed side length. The side length of the bottom cell that is not parallel to the X-axis remains unchanged. The radial stress of the notch cell is obtained from the radial stress of the bevel cell, with the following logic: Set a reduction factor, which is greater than 0 and less than 1. Sort each bevel cell according to the equivalent distance and obtain the serial number of each bevel cell. Multiply the radial stress of a single bevel cell, the reduction factor and the reciprocal of the serial number to obtain the product. Then sum the products formed by the bevel cells. The sum is the radial stress of the notch cell.

[0016] Furthermore, the equivalent stress of the notched cell is obtained through the von Mises yield criterion, with the following logic: The square of the axial stress is calculated as parameter 1, the square of the radial stress is calculated as parameter 2, and the product of the axial stress and radial stress is calculated as parameter 3. The equivalent stress is obtained by taking the square root of the quotient of parameter 1 plus parameter 2 and then subtracting parameter 3. The equivalent stress is compared with the yield strength. When the equivalent stress exceeds the yield strength, the notched cell is considered to have entered plastic deformation; otherwise, the cell continues to undergo elastic deformation. Meanwhile, other cells in the bevel cell compare the axial stress with the yield limit in real time. When the axial stress exceeds the yield limit, the cell is considered to have entered plastic deformation; otherwise, the cell continues to be elastic deformation. Furthermore, starting from the gap cell, the cells at the bottom of the slope are numbered in the negative Y-axis direction. The cell with number 1 is the gap cell. When the cell reaches the plastic deformation stage, the cell is considered to have disappeared. The cell with number 2 is the gap cell. The equivalent stress of the cell is calculated and compared with the yield limit, and so on. When all cells in the bottom cell have reached the plastic deformation stage, the simulated specimen is considered to have reached the plastic deformation stage. The stretching is stopped and the total step length and total stress are recorded at this time. The total stress and total step length are then visualized. Obtain the coordinates of all cells in the simulated specimen. Using each cell in a typical plane as a reference, each cell represents a column of cells along the Z-axis. The side length changes of the column of cells are the same as those of the cell itself. Visualize the side length changes of all cells in the simulated specimen.

[0017] Compared with the prior art, the beneficial effects of the present invention are: This invention establishes a three-dimensional model of a simulated specimen with a notch based on actual stress-strain curves and divides it into cells. By selecting typical planes and dividing them into bevel cells, slope bottom cells, tension cells, and notch cells, it facilitates accurate simulation analysis at each location. The tension cells directly simulate the real tension effect. At the bevel cells, the radial stress is obtained based on the rotational trend generated by intermolecular forces. The notch cells and slope bottom cells, which are stress concentration points, are used to determine whether they are in the elastic deformation stage using the von Mises yield criterion. The deformation of each cell under stress is visualized, intuitively showing the process and results of abnormal test results caused by the notch.

[0018] By introducing a progressive stretching and refined cell analysis method, the stress and deformation state of the material in each stretching step can be accurately simulated. In particular, for specimens with notches, the stress state of each cell can be dynamically evaluated, and it can be determined in real time whether it has entered the plastic deformation stage, thereby accurately predicting the plastic deformation location and stretching amount of the material. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the system structure of the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0021] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0022] Please see Figure 1 The present invention provides a technical solution: A physical experiment simulation system, specifically comprising: Data construction module: used to obtain stress-strain curves and elastic modulus of material specimens, construct a three-dimensional model of a simulated specimen with a notch, and divide the parallel segments of the simulated specimen into multiple cells and establish an orthogonal coordinate system. Based on the bevel and the coordinates of the bevel, a typical plane is selected, and the cells in the typical plane are divided into bevel cells, slope bottom cells, tension cells and notch cells. The data construction module includes the following components: The specimen was subjected to an actual tensile test to obtain its stress-strain curve, and the elastic modulus and yield strength of the elastic deformation stage in the stress-strain curve were obtained.

[0023] The elastic modulus is a measure of a material's resistance to elastic deformation, while the yield strength is the threshold for a material to enter the plastic stage. Directly using experimental values ​​instead of theoretical values ​​means that the simulation system has been upgraded from a "general theoretical deduction tool" to a "predictive system for specific material specimens." This allows the simulation results to directly correlate with and predict the actual mechanical behavior of the batch and the material, providing realistic input parameters for all subsequent calculations and achieving a precise mapping from the physical world to the digital space.

[0024] A model of the simulated specimen is constructed, and the material of the simulated specimen is set to be the same as that of the specimen in the actual experiment. The parallel sections of the simulated specimen are provided with bevels. The simulated specimen is then meshed, and the meshing logic is as follows: The parallel segment of the simulated specimen is divided into multiple closely connected cubes, each cube being a cell. The side length of the cube is less than the bevel length. The bevel is filled in to form a complete cube where it is not long enough. The bottom of the bevel is located at the center of one of the cubes. The cell corresponding to the bottom of the bevel is marked as the gap cell. Discretizing the specimen into cells is fundamental to numerical simulation. The setting that "cell side length is less than bevel length" ensures that there are enough cells at the root of the notch where stress changes most drastically to depict the stress gradient, avoiding the smoothing of peak stress due to an overly large mesh. Filling in areas that cannot form complete cells ensures the geometric integrity of the computational model and prevents mesh voids that could interrupt force flow. Finally, the cell at the bottom of the slope is designated as the "notch cell," which is like installing a high-powered microscope probe on the digital model, clarifying the focus of the entire system analysis and providing a clear object for all subsequent analyses regarding stress concentration and plastic initiation.

[0025] An orthogonal coordinate system is established along the axial direction. The X-axis of the coordinate system coincides with the axis of the simulated specimen, and the positive direction of the X-axis is towards one of the directions of the axis of the model specimen. The positive direction of the Y-axis is perpendicular to the axis and points to the centroid of the bevel. Point O is the intersection of the X-axis and the Y-axis. The positive direction of the Z-axis is selected to be perpendicular to one of the directions of the XOY plane.

[0026] Aligning the X-axis with the central axis allows for the most intuitive representation and calculation of all deformations and stresses (axial) along the specimen's direction. Pointing the Y-axis to the bevel centroid naturally directs attention to the bevel direction that causes asymmetry. This coordinate system precisely aligns the specimen's geometric features (central axis, bevel direction) with the directions of mechanical analysis (axial, radial), greatly simplifying the subsequent descriptions and programming of distance projection, stress direction decomposition, and moment calculations. It serves as a bridge connecting the geometric model and the mechanical algorithm.

[0027] Select the cells in the plane containing XOY as the typical plane, and divide the cells within the classic plane according to the following logic: The cells immediately adjacent to the bevel in the typical plane are marked as bevel cells, the column of cells parallel to the Y-axis where the bottom of the slope is located is marked as bottom cells, and the remaining cells are marked as stretch cells.

[0028] For many symmetrical or quasi-symmetrical specimens, representing the behavior of the entire three-dimensional body through a characteristic profile (typical plane) is an efficient and reliable method in engineering analysis. Based on this, dividing the cells into "stretch cells," "bevel cells," and "bottom cells" essentially assigns them roles in the overall mechanical drama: stretch cells represent the "background region" far from the notch and with a simple stress state; bevel cells represent the "transition region" with a complex stress state due to notch geometric perturbation; and bottom cells represent the "core region" with the most severe stress concentration. This classification lays the foundation for subsequently using different simulation rules with increasing complexity (from simple uniaxial stress to complex multiaxial stress), achieving optimized allocation of computational resources.

[0029] The stretching cell simulation module is used to perform unilateral stretching simulation on the simulated specimen. It sets the stretching step size for each step and performs the stretching simulation of the simulated specimen step by step according to the set step size. After each stretching step, the total stress of the simulated specimen is obtained according to the elastic modulus and stress-strain curve. The axial side length change and axial stress of the stretching cell are obtained according to the total stress and stress-strain curve. The stretched cell simulation module includes the following: One end of the simulated specimen is fixed, and the other end is marked as the tensile end and a tensile force is applied. The parallel section is set as the strain region, while the clamping section and the transition arc region do not generate strain and only transmit force. The force transmission path was clearly defined (from the tensile end through the clamping section and the transition section, ultimately acting entirely on the parallel section), and the influence of deformation in the non-test area (clamping section) on the results was eliminated. This ensured the "experimental comparability" of the simulation, allowing the simulated total stress-total deformation relationship to be directly calibrated and verified with the real stress-strain curve, establishing a correct and verifiable mechanical response baseline for the entire system.

[0030] Set the stretching step size so that the stretching end moves by one step each time, and calculate the total stress applied to the parallel segment. The logic for calculating the total stress of the parallel segment is as follows: The total stress is obtained by multiplying the elastic modulus by the step size and then by the number of moves.

[0031] The step size controls the simulation's accuracy and computational load. A "displacement-controlled" rather than "force-controlled" loading method is used (the step size is given first, then the resulting stress is calculated), consistent with the control modes of many practical testing machines. The "total displacement" (step size × number of simulations) is converted to "total stress" using the elastic modulus. The underlying physical logic is that in the overall elastic phase, the specimen acts like a linear spring, its overall stiffness determined by the material (elastic modulus) and geometry (initial length of the parallel segment, implicitly included in the calculation). This step provides the system with the global driving force (total stress) value at each simulation moment, serving as the source for distributing stress to each cell.

[0032] The cell is stretched according to the stress-strain curve. The stretching logic is as follows: change the side length of the cell parallel to the axis, obtain the stress at the current moment, obtain the stretch amount corresponding to the stress by referring to the stress-strain curve, and change the side length of the cell parallel to the axis in the unstressed state by adding the stretch amount, while the other side lengths remain unchanged. The marked stretch cell is only subjected to stress in the axial direction, and the stress magnitude is equal to the total stress magnitude; there is no stress in the radial direction.

[0033] The stretching cell strictly adheres to the classic assumption of uniaxial tension: uniform stress distribution and deformation occurring only in the direction of force. This definition has a dual significance: firstly, it provides the most direct scenario for the application of stress-strain curves—the elongation of the cell is entirely determined by the current total stress through curve lookup, making the behavior clear and predictable; secondly, it establishes a baseline value (equal to the total stress) for the stress state of the "stretching cell." Regardless of how the stress in subsequent "bevel cells" changes, their calculations must be based on this baseline value, thus ensuring the coordination and logical consistency of stress calculations throughout the entire simulation system.

[0034] Bevel cell simulation module: After each stretching step, it forms an equivalent distance based on the distance between each bevel cell and the notch cell, obtains the axial stress of each bevel cell based on the equivalent distance and the axial stress of the stretching cell, and obtains the radial stress based on the torque generated by the axial stress of each bevel cell. The bevel cell simulation module includes the following: Project each bevel cell onto the Y-axis, mark the distance of each projection from the notch cell as the equivalent distance of the bevel cell, stretch each bevel cell, and the stretching process of each bevel cell is the same as that of its adjacent stretching cells. The primary contradiction is that stress attenuates most significantly along the direction perpendicular to the notch (Y-axis) as it diffuses outward from the notch root. The equivalent distance provides a "position coordinate" for each bevel cell, enabling the stress gradient distribution rule to be implemented. Using a simple geometric mapping to simulate the physical phenomenon that stress field contour lines are approximately perpendicular to the notch leading edge is a key mathematical tool for realizing the transition from a uniform stress field to a non-uniform stress field.

[0035] The marked bevel cell is subjected to stress not only in the axial direction but also in the radial direction, as follows: The axial stress is calculated based on the equivalent distance of each bevel cell, as follows: Set the bevel element adjacent to the notch cell to have the same axial stress as the tension cell, and set a gradient value so that the axial stress of each bevel cell decreases by the gradient value as the equivalent distance increases. Although the stress state of the beveled cells is more complex, they are geometrically bonded to the adjacent material (represented by the stretched cells), therefore their displacements in the axial direction must be continuous. This definition prevents non-physical "detachment" or "overlap" in the simulation, ensuring the kinematic validity of the model. It means that the complex stress of the beveled cells is a result of their "forced" deformation along with the surrounding material, which is a manifestation of stress redistribution caused by strain coordination.

[0036] Saint-Venant's principle states that local non-uniformity at the point of load application decays rapidly with increasing distance. Here, setting the stress in the adjacent notch element equal to the stress in the tensile cell (i.e., undecayed), and then decreasing at a uniform gradient with increasing equivalent distance, is a simplified numerical implementation of this principle. This allows the axial stress in the bevel region to smoothly transition from a high value (potentially exceeding the average stress) at the notch to the average stress value at the far end, intuitively constructing a distribution model for axial stress concentration and dissipation.

[0037] The radial stress is obtained based on the equivalent distance and axial stress of each bevel element, as follows: Each bevel cell is tightly bound to a stretching cell. There is a molecular force between the two cells, which ensures that the two cells do not slip when the bevel cell is subjected to axial force. The direction of this anti-slipping force is opposite to the axial stress, and the point of application is located outside the cell. It generates a torque on the center of the bevel cell. The value of this torque is obtained. The radial force is obtained by multiplying half the side length of the bevel cell parallel to the X-axis by half the radial force and making the product equal to the value of the torque.

[0038] Stress concentration not only increases axial stress but also induces transverse (radial) stress. The logical chain is as follows: due to its special location, the axial force of the beveled cell differs from that of adjacent cells; to maintain deformation compatibility (non-slippage), shear forces are generated on the cell contact surface; this shear force creates a torque about the center of the cell; to balance this torque, a reverse radial force must be generated on the other side of the cell. Thus, starting from the macroscopic geometric discontinuity (bevel), the existence of radial stress is naturally derived through mechanical equilibrium conditions. This allows the simulation system to transcend simple uniaxial tension models and describe the real multiaxial stress state at the notch root, which is crucial for predicting material yielding and failure.

[0039] Slope bottom cell simulation module: After each stretching step, it obtains the axial stress of each slope bottom cell based on the total stress and the number of cells in the slope bottom cell plane, determines the side length change of the slope bottom cell based on the stress-strain curve of the axial stress gauge, and obtains the equivalent stress of the notch cell based on the radial stress of the notch cell and the von Mises yield criterion, so as to determine whether the notch cell and each slope bottom cell are in the elastic deformation stage after each stretching step. The slope bottom cell simulation module includes the following: Select a plane in the parallel segment that does not contain the bevel region and is parallel to the YOZ plane. Obtain the number of cells in this plane and mark it as the nominal number. Obtain the number of cells in the YOX plane where the bevel cell is located and mark it as the variation number. Calculate the axial stress of the bevel cell using the nominal number, the variation number, and the axial stress of the tension cell. The logic is as follows: Multiply the axial stress of the stretch cell by the nominal quantity to obtain the product, divide the product by the variation quantity to obtain the quotient, which is the axial stress of the bevel cell. The total axial force on any cross-section of a parallel segment is the same (ignoring inertia). In a complete cross-section (nominal number of cells), the force is distributed among more cells, resulting in lower stress in each individual cell. In a notched cross-section (variable number of cells), the same total force is borne by fewer cells, therefore the axial stress in each cell must increase proportionally (multiplied by the nominal / variable ratio). This quantitative relationship is the core of the stress concentration factor concept. From a macroscopic equilibrium perspective, it directly provides the amplification factor of the average axial stress in the notched cross-section and is the fundamental basis for calculating the axial stress in the slope bottom cells (including notched cells).

[0040] In the calibration bevel cells, only the notched cells have radial force, while the others only have axial force. During the stretching process, the side length of the bottom bevel cells is changed, with the following logic: Obtain the axial stress of the bottom cell, and obtain the elongation under the axial stress according to the stress-strain curve. Add the elongation to the side of the bottom cell that is parallel to the X-axis when it is not subjected to axial force to obtain the changed side length. The side length of the bottom cell that is not parallel to the X-axis remains unchanged. The radial stress of the notch cell is obtained from the radial stress of the bevel cell, with the following logic: Set a reduction factor, which is greater than 0 and less than 1. Sort each bevel cell according to the equivalent distance and obtain the serial number of each bevel cell. Multiply the radial stress of a single bevel cell, the reduction factor and the reciprocal of the serial number to obtain the product. Then sum the products formed by the bevel cells. The sum is the radial stress of the notch cell.

[0041] The radial compressive stress borne by the notched cell is the sum of the effects "applied" by each upstream (along the Y-axis) bevel cell to balance its own moment. The reciprocal of the ordinal number serves as a weight, simulating the weakening of the effect with increasing distance; the reduction factor further reflects the dissipation during stress transfer. This method makes the radial stress of the notched cell a "resultant force" that integrates the states of all surrounding cells, which is more reasonable than static assignment and dynamically reflects the construction process of the stress field.

[0042] The equivalent stress of the notched cell is obtained using the von Mises yield criterion, with the following logic: The square of the axial stress is calculated as parameter 1, the square of the radial stress is calculated as parameter 2, and the product of the axial stress and radial stress is calculated as parameter 3. The equivalent stress is obtained by taking the square root of the quotient of parameter 1 plus parameter 2 and then subtracting parameter 3. By transforming complex multiaxial stress states into an equivalent stress comparable to the material's uniaxial yield strength, the initiation of plastic deformation can be scientifically predicted. At the notch root, the material is under biaxial stress, both axially and radially, and yielding cannot be simply determined by whether the axial stress exceeds the uniaxial yield strength. The von Mises criterion calculates the equivalent stress using a formula that incorporates all stress components; this value represents the combined driving effect of the multiaxial stress state on material yielding. Comparing this with the yield limit measured by uniaxial tests is the standard method in engineering for determining whether a material enters plasticity under complex stress. This gives the simulation system the crucial ability to predict "where" and "when" plastic deformation occurs.

[0043] The equivalent stress is compared with the yield strength. When the equivalent stress exceeds the yield strength, the notched cell is considered to have entered plastic deformation; otherwise, the cell continues to undergo elastic deformation. Meanwhile, other cells in the bevel cell compare the axial stress with the yield limit in real time. When the axial stress exceeds the yield limit, the cell is considered to have entered plastic deformation; otherwise, the cell continues to be in elastic deformation.

[0044] While the notched cell is the most dangerous, large-area yielding can also occur in engineering projects due to overall cross-sectional weakening. Continuously comparing the axial stress and yield limit of other cells ensures that the system can capture both early local yielding caused by multiaxial stress (at the notch) and large-scale yielding caused by overall overload. This enhances the robustness and engineering applicability of the simulation.

[0045] Plastic Deformation Positioning Module: Used to determine the elastic deformation state of all slope bottom cells and form the judgment condition for the simulated specimen to reach plastic deformation, and record the total step length and total stress when plastic deformation is reached.

[0046] The visualization module includes the following: Starting from the gap cell, number the cells at the bottom of the slope in the negative Y-axis direction. The cell with number 1 is the gap cell. When the cell reaches the plastic deformation stage, the cell is considered to have disappeared and is not included in any calculation. The cell with number 2 is the gap cell. Continue to calculate the equivalent stress of the cell and compare it with the yield limit, and so on. Once the notched cell yields, it is considered to have "disappeared" (i.e., lost its load-bearing capacity or developed a macroscopic crack), and the focus of the mechanical analysis automatically shifts to the next cell. This is essentially simulating a very simplified crack propagation model: the initial notch becomes blunt or cracked due to yielding, causing the "effective notch" to move forward. This allows the simulation to go beyond "initial prediction" and qualitatively demonstrate the failure process, providing a dynamic perspective for understanding the final fracture mode of the specimen.

[0047] When all cells in the bottom cell have reached the plastic deformation stage, the simulated specimen is considered to have reached the plastic deformation stage. The stretching is stopped and the total step length and total stress are recorded at this time. The total stress and total step length are then visualized. The total step length corresponds to the total deformation, and the total stress corresponds to the maximum bearing capacity (approximate ultimate load). These two data points are the most direct outputs for evaluating material or structural performance and can be directly used for design verification, safety assessment, or comparison with other test results. This completes the closed loop from microscopic mechanism analysis to macroscopic performance evaluation.

[0048] Obtain the coordinates of all cells in the simulated specimen. Using each cell in a typical plane as a reference, each cell represents a column of cells along the Z-axis. The side length changes of the column of cells are the same as those of the cell itself. Visualize the side length changes of all cells in the simulated specimen.

[0049] Assuming that deformation along the Z-axis (thickness direction) is synchronized with the typical XOY plane, the system can efficiently generate a three-dimensional solid model from two-dimensional "slice analysis." This allows users to intuitively observe how the specimen gradually deforms, yields, and eventually fails during tensile testing, especially in the notch area. This visualization is not only a display of results but also a powerful tool for understanding mechanisms, verifying the rationality of simulations, and conveying conclusions to non-experts.

[0050] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0051] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0052] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0053] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A physical experiment simulation system, characterized in that, Specifically, it includes: Data construction module: used to obtain stress-strain curves and elastic modulus of material specimens, construct a three-dimensional model of a simulated specimen with a notch, and divide the parallel segments of the simulated specimen into multiple cells and establish an orthogonal coordinate system. Based on the bevel and the coordinates of the bevel, a typical plane is selected, and the cells in the typical plane are divided into bevel cells, slope bottom cells, tension cells and notch cells. The stretching cell simulation module is used to perform unilateral stretching simulation on the simulated specimen. It sets the stretching step size for each step and performs the stretching simulation of the simulated specimen step by step according to the set step size. After each stretching step, the total stress of the simulated specimen is obtained based on the elastic modulus and stress-strain curve. The axial side length change and axial stress of the stretching cell are obtained based on the total stress and stress-strain curve. Bevel cell simulation module: After each stretching step, it forms an equivalent distance based on the distance between each bevel cell and the notch cell, obtains the axial stress of each bevel cell based on the equivalent distance and the axial stress of the stretching cell, and obtains the radial stress based on the torque generated by the axial stress of each bevel cell. Slope bottom cell simulation module: After each stretching step, it obtains the axial stress of each slope bottom cell based on the total stress and the number of cells in the slope bottom cell plane, determines the side length change of the slope bottom cell based on the stress-strain curve of the axial stress gauge, and obtains the equivalent stress of the notch cell based on the radial stress of the notch cell and the von Mises yield criterion, so as to determine whether the notch cell and each slope bottom cell are in the elastic deformation stage after each stretching step. Plastic Deformation Positioning Module: Used to determine the elastic deformation state of all slope bottom cells and form the judgment condition for the simulated specimen to reach plastic deformation, and record the total step length and total stress when plastic deformation is reached.

2. The physical experiment simulation system according to claim 1, characterized in that: The specimen was subjected to an actual tensile test to obtain its stress-strain curve, and the elastic modulus and yield strength of the elastic deformation stage in the stress-strain curve were obtained.

3. The physical experiment simulation system according to claim 2, characterized in that: A three-dimensional model of the simulated specimen is constructed. The material of the simulated specimen is set to be the same as that of the specimen in the actual experiment. The parallel sections of the simulated specimen are beveled. The simulated specimen is then meshed, and the meshing logic is as follows: The parallel segment of the simulated specimen is divided into multiple closely connected cubes, each cube being a cell. The side length of the cube is less than the bevel length. The bevel is not long enough to form a complete cube, so it is filled in to form a complete cube. The bottom of the bevel is located at the center of one of the cubes. The cell corresponding to the bottom of the bevel is marked as the gap cell. An orthogonal coordinate system is established along the axial direction. The X-axis of the coordinate system coincides with the axis of the simulated specimen, and the positive direction of the X-axis is towards one of the directions of the axis of the model specimen. The positive direction of the Y-axis is perpendicular to the axis and points to the centroid of the bevel. Point O is the intersection of the X-axis and the Y-axis. The positive direction of the Z-axis is selected to be perpendicular to one of the directions of the XOY plane.

4. The physical experiment simulation system according to claim 3, characterized in that: Select the cells in the plane containing XOY as the typical plane, and divide the cells within the classic plane according to the following logic: The cells immediately adjacent to the bevel in the typical plane are marked as bevel cells, the column of cells parallel to the Y-axis where the bottom of the slope is located is marked as bottom cells, and the remaining cells are marked as stretch cells.

5. A physical experiment simulation system according to claim 4, characterized in that: Set the stretching step: Fix one end of the simulated specimen, mark the other end as the stretching end and apply tension. Set the parallel section as the strain region. The clamping section and the transition arc region do not generate strain, but only transmit force. Set the stretching step size so that the stretching end moves by one step each time, and calculate the total stress applied to the parallel segment. The logic for calculating the total stress of the parallel segment is as follows: The total stress is obtained by multiplying the elastic modulus by the step size and then by the number of moves.

6. A physical experiment simulation system according to claim 5, characterized in that: The cell is stretched according to the stress-strain curve. The stretching logic is as follows: change the side length of the cell parallel to the axis, obtain the stress at the current moment, obtain the stretch amount corresponding to the stress by referring to the stress-strain curve, and change the side length of the cell parallel to the axis in the unstressed state by adding the stretch amount, while the other side lengths remain unchanged. The marked stretch cell is only subjected to stress in the axial direction, and the stress magnitude is equal to the total stress magnitude; there is no stress in the radial direction.

7. A physical experiment simulation system according to claim 6, characterized in that: Project each bevel cell onto the Y-axis, mark the distance of each projection from the notch cell as the equivalent distance of the bevel cell, stretch each bevel cell, and the stretching process of each bevel cell is the same as that of its adjacent stretching cells. The marked bevel cell is subjected to stress not only in the axial direction but also in the radial direction, as follows: The axial stress is calculated based on the equivalent distance of each bevel cell, as follows: Set the bevel element adjacent to the notch cell to have the same axial stress as the tension cell, and set a gradient value so that the axial stress of each bevel cell decreases by the gradient value as the equivalent distance increases. The radial stress is obtained based on the equivalent distance and axial stress of each bevel element, as follows: Each bevel cell is tightly bound to a stretching cell. There is a molecular force between the two cells, which ensures that the two cells do not slip when the bevel cell is subjected to axial force. The direction of this anti-slipping force is opposite to the axial stress, and the point of application is located outside the cell. It generates a torque on the center of the bevel cell. The value of this torque is obtained. The radial force is obtained by multiplying half the side length of the bevel cell parallel to the X-axis by half the radial force and making the product equal to the value of the torque.

8. A physical experiment simulation system according to claim 7, characterized in that: Select a plane in the parallel segment that does not contain the bevel region and is parallel to the YOZ plane. Obtain the number of cells in this plane and mark it as the nominal number. Obtain the number of cells in the YOX plane where the bevel cell is located and mark it as the variation number. Calculate the axial stress of the bevel cell using the nominal number, the variation number, and the axial stress of the tension cell, as follows: Multiply the axial stress of the stretch cell by the nominal quantity to obtain the product, divide the product by the variation quantity to obtain the quotient, which is the axial stress of the bevel cell. In the calibration bevel cells, only the notched cells have radial force, while the others only have axial force. During the stretching process, the side length of the bottom bevel cells is changed, with the following logic: Obtain the axial stress of the bottom cell, and obtain the elongation under the axial stress according to the stress-strain curve. Add the elongation to the side of the bottom cell that is parallel to the X-axis when it is not subjected to axial force to obtain the changed side length. The side length of the bottom cell that is not parallel to the X-axis remains unchanged. The radial stress of the notch cell is obtained from the radial stress of the bevel cell, with the following logic: Set a reduction factor, which is greater than 0 and less than 1. Sort each bevel cell according to the equivalent distance and obtain the serial number of each bevel cell. Multiply the radial stress of a single bevel cell, the reduction factor and the reciprocal of the serial number to obtain the product. Then sum the products formed by the bevel cells. The sum is the radial stress of the notch cell.

9. A physical experiment simulation system according to claim 8, characterized in that: The equivalent stress of the notched cell is obtained using the von Mises yield criterion, with the following logic: The square of the axial stress is calculated as parameter 1, the square of the radial stress is calculated as parameter 2, and the product of the axial stress and radial stress is calculated as parameter 3. The equivalent stress is obtained by adding parameter 1 to parameter 2 and subtracting parameter 3, and then taking the square root of the quotient. The equivalent stress is compared with the yield strength. When the equivalent stress exceeds the yield strength, the notched cell is considered to have entered plastic deformation; otherwise, the cell continues to undergo elastic deformation. Meanwhile, other cells in the bevel cell compare the axial stress with the yield limit in real time. When the axial stress exceeds the yield limit, the cell is considered to have entered plastic deformation; otherwise, the cell continues to be elastic deformation.

10. A physical experiment simulation system according to claim 9, characterized in that: Starting from the gap cell, number the cells at the bottom of the slope in the negative Y-axis direction. The cell with number 1 is the gap cell. When the cell reaches the plastic deformation stage, the cell is considered to have disappeared. The cell with number 2 is the gap cell. Continue to calculate the equivalent stress of the cell and compare it with the yield limit, and so on. When all cells in the bottom cell have reached the plastic deformation stage, the simulated specimen is considered to have reached the plastic deformation stage. The stretching is stopped and the total step length and total stress are recorded at this time. The total stress and total step length are then visualized. Obtain the coordinates of all cells in the simulated specimen. Using each cell in the typical plane as a reference, each cell represents a column of cells in the Z-axis direction. The side length of the column of cells changes in the same way as that of the cell.

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