A virtual tensile experiment teaching system based on lightweight CAE
The lightweight CAE virtual tensile experiment teaching system solves the problems of expensive and complex operation of traditional experimental equipment, and realizes low-cost, safe and repeatable material mechanics experiment teaching, enhancing students' interactivity and intuitive understanding.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JILIN UNIVERSITY
- Filing Date
- 2026-06-05
- Publication Date
- 2026-07-10
AI Technical Summary
Existing teaching methods for tensile mechanics experiments suffer from problems such as expensive equipment, high costs, complex operation, poor safety, poor interactivity, and insufficient repeatability, making it difficult to meet the teaching needs of most undergraduate students.
Design a virtual tensile test teaching system based on lightweight CAE, including a virtual laboratory environment module, a user interaction and UI design module, and a calculation program code module. Integrate modeling, calculation, and visualization functions, and simplify the operation process and reduce the calculation requirements by automatically generating sample models and meshes and adopting a branching algorithm and incremental loading-result frame playback mechanism.
It lowers teaching costs and barriers, enhances interactivity and teaching intuitiveness, and achieves safety and repeatability. Students can conduct multiple experiments anytime and anywhere to intuitively understand the impact of material parameters on mechanical properties.
Smart Images
Figure CN122369322A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of virtual simulation experimental teaching technology, and in particular relates to a virtual stretching experimental teaching system based on lightweight CAE. Background Technology
[0002] Tensile testing is one of the most important experiments in the teaching of mechanics of materials. By observing the mechanical phenomena of ductile and brittle materials during the tensile process, students can understand the concepts of elasticity, plasticity, yield, necking, and fracture, as well as the physical meaning of parameters such as elastic modulus and yield strength.
[0003] Currently, there are three main teaching methods for tensile experiments in mechanics of materials, each with its own obvious drawbacks:
[0004] (1) Traditional physical experiment teaching: Equipment such as electronic universal testing machines are expensive and have high maintenance costs. Tensile specimens are consumable materials, which are also expensive. At the same time, due to limitations of space, class time and safety factors, students can usually only watch the teacher's demonstration or complete the experiment in groups once, and it is difficult to operate repeatedly and independently.
[0005] (2) Virtual simulation experiment teaching: Most existing virtual laboratories focus on demonstrating the experimental process, and the display of the mechanical properties of the materials themselves is relatively simplified. Although some systems can display stress-strain curves, they are limited to the demonstration of a few preset materials. Students cannot generate corresponding simulation phenomena in real time according to different input material parameters, and it is difficult to intuitively understand the impact of parameter changes on experimental results.
[0006] (3) Numerical simulation teaching based on professional finite element software: Although commercial finite element software (such as ANSYS and Abaqus) can perform high-precision simulations, its operation is complex, involving multiple professional steps such as geometric modeling, mesh generation, and solution control. The learning cost is high and the computer configuration requirements are high, making it unsuitable as a rapid teaching tool for most undergraduate students.
[0007] Therefore, there is an urgent need for a virtual stretching experiment teaching system that can balance intuitive teaching, convenient operation, low dependence on computing power, and interactive parameters. Summary of the Invention
[0008] The purpose of this invention is to provide a virtual stretching experiment teaching system based on lightweight CAE, which aims to solve the problems mentioned in the background art.
[0009] The present invention is implemented as follows: a virtual stretching experiment teaching system based on lightweight CAE, comprising:
[0010] The virtual laboratory environment module is used to simulate a real laboratory environment, including models of experimental instruments.
[0011] The user interaction and UI design module provides an interface for users to interact with the experimental instrument model and receives user input of material type and material property parameters; and
[0012] The computational program code module integrates modeling, computation, and visualization functions, including:
[0013] The modeling and mesh generation submodule is used to automatically generate the specimen model and mesh based on the preset standard specimen size and mesh generation number.
[0014] The core calculation submodule is used to call the corresponding plastic material simulation calculation process or brittle material simulation calculation process according to the material type selected by the user, and calculate the mechanical response data of the specimen in each incremental loading step.
[0015] The results visualization submodule is used to save the mechanical response data generated by the core calculation submodule as result frames, play them sequentially to form a continuous stretching animation, and output the simulation results.
[0016] The present invention provides a virtual stretching experiment teaching system based on lightweight CAE, the advantages of which are as follows:
[0017] (1) Reduce teaching costs and barriers: Through a fully virtualized environment, there is no need for expensive physical testing machines and consumable specimens. The system automatically completes complex operations such as modeling and mesh generation. Users only need to select the material type and input a few parameters to start the simulation, which greatly reduces the operating threshold.
[0018] (2) Enhance interactivity and intuitiveness of teaching: Users can freely input various material parameters such as elastic modulus and yield strength. The system can generate corresponding tensile animations, stress / strain cloud diagrams and fracture effects in real time, enabling students to intuitively and deeply understand the influence of different material parameters on mechanical properties.
[0019] (3) Achieve lightweight calculation: By adopting a branched special simplification algorithm for ductile and brittle materials and using an "incremental loading-result frame playback" mechanism, the complete nonlinear iterative solution in traditional finite element software is avoided, which significantly reduces the demand for computer computing power and ensures smooth operation in teaching scenarios.
[0020] (4) Improve teaching safety and repeatability: Students can conduct experiments anytime and anywhere, repeatedly without any safety risks, which helps to consolidate and deepen theoretical knowledge. Attached Figure Description
[0021] Figure 1 Modeling diagram of the electronic universal testing machine;
[0022] Figure 2A model diagram for a micrometer;
[0023] Figure 3 A model diagram for the virtual laboratory;
[0024] Figure 4 This is the input interface for brittle material parameters.
[0025] Figure 5 This is the input interface for ductile material parameters;
[0026] Figure 6 A schematic diagram of a virtual tensile experiment teaching system based on lightweight CAE provided in an embodiment of the present invention;
[0027] Figure 7 A flowchart of a virtual stretching experiment teaching system based on lightweight CAE provided for embodiments of the present invention;
[0028] Figure 8 This is the system prompt interface;
[0029] Figure 9 This is the material selection interface.
[0030] In the attached diagram: Virtual laboratory environment module 1; User interaction and UI design module 2; Calculation program code module 3; Modeling and mesh generation sub-module 31; Core calculation sub-module 32; Result visualization sub-module 33. Detailed Implementation
[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.
[0032] The specific implementation of the present invention will be described in detail below with reference to specific embodiments.
[0033] like Figure 6 As shown, a virtual stretching experiment teaching system based on lightweight CAE is provided in one embodiment of the present invention, comprising:
[0034] Virtual Laboratory Environment Module 1: This module simulates a real laboratory environment. To accurately reproduce the environment layout and equipment structure, SolidWorks was used to create detailed models of important instruments such as the electronic universal testing machine and micrometer (see...). Figure 1 , Figure 2 The experimental instrument model was obtained, and then imported into a classroom scene built with the Unity3D engine and placed in the corresponding positions to recreate the original appearance of the laboratory (see...). Figure 3 This allows users to familiarize themselves with the laboratory environment and the function of each piece of equipment in advance.
[0035] User Interaction and UI Design Module 2 provides an interface for users to interact with virtual experimental instruments and receives user input of material types and material property parameters. This module enhances the realism and operability of the virtual laboratory by enabling users to interact with experimental instrument models within the scene (e.g., using a micrometer to measure sample diameter) through editing interaction scripts for virtual characters and objects in the scene (such as a micrometer).
[0036] The specific operating procedures are as follows: Figure 7 As shown: After the user approaches the virtual tensile testing machine in the virtual scene, the system pops up a prompt "Press the F key to conduct the experiment" (see...). Figure 8 After pressing the F key, the user enters the material selection interface, where they can choose "ductile materials" (i.e., plastic materials) or "brittle materials" (see...). Figure 9 After selection, the system will enter the corresponding parameter input interface (see...). Figure 4 , Figure 5 Users fill in the material properties as required and click "Start Simulation." The system then automatically calls the calculation program code module 3 for subsequent processing. This UI design is simple and clear, greatly simplifying the simulation operation.
[0037] Calculation program code module 3, which is the core of this invention, integrates modeling, calculation, and visualization functions, and specifically includes:
[0038] Modeling and Meshing Submodule 31: The system pre-sets the dimensions (including length, width, and thickness) and mesh size of standard tensile specimens. It can automatically generate specimen models and meshes without requiring users to manually create specimen models or meshes.
[0039] For ductile materials: the system uses a dog-bone shaped specimen grid with transition sections to accurately determine the location of localized necking during tensile testing.
[0040] For brittle materials: The system adopts an independent continuous mesh generation method to avoid pre-set mid-seam or ductile necking mesh features, so that the brittle sample remains continuous and intact before fracture and is separated after the fracture condition is met.
[0041] Core Calculation Submodule 32: The core idea of this invention is to simplify the complex modeling, solving, and post-processing processes in engineering-grade finite element software into a lightweight algorithm based on physical principles and numerical calculation methods, geared towards teaching. The system executes a branched calculation process according to the material type.
[0042] The result visualization submodule 33 is used to save the result of each loading step generated by the core calculation submodule as a result frame and play them in sequence to form a continuous stretching animation. At the same time, the simulation results are output through color cloud map, legend and text.
[0043] For the core computing submodule 32, the relevant computing process is as follows:
[0044] (1) The simulation calculation process for plastic materials is as follows:
[0045] For plastic materials, the material property parameters entered by the user include the elastic modulus. Poisson's ratio Yield strength Strength coefficient strain hardening index elongation and total tensile displacement The system converts the aforementioned material property parameters into internal control quantities such as yield, hardening, necking, damage, and fracture, thereby simulating the entire tensile process of ductile materials.
[0046] Elastic phase: The system is based on the elastic modulus Compared to Poisson Estimate the longitudinal tensile and transverse shrinkage tendencies of the specimen using the elastic modulus. Calculate the longitudinal yield strain using Poisson's ratio. Control the overall transverse shrinkage coefficient so that the sample is stretched in the longitudinal direction while shrinking in the transverse direction.
[0047] Yield strain :
[0048]
[0049] in, Indicates will Limited to the interval [ , [Within]. This limitation can prevent extreme parameter inputs from causing instability or distortion in the teaching animation.
[0050] Yield stage: The system calculates the engineering strain based on the current tensile displacement. ,Right now:
[0051]
[0052] in, The length is preset for the sample. The stretching displacement at the current moment increases over time.
[0053] When the engineering strain exceeds the yield strain This indicates that the material has transitioned from elastic deformation to plastic deformation, and the system begins to undergo equivalent plastic strain. The calculation, It is a physical quantity used to represent the degree of plastic deformation of a material. Due to the complexity and high computational requirements of rigorously solving PEEQ, this system calculates... It is not a strict PEEQ, but a simplified version that retains the physical meaning of PEEQ as an estimate reflecting the equivalent plastic strain of an object.
[0054] For the spatial coordinates of the specimen in the longitudinal direction at any node of the plastic deformation stage The system uses the following formula to calculate the equivalent plastic strain:
[0055]
[0056] in, for The equivalent plastic strain, For pre-localization coefficients, This is the scaling factor for the plastic progress. For localization functions, To take the larger of the two values.
[0057] Strengthening and Necking Stages: Most metallic materials exhibit power-law hardening behavior during plastic deformation. Based on the Ludwik-Hollomon power-law hardening concept, the following power-law hardening form describes the flow stress after yielding:
[0058]
[0059] In the formula, This refers to flow stress.
[0060] The corresponding hardening modulus can be obtained from the above formula. :
[0061]
[0062] Hardening modulus It is an indicator of a material's ability to continue hardening. During tensile testing, when the increase in the material's hardening ability is insufficient to offset the decrease in load-bearing capacity caused by the reduction in cross-section, uniform tensile instability occurs and localized necking takes place.
[0063] The system then calculates the necking trigger threshold based on Considerre's instability theory, while also considering the influence of elastic strain, resulting in the following formula:
[0064]
[0065] The above and Substituting into the above formula, we get the following: A univariate equation, obtained by solving the equation. The value is recorded as the neck constriction trigger threshold. .when When this value is reached, it indicates that the sample has begun to neck.
[0066] Next, the system calculates the necking progress variable based on the equivalent plastic strain at the center location. :
[0067]
[0068] In the above formula, This represents the equivalent plastic strain at the center of the specimen. The maximum equivalent plastic strain is obtained by converting the elongation. Indicates will Limited to the interval [ , ]Inside, It is a smooth transition function used to smoothly transition the calculated data from 0 to 1, which can make the necking phenomenon more consistent and avoid abrupt changes in the sample shape.
[0069] To ensure that necking occurs in the middle of the specimen, the system introduces a Gaussian localization weighting function centered on the middle of the specimen. :
[0070]
[0071]
[0072] in, The coordinates of the center position of the sample are This refers to the area affected by neck constriction. It is the localization shape index. It is a localized shaping function in the system that causes necking to occur at the center.
[0073] Based on the physical principle that the cross-sectional dimensions of the specimen decrease locally during the necking stage, the system is subjected to overall tensile process. necking progress variable and localization functions Calculate the equivalent section shrinkage ratio in a two-dimensional display. :
[0074]
[0075]
[0076] in, Indicates will Limited to the interval [ , ]Inside, Indicates will Limited to the range Inside, The overall lateral contraction coefficient is controlled by Poisson's ratio. This is the maximum local necking depth coefficient. This is the neck contraction evolution index. It is the minimum equivalent cross-sectional ratio. It mainly controls the shrinkage size in the transverse direction of the specimen, and is used to represent the necking phenomenon where the middle gradually shrinks during the later stage of stretching.
[0077] Fracture: Elongation It is a commonly used ductility index in material tensile testing, and it is defined as:
[0078]
[0079] in, This is the original gauge length. This is the gauge length after the break. The larger the value, the greater the plastic deformation the material can withstand before fracture. The smaller the value, the weaker the material's ductility, making it more prone to fracture.
[0080] This invention utilizes elongation Calculate the approximate true fracture strain :
[0081]
[0082] Subtracting the strain from the elastic yield portion yields the equivalent plastic strain at fracture. :
[0083]
[0084] It is also known that ductile fracture is closely related to stress triaxiality, and the stress triaxiality at a point... :
[0085]
[0086] in, The stress triaxiality under uniaxial tension is... This is the triaxial magnification factor.
[0087] Then, based on the ductile fracture principle that "fracture strain decreases with increasing triaxiality," the obtained equivalent plastic strain of fracture is... This serves as the benchmark value for subsequent stress triaxiality-corrected fracture progression. The local plastic fracture progression is corrected using stress triaxiality to obtain the corrected equivalent plastic strain at that point. :
[0088]
[0089] In the above formula, This is the triaxiality sensitivity coefficient. Indicates will Limited to the range The formula indicates that when the stress triaxiality in the necking region increases, the local plastic fracture deformation rate decreases, causing damage to accumulate in the necking center region.
[0090] This system uses damage variables. This variable measures the degree of fracture. It draws upon the theories of ductile damage models and cumulative damage fracture criteria. Based on the fracture physics of materials, the system utilizes the equivalent plastic strain increment. Calculate damage variables .
[0091] The equivalent plastic strain increment of the i-th node and damage variables The calculation formula is as follows (for the i-th node, between adjacent loading steps, we have):
[0092]
[0093]
[0094] in, This is the starting point of the plastic progress where damage begins to accumulate, and ; That is, between adjacent loading steps difference; For the next step , The time step for each loading step; For the current step ; Let be the equivalent plastic strain at the fracture point i. Let be the stress triaxiality at the i-th node; Let be the damage variable for the next step of the i-th node; Let i be the damage variable for the i-th node in the current step; Indicates will Limited to the range Inside.
[0095] Based on the Johnson-Cook cumulative damage model, the cumulative damage variable is usually used. A value of 1 is used as the criterion for material failure. To avoid extreme numerical problems that may occur during interpolation calculations, this system uses a fracture threshold. Set as The system uses the maximum damage variable as the fracture criterion. When the following formula is satisfied, the ductile material enters the fracture stage, and the specimen is subjected to fracture display.
[0096]
[0097] in, This represents the maximum damage variable value among all nodes at the current moment. After fracture, the broken specimen is stretched to a certain displacement, completing the tensile process simulation.
[0098] Incremental loading step and result frame: Total stretch displacement The system breaks down the process into several incremental loading steps:
[0099]
[0100] in, For the preset displacement increment, The number of steps to load.
[0101] In each loading step, the system calculates the engineering strain based on the current displacement, and then sequentially calculates the position of each node and the equivalent plastic strain. necking progress variable Localization functions Stress triaxiality Fracture equivalent plastic strain Damage variables Equivalent section shrinkage ratio von Mises stress And the state of the fracture opening. Finally, the above data is saved as a result frame, and played sequentially by the visualization module to form a continuous stretching animation.
[0102] Compared to real-time execution of complete nonlinear iterative solutions, this result frame mechanism can significantly reduce computing power requirements and ensure a smooth teaching demonstration process.
[0103] (2) The simulation calculation process for brittle materials is as follows:
[0104] For brittle materials, the parameters input by the user include the elastic modulus. Poisson's ratio ,tensile strength fracture energy and total tensile displacement .
[0105] Brittle materials are primarily calculated based on linear elastic relationships before fracture:
[0106]
[0107]
[0108]
[0109]
[0110]
[0111] in, and These are the normal stresses in the x and y directions, respectively. and The strains in the x and y directions are respectively. For shear stress, For shear strain;
[0112] Since this system simulates a standard uniaxial tensile process, there is no shear displacement or shear load, and shear strain... Set it to 0.
[0113] The system calculates the maximum principal stress in each loading step. :
[0114]
[0115] User-input tensile strength This is set as the crack initiation threshold for brittle materials. When the condition is met... When the system determines that the material has reached the brittle initiation condition, it begins fracture-related calculations.
[0116] At this point, the system records the corresponding maximum principal strain as the crack initiation principal strain. :
[0117]
[0118] The maximum principal strain is obtained from the formula for calculating the principal strain under plane strain conditions. :
[0119]
[0120] To determine the extent of crack propagation, an equivalent crack initiation displacement is introduced into the system. :
[0121]
[0122] in, The characteristic length of the grid is used to convert dimensionless strain increments into equivalent displacements with length dimensions, and is estimated based on the sample grid size.
[0123] The system uses fracture energy Controlling damage evolution and utilizing fracture energy Calculate the crack displacement threshold :
[0124]
[0125] Then based on the current equivalent crack displacement With crack displacement threshold Ratio calculation of damage variable :
[0126]
[0127] When the damage variable reaches a preset threshold, the system determines that the brittle material has fractured and causes the sample to separate at the fracture site. This reflects the characteristics of brittle materials, which exhibit less plastic deformation and fracture rapidly after reaching the fracture condition.
[0128] like Figures 7-9 As shown, the complete workflow of the system in this embodiment is as follows:
[0129] Step 1: The user enters the virtual laboratory scene and approaches the virtual tensile testing machine.
[0130] Step 2: The system prompts the user to press the interaction key F to enter the tensile test simulation interface, where the user selects the material type (plastic material or brittle material).
[0131] Step 3: The system displays the corresponding parameter input interface according to the material type, and the user inputs the material parameters and total tensile displacement.
[0132] Step 4: The system automatically generates the sample model and mesh based on the preset standard sample size.
[0133] Step 5: The system calls the corresponding simulation process for ductile or brittle materials based on the material type.
[0134] Step 6: The system calculates the node position, equivalent stress, equivalent plastic strain, damage progress, equivalent section shrinkage ratio and fracture state for each loading step using an incremental loading method.
[0135] Step 7: The system saves each loading step as a result frame and plays them in sequence to form a stretching animation. The simulation results are output through color cloud map, legend, display field switching and result text.
[0136] Through the above process, users can complete virtual simulations of material tensile tests without needing to master professional finite element software knowledge, and intuitively understand the impact of changes in material parameters on mechanical properties.
[0137] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A virtual stretching experiment teaching system based on lightweight CAE, characterized in that, include: The virtual laboratory environment module is used to simulate a real laboratory environment, including models of experimental instruments. The user interaction and UI design module provides an interface for users to interact with the experimental instrument model and receives user input of material type and material property parameters. as well as The computational program code module integrates modeling, computation, and visualization functions, including: The modeling and mesh generation submodule is used to automatically generate the specimen model and mesh based on the preset standard specimen size and mesh generation number. The core calculation submodule is used to call the corresponding plastic material simulation calculation process or brittle material simulation calculation process according to the material type selected by the user, and calculate the mechanical response data of the specimen in each incremental loading step. The results visualization submodule is used to save the mechanical response data generated by the core calculation submodule as result frames, play them sequentially to form a continuous stretching animation, and output the simulation results.
2. The virtual stretching experiment teaching system based on lightweight CAE according to claim 1, characterized in that, For the core calculation submodule, the simulation calculation process for plastic materials is as follows: For plastic materials, the material property parameters entered by the user include the elastic modulus. Poisson's ratio Yield strength Strength coefficient strain hardening index elongation and total tensile displacement ; Elastic phase: The system is based on the elastic modulus Compared to Poisson Estimate the longitudinal tensile and transverse shrinkage tendencies of the specimen; use the elastic modulus Calculate the longitudinal yield strain using Poisson's ratio. Control the overall transverse shrinkage coefficient so that the sample is stretched in the longitudinal direction while shrinking in the transverse direction. Yield strain : in, Indicates will Limited to the interval [ , ]Inside; Yield stage: The system calculates the engineering strain based on the current tensile displacement. ,Right now: in, The length is preset for the sample. The stretch displacement at the current moment; When the engineering strain exceeds the yield strain Then, the system begins to undergo equivalent plastic strain. Calculation; For the spatial coordinates of the specimen in the longitudinal direction at any node of the plastic deformation stage The system uses the following formula to calculate the equivalent plastic strain: in, for The equivalent plastic strain, For pre-localization coefficients, This is the scaling factor for the plastic progress. For localization functions, To take the larger of the two values; Strengthening and Necking Stages: Based on the Ludwik-Hollomon power-law hardening concept, the following power-law hardening form is used to describe the flow stress after material yielding: In the formula, For flow stress; The corresponding hardening modulus is obtained from the above formula. : Based on the Considerre instability theory, the necking trigger threshold was calculated, resulting in the following formula: Will and Substituting into the above formula, we get the following: A univariate equation, obtained by solving the equation. The value is recorded as the neck constriction trigger threshold. ; Next, the system calculates the necking progress variable based on the equivalent plastic strain at the center location. : In the above formula, This represents the equivalent plastic strain at the center of the specimen. The maximum equivalent plastic strain is obtained by converting the elongation. Indicates will Limited to the interval [ , ]Inside, This is a smooth transition function used to smoothly transition the data being processed from 0 to 1; Introducing a Gaussian localization weighting function centered on the middle of the sample : in, The coordinates of the center position of the sample are This refers to the area affected by neck constriction. For localization shape index; Based on the physical principle that the cross-sectional dimensions of the specimen decrease locally during the necking stage, the system is subjected to overall tensile process. necking progress variable and localization functions Calculate the equivalent section shrinkage ratio in a two-dimensional display. : in, Indicates will Limited to the interval [ , ]Inside, Indicates will Limited to the range Inside, The overall lateral contraction coefficient is controlled by Poisson's ratio. This is the maximum local necking depth coefficient. This is the neck contraction evolution index. The minimum equivalent section ratio; Fracture: Elongation The definition of is: in, This is the original gauge length. This is the gauge length after the break. Using elongation Calculate the approximate true fracture strain : Subtracting the strain from the elastic yield portion yields the equivalent plastic strain at fracture. : Stress triaxiality at a point : in, The stress triaxiality under uniaxial tension is... This is the triaxial magnification factor; Then, the obtained fracture equivalent plastic strain This serves as the benchmark value for subsequent stress triaxiality-corrected fracture progression; by correcting the local plastic fracture progression using stress triaxiality, the corrected equivalent plastic strain at that point is obtained. : In the above formula, This is the triaxiality sensitivity coefficient. Indicates will Limited to the range Inside; Using damage variables To measure the degree of fracture, based on the fracture physics mechanism of materials, the system utilizes the equivalent plastic strain increment. Calculate damage variables ; The equivalent plastic strain increment of the i-th node and damage variables The calculation formula is as follows: in, This is the starting point of the plastic progress where damage begins to accumulate, and ; For the next step , The time step for each loading step; For the current step ; Let be the equivalent plastic strain at the fracture point i. Let be the stress triaxiality at the i-th node; Let be the damage variable for the next step of the i-th node; Let i be the damage variable for the i-th node in the current step; Indicates will Limited to the range Inside; Based on the Johnson-Cook cumulative damage model, the cumulative damage variable... The system uses 1 as the criterion for material failure; the system uses the maximum damage variable as the fracture criterion. When the following formula is satisfied, the ductile material enters the fracture stage and the specimen is subjected to fracture display. in, The fracture threshold; This represents the maximum value of the damage variable across all nodes at the current moment. Incremental loading step and result frame: Total stretch displacement The system breaks down the process into several incremental loading steps: in, For the preset displacement increment, To load the number of steps; In each loading step, the system calculates the engineering strain based on the current displacement, and then sequentially calculates the position of each node and the equivalent plastic strain. necking progress variable Localization functions Stress triaxiality Fracture equivalent plastic strain Damage variables Equivalent section shrinkage ratio von Mises stress The data includes the fracture opening status; finally, the above data is saved as a result frame and played sequentially by the visualization module to form a continuous stretching animation.
3. The virtual stretching experiment teaching system based on lightweight CAE according to claim 2, characterized in that, Fracture threshold Set to 0.
995.
4. The virtual stretching experiment teaching system based on lightweight CAE according to claim 1, characterized in that, For the core computational submodule, the simulation computation process for brittle materials is as follows: For brittle materials, the parameters input by the user include the elastic modulus. Poisson's ratio ,tensile strength fracture energy and total tensile displacement ; Brittle materials are calculated based on linear elasticity before fracture: in, and These are the normal stresses in the x and y directions, respectively; and The strains are in the x and y directions, respectively. Shear stress; For shear strain, and shear strain Set to 0; The system calculates the maximum principal stress in each loading step. : User-input tensile strength Set as the crack initiation threshold for brittle materials, when the following conditions are met... When the system determines that the material has reached the brittle initiation condition, it begins fracture-related calculations. At this point, the system records the corresponding maximum principal strain as the crack initiation principal strain. : The maximum principal strain is obtained from the formula for calculating the principal strain under plane strain conditions. : To determine the extent of crack propagation, an equivalent crack initiation displacement is introduced into the system. : in, The mesh feature length is used to convert dimensionless strain increments into equivalent displacements with length dimensions. The system uses fracture energy Controlling damage evolution and utilizing fracture energy Calculate the crack displacement threshold : Then based on the current equivalent crack displacement With crack displacement threshold Ratio calculation of damage variable : When the damage variable reaches a preset threshold, the system determines that the brittle material has fractured and causes the sample to separate at the fracture site.
5. The virtual stretching experiment teaching system based on lightweight CAE according to claim 1, characterized in that, The modeling and mesh generation submodule uses a dog-bone shaped sample mesh with transition sections for ductile materials and a continuous mesh without preset midline or necking features for brittle materials.
6. The virtual stretching experiment teaching system based on lightweight CAE according to claim 1, characterized in that, The user interaction and UI design module is configured such that when a user approaches the virtual tensile testing machine in the virtual scene, an interactive prompt pops up; after the user triggers the interaction, they enter the material selection interface, and the corresponding parameter input interface is displayed according to the selected material type. After the user fills in the material properties as required and starts the simulation, the system automatically calls the calculation program code module for subsequent processing.