Simulation analysis method for compression set characteristics of rubber pad

Abstract

The application provides a simulation analysis method for compression deformation characteristics of a rubber pad, and relates to the field of rubber pad product testing. The application constructs a finite element grid model based on geometric parameters and initial material parameters of the rubber pad, identifies geometric singularity regions with displacement gradient mutation; applies a test loading load on the model, extracts displacement path curvature and performs gradient correction on material parameters, and constructs a local material constitutive relation; performs compression deformation simulation based on the local constitutive relation, analyzes strain energy accumulation sequence and determines an energy transmission control region; determines a dominant constraint mode in combination with the spatial corresponding relationship between the energy transmission control region and the geometric singularity region, and performs incremental correction on the simulation result, so as to realize accurate prediction of non-uniform compression deformation characteristics of the rubber pad.

Description

Technical Field

[0001] This invention relates to the field of rubber pad product testing technology, and in particular to a simulation analysis method for the compressive deformation characteristics of rubber pads. Background Technology

[0002] Rubber materials, due to their excellent elasticity, cushioning, and vibration isolation properties, are widely used in automobiles, machinery, and bridge construction to achieve vibration reduction and isolation functions. However, under long-term service conditions, rubber pads are usually subjected to continuous compressive loads, which leads to non-uniform deformation characteristics inside them. This deformation difference is more prominent, especially in the edge area of ​​the pad, which can easily cause local over-compression or even cracking damage to the material, thereby reducing the service life of the rubber pad and affecting the overall operational reliability of the equipment.

[0003] Currently, finite element simulation is often used in engineering to predict the deformation behavior and service performance of rubber pads. However, traditional finite element analysis is generally based on the assumption that the stress state of each region of the material is uniform, and fails to take into account the non-uniform compression deformation effect unique to the edge region of the rubber pad under actual working conditions. This results in a certain deviation between the simulation results and the actual situation, making it difficult to effectively prevent local failures of the product during actual operation.

[0004] Therefore, existing technologies urgently need a more accurate simulation analysis method for the compression deformation of rubber pads that closely matches actual working conditions, in order to solve the problem of local failure caused by non-uniform compression deformation and ensure the long-term safe and reliable operation of products. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art; to this end, the present invention proposes a simulation analysis method for the compressive deformation characteristics of rubber pads.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A simulation analysis method for the compressive deformation characteristics of a rubber pad includes: A finite element mesh model is constructed based on the three-dimensional geometric parameters and initial material parameters of the rubber pad, and the target region with geometric singularity potential with displacement gradient mutation potential is determined according to the spatial topological connection relationship of the mesh elements in the finite element mesh model. An initial trial load is applied to the finite element mesh model, and the displacement path curvature distribution of the mesh elements in the geometric singularity target region during the loading process is extracted. Using this as a constraint, the initial material parameters are spatially redistributed to construct a local material constitutive relation with gradient correction characteristics. Based on the local material constitutive relation, the finite element mesh model is subjected to compression deformation analysis to obtain preliminary simulation deformation results. Based on the strain energy accumulation order of mesh elements in the geometric singularity target region in the preliminary simulation deformation results, the energy transfer control region is determined. Based on the spatial correspondence between the energy transfer control region and the geometric singularity target region, the dominant constraint mode of the rubber pad compression deformation is determined, and the preliminary simulation deformation results are incrementally corrected according to the dominant constraint mode to output the final compression deformation characteristic simulation results.

[0007] Furthermore, the process of determining the geometric singularity target region includes: Based on the finite element mesh model, a topological connection network reflecting the continuity of geometric constraints is constructed according to the shared nodes and shared edges between mesh elements; In the topological interconnection network, the set of units in which geometric constraints undergo directional abrupt changes during topological propagation is identified as the geometric inducing feature of displacement gradient evolution; Based on the spatial aggregation state of the unit set in the finite element mesh model, the geometric singularity target region with displacement gradient mutation potential is determined.

[0008] Furthermore, the construction of the topological connection network reflecting the continuity of geometric constraints includes: Using the geometric adjacency relationship of mesh cells as constraints, multi-directional topological connection paths between cells are generated; Based on the continuity constraint of the relative spatial orientation characteristics of the elements in the topological connection path, the topological connection path is screened to obtain a topological connection network for predicting the evolution of displacement gradient.

[0009] Furthermore, the construction of the local material constitutive relation with gradient correction characteristics includes: During the initial trial loading process, the spatial trajectory of the displacement of the mesh element in the geometric singularity target area is extracted in real time with time step, and the curvature distribution of the displacement path is calculated. The displacement path curvature distribution is used as a weighting factor and mapped to the spatial distribution matrix of the initial material parameters to generate a local material constitutive relation constrained by the displacement path curvature.

[0010] Furthermore, the calculation logic for the curvature distribution of the displacement path is as follows: During the continuous loading phase, the coordinate evolution sequence of the displacement trajectory of the mesh element in the geometric singularity target area is recorded in three-dimensional space; Based on the spatial deflection vector of the coordinate evolution sequence between adjacent loading steps, a displacement path curvature distribution is formed to describe the degree of bending of the displacement path.

[0011] Furthermore, the process of determining the energy transfer control region includes: In the process of compressive deformation analysis based on local material constitutive relations, the strain energy evolution records of each mesh element in the geometric singularity target region at different loading stages are obtained; Based on the relationship between the spatial location and the order of occurrence of strain energy in the loading stage, an energy transfer sequence reflecting the dominant propagation direction of strain energy is constructed. The energy transfer control region is determined based on the spatial convergence location of the energy transfer sequence in the finite element mesh model.

[0012] Furthermore, the construction of the energy transfer sequence reflecting the strain energy-dominated propagation direction includes: In the strain energy evolution record, identify the spatially connected grid cell sequence that first reaches the preset threshold and continues to expand to the neighborhood; Based on the spatial extension direction of the mesh element sequence in the finite element mesh model, an energy transfer sequence is formed to characterize the dominant propagation direction of strain energy.

[0013] Furthermore, determining the dominant constraint mode for the compression deformation of the rubber pad includes: The spatial distribution of the energy transfer control region in the finite element mesh model is mapped to the spatial range of the geometric singularity target region, and the spatial topological mapping relationship between regions is established. Based on the physical damping effect of the energy transfer control region on the deformation path of the geometric singularity target region in the spatial location topological mapping relationship, the dominant constraint mode of the rubber pad compression deformation is determined.

[0014] Furthermore, the process of establishing the spatial location topological mapping relationship between the regions includes: Using the geometric boundary of the geometric singularity target region as a spatial reference, determine the relative coordinates of the energy transfer control region within or at the edge of the geometric singularity target region; Based on the geometric constraint interference range formed by the relative coordinates in the geometric singularity target region, a spatial location topological mapping relationship is constructed to describe the constraint relationship between regions.

[0015] Furthermore, the final output simulation results of the pressure transformer characteristics include: Based on the topology of the grid cells within the geometric singularity target region, the topological response weights of the energy transfer control region to the geometric singularity target region under the dominant constraint mode are analyzed. Based on the topological response weights, the local constraint increment of the energy transfer control region on the compressive deformation of the geometric singularity target region is quantitatively calculated; Based on the local constraint increment, the compressive stress response data corresponding to the preliminary simulation deformation results are corrected, and the final compressive stress characteristic simulation results are output.

[0016] Compared with the prior art, the beneficial effects of the present invention are: This invention introduces a geometric singularity identification mechanism based on the spatial topological connection relationship of mesh elements in the finite element modeling stage. This mechanism can locate key regions with potential for abrupt displacement gradient changes in the early stages of simulation. This allows the compression deformation analysis to no longer rely on the overall uniformity assumption, but instead focus on the analysis of local geometry and constraints, thereby effectively improving the pertinence and reliability of the prediction of non-uniform compressive deformation behavior of rubber pads.

[0017] This invention introduces displacement path curvature constraints during compression loading to spatially redistribute initial material parameters and construct a local material constitutive relation with gradient correction characteristics. This allows the material mechanical response to be dynamically adjusted according to the actual deformation path, thereby more realistically reflecting the local compression characteristics of the rubber pad under boundary effects and avoiding simulation result deviations caused by material parameter homogenization.

[0018] This invention identifies the energy transfer control region based on the strain energy accumulation sequence and determines the dominant constraint mode of compression deformation by combining its spatial correspondence with the geometric singularity region. It then performs targeted incremental corrections on the preliminary simulation results, enabling the final compressive deformation characteristics to accurately reflect the local constrained deformation and energy transfer features. This improves the matching degree between the simulation results and the actual service conditions, providing a more reliable analytical basis for the optimization of rubber pad structure and life assessment. Attached Figure Description

[0019] Figure 1 This is a flowchart of a simulation analysis method for the compressive deformation characteristics of a rubber pad in Example 1.

[0020] Figure 2 This is a schematic diagram of the finite element mesh generation for the rubber pad block in Example 1.

[0021] Figure 3 This is a preliminary simulation diagram of the deformation and stress distribution of the rubber pad in Example 1.

[0022] Figure 4 The image shows the simulation results of the permanent deformation characteristics of the rubber pad in Example 1. Detailed Implementation

[0023] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0024] Example 1 Please see Figure 1 This invention provides a simulation analysis method for the compressive deformation characteristics of rubber pads, including: A finite element mesh model is constructed based on the three-dimensional geometric parameters and initial material parameters of the rubber pad, and the target region with geometric singularity potential with displacement gradient mutation potential is determined according to the spatial topological connection relationship of the mesh elements in the finite element mesh model. In implementation, the process of determining the geometric singularity target region includes: Based on the finite element mesh model, a topological connection network reflecting the continuity of geometric constraints is constructed according to the shared nodes and shared edges between mesh elements; It should be noted that the purpose of the topological connection network is to reflect the spatial geometric constraints between the grid cells of the rubber pad, so as to accurately identify the regions where displacement gradient changes may occur. Specifically, in this embodiment, the shared node refers to a common node that belongs to the vertices of two or more adjacent grid cells at the same time, and the shared edge refers to an edge line that connects two adjacent cells and is shared by the two cells. The topological connection network is generated by analyzing the relationship between the shared nodes and shared edges of each grid cell and its adjacent cells, and is used to determine the regions where displacement gradient changes abruptly.

[0025] The construction of the topological connection network reflecting the continuity of geometric constraints includes: Using the geometric adjacency relationship of mesh cells as constraints, multi-directional topological connection paths between cells are generated; Specifically, the geometric adjacency relationship refers to the spatial positional relationship between each mesh element and its directly adjacent mesh elements in the finite element mesh model. Based on this relationship, multi-directional generation of topological paths is performed to ensure that the topological connection network can fully represent the geometric adjacency constraints between elements; such as... Figure 2 As shown, this case uses a hexahedral mesh for discretization to ensure both computational speed and mesh quality requirements.

[0026] In one specific embodiment, taking a certain grid cell of the rubber pad as the center, firstly determine all its directly adjacent cells, then connect the central cell to each directly adjacent cell to form a topological path between multiple cells, and repeat the above process until the entire spatial region of the finite element mesh model is covered.

[0027] Based on the continuity constraint of the relative spatial orientation characteristics of the elements in the topological connection path, the topological connection path is screened to obtain a topological connection network for predicting the evolution of displacement gradient.

[0028] Specifically, the spatial orientation features of the units include, but are not limited to, spatial geometric features such as the angle between the normal vectors of adjacent units and the angle between the tangent planes of the unit surface; the principle of topology connection path screening is to eliminate paths with excessive spatial orientation changes that may cause obvious failure of geometric constraints, and retain paths with good spatial orientation continuity; for example, if the angle between the normal vectors of two adjacent units is greater than a preset angle threshold (such as 30°), it is considered that the geometric constraint continuity between these two units is weak and the path is removed; otherwise, the path is retained and enters the topology connection network.

[0029] In the topological interconnection network, the set of units in which geometric constraints undergo directional abrupt changes during topological propagation is identified as the geometric inducing feature of displacement gradient evolution; Specifically, directional mutation refers to a situation where a topological connection path undergoes a significant directional deflection or a marked change in geometric orientation during propagation. In practice, the location of directional mutation can be further determined by calculating the quantitative value of the orientation change between consecutive adjacent units in each path. For example, for a path consisting of three consecutive adjacent units, the orientation change angle of the units in the path can be calculated by analyzing the change in the angle between two consecutive line segments of the path. When the orientation change angle is greater than a set angle (such as 45°), the unit corresponding to this position is marked as the location of directional mutation, thus forming a unit set.

[0030] For example, if a certain edge region of a rubber pad has a geometric feature with large curvature, the mesh cells in this region are prone to abrupt changes in orientation of consecutive adjacent cells during topology propagation. This allows for the rapid identification of the cell set in this region as a geometric inducing feature for subsequent displacement gradient analysis.

[0031] Based on the spatial aggregation state of the unit set in the finite element mesh model, the geometric singularity target region with displacement gradient mutation potential is determined.

[0032] In specific implementation, spatial aggregation state refers to the spatial distribution characteristics of a set of directional mutation units, including the spatial density, spatial continuity, and spatial positional relationship of the unit set. In this embodiment, the spatial position of the unit set is processed by cluster analysis method. Specifically, a spatial clustering algorithm (such as the DBSCAN algorithm) is used to analyze the spatial coordinate distribution of the units in the unit set in order to identify the spatially dense region as the geometric singularity target region.

[0033] Specifically, the DBSCAN algorithm performs the following clustering process on the cell set: First, define the spatial distance threshold. and the minimum neighborhood unit threshold In this embodiment, the spatial distance threshold The value is 5mm, which is the minimum neighborhood cell threshold. The possible values ​​are 4; Then, for any element node p in the element set, if the radius is centered at node p... At least within the range If there are 1 node, then node p is considered the core node, and all nodes in its neighborhood are assigned to the same cluster; if the radius is within 1 / 2... Insufficient within the range If a node is not a neighbor of any core node, it is marked as a noise node. Repeat the above process until all nodes in the cell set have been clustered and labeled, thereby obtaining multiple spatially dense cell regions; then, based on the clustering results, determine one or more clustered regions with the largest spatial range and the most nodes, which are then used as the geometric singularity target regions.

[0034] For example, in the specific implementation of the rubber pad block simulation model, after the above clustering analysis, a certain edge area was found to have an obvious spatially dense unit area with more than 200 unit nodes and a unit spatial density of more than 50 units per cubic centimeter. Thus, this area was identified as a geometric singularity target area for subsequent more refined compressive deformation characteristic analysis.

[0035] An initial trial load is applied to the finite element mesh model, and the displacement path curvature distribution of the mesh elements in the geometric singularity target region during the loading process is extracted. Using this as a constraint, the initial material parameters are spatially redistributed to construct a local material constitutive relation with gradient correction characteristics. It should be noted that the initial test load is a preset proportion of compression load, expressed as a percentage of the initial thickness of the pad. For example, if the initial thickness of the pad is 12.5 mm, the compression displacement can be set to 25% of the pad thickness, i.e., 3.125 mm, in a specific embodiment. The initial test load is applied as an axial compression displacement constraint perpendicular to the upper surface of the rubber pad, while a fixed constraint is applied to the lower surface to prevent the pad from undergoing overall rigid displacement during loading.

[0036] Specifically, the construction of local material constitutive relations with gradient correction features includes: During the initial trial loading process, the spatial trajectory of the displacement of the mesh element in the geometric singularity target area is extracted in real time with time step, and the curvature distribution of the displacement path is calculated. In practical implementation, the real-time extraction of the spatial trajectory formed by the displacement of the mesh elements refers to recording the three-dimensional spatial displacement coordinates of each mesh element through finite element simulation calculation at each time step after the load is applied.

[0037] For example, the recorded spatial coordinate data is as follows: This indicates that t is the time step number in the loading process; for a loading process, such as a 10-day loading process, if displacement data is recorded once every day, then t changes from 1 to 10.

[0038] In implementation, the calculation logic for the curvature distribution of the displacement path is as follows: During the continuous loading phase, the coordinate evolution sequence of the displacement trajectory of the mesh element in the geometric singularity target area is recorded in three-dimensional space; Specifically, within each time step t of the continuous loading, the spatial position coordinates of each i-th mesh element in the geometrically singular target region are recorded. For example, for the i-th mesh element, its displacement trajectory coordinate sequence can be represented as: ; In the formula, This represents the spatial coordinates of the i-th grid cell at each time step in the loading process, and n represents the total number of time steps in the loading process.

[0039] Based on the displacement increment vector generated between adjacent loading steps according to the coordinate evolution sequence, the displacement path curvature distribution used to describe the spatial curvature of the displacement path is calculated; the specific calculation process includes: First, determine the preceding displacement increment vector of the i-th mesh element at time step t. With subsequent displacement increment vector : , ; Secondly, based on the Menger curvature principle, the discrete curvature at the t-th time step is calculated. Specifically, it is expressed as: ; In the formula, This represents the Euclidean magnitude of the vector.

[0040] It is understandable that by calculating the reciprocal of the radius of the circumcircle formed by three adjacent points in the trajectory sequence, the path evolution characteristics of the rubber material during the compression process can be accurately quantified.

[0041] It should be noted that, in this embodiment, when the loading step is at the starting position... or termination position At that time, due to the lack of complete adjacent points, the curvature value at that point was uniformly set. Set it to 0; at the same time, if the magnitude of any term in the denominator approaches zero during the calculation process (i.e., the element is at rest or in a state of minimal displacement), then the curvature of that step is determined to be 0 to ensure the stability of the numerical calculation; thus, the displacement path curvature distribution of each mesh element during the entire loading process is obtained.

[0042] The displacement path curvature distribution is used as a weighting factor and mapped to the spatial distribution matrix of the initial material parameters to generate a local material constitutive relation constrained by the displacement path curvature.

[0043] In practical implementation, the initial material parameters are mainly the parameters of the hyperelastic constitutive model of rubber material, such as the two parameters C10 and C01 of the Mooney-Rivlin model. The initial parameters of the rubber material are C10 = 1.5 × 10^5 Pa and C01 = 1.5 × 10^4 Pa.

[0044] It is understandable that these initial parameters are uniformly distributed material parameters without considering the effects of displacement curvature.

[0045] In one specific embodiment, the displacement path curvature value corresponding to each grid cell is first standardized (e.g., using Min-Max normalization) to obtain a standardized weighting factor.

[0046] For example, the normalized weighting factor of the i-th grid cell The calculation is as follows: ; In the formula, This represents the displacement path curvature value of the i-th mesh element. , These represent the maximum and minimum values ​​of the displacement path curvature in all mesh elements within the geometric singularity region, respectively.

[0047] Subsequently, the aforementioned weighting factors are used to adjust the initial material parameters; for example, the corrected material parameters for the i-th mesh element. , The calculation formula is as follows: ; In the formula, This represents the correction factor, the specific value of which can be calibrated based on the actual pressure transformer experiment, and the range is 0.1 to 0.5.

[0048] Finally, the spatial distribution matrix of local material constitutive parameters for each mesh element within the entire geometric singularity target region is obtained through the above method, thereby constructing a local material constitutive relation with gradient correction characteristics, providing a foundation for the next step of fine pressure-transformation simulation.

[0049] Based on the local material constitutive relation, the finite element mesh model is subjected to compression deformation analysis to obtain preliminary simulation deformation results. Based on the strain energy accumulation order of mesh elements in the geometric singularity target region in the preliminary simulation deformation results, the energy transfer control region is determined. In specific implementation, the process of obtaining the preliminary simulation deformation results is as follows: the spatial distribution matrix corresponding to the local material constitutive relation is mapped to the mesh model element attributes, a compressive load is applied and a finite element solution is performed to obtain the overall displacement field, strain field and stress field of the rubber pad.

[0050] It should be noted that the strain field distribution data in the preliminary simulation deformation results serve as an important basis for determining the energy transfer control region in the next step; such as Figure 3 As shown, the preliminary simulation results demonstrate the stress concentration distribution of the model under a specified load.

[0051] Specifically, the process of determining the energy transfer control region includes: In the process of compressive deformation analysis based on local material constitutive relations, the strain energy evolution records of each mesh element in the geometric singularity target region at different loading stages are obtained; Specifically, the strain energy evolution record refers to the strain energy value of each mesh element at every moment during the entire loading process, which can be directly obtained by outputting from finite element analysis software; the strain energy is calculated based on the hyperelastic strain energy density function of the rubber material, for example, the strain energy density function of the Mooney-Rivlin model is in the form of: ; In the formula, Represents strain energy density. , For local material constitutive parameters, , Let represent the first and second invariants of the Cauchy-Green deformation tensor, respectively, and define them as follows: ; In the formula, The main stretch ratio.

[0052] It should be understood that, in specific embodiments, the strain energy of each grid cell can be obtained by integrating the corresponding cell volume, specifically expressed as follows: ; In the formula, This represents the strain energy of the i-th mesh element. Let represent the volume of the i-th mesh cell. The integration calculation can be completed automatically by simulation software.

[0053] Based on the relationship between the spatial location and the order of occurrence of strain energy in the loading stage, an energy transfer sequence reflecting the dominant propagation direction of strain energy is constructed. Specifically, the energy transfer sequence is obtained by analyzing the order in which the strain energy of the grid cells reaches a preset threshold; in a specific embodiment, a strain energy threshold is first set, for example, 50% of a certain maximum strain energy value in the initial loading stage is used as the threshold. : ; In the formula, This represents the maximum strain energy value within the singular region during the initial loading phase.

[0054] Furthermore, the strain energy of each grid element was recorded to be greater than or equal to the first time. The time steps are used to sort these units from earliest to latest according to the time step when they first reach the threshold, forming the energy transfer sequence of the units.

[0055] The construction of the energy transfer sequence reflecting the dominant propagation direction of strain energy includes: In the strain energy evolution record, identify the spatially connected grid cell sequence that first reaches the preset threshold and continues to expand to the neighborhood; In the implementation process, the identification method of spatially connected grid cell sequence is as follows: starting from the first cell that reaches the threshold, it is gradually determined whether the adjacent cells reach the threshold in sequence and continue to appear until a spatially continuous grid cell group is formed; for example, assuming that the cell number that initially reaches the threshold is cell 100, then it is further checked whether the spatially adjacent cells around cell 100, such as cells 101, 102, 103, etc., reach the threshold in sequence. If a spatially continuous sequence of at least 3 cells is formed, then the sequence is confirmed as one of the energy transfer sequences.

[0056] Based on the spatial extension direction of the mesh element sequence in the finite element mesh model, an energy transfer sequence is formed to characterize the dominant propagation direction of strain energy.

[0057] Specifically, the spatial extension direction refers to the principal direction vector between the coordinates of the center positions of a continuous sequence of spatial units. For example, the direction of the line connecting the first and last units can be defined as the principal direction of energy transfer. Exemplarily, it can be determined by coordinate differences; for example, the center coordinates of the first unit to reach the threshold are... The last unit is Then the principal direction vector Represented as: .

[0058] The energy transfer control region is determined based on the spatial convergence location of the energy transfer sequence in the finite element mesh model.

[0059] Specifically, the spatial convergence location refers to the region where multiple energy transfer sequences intersect or are spatially adjacent during the loading process, which can be understood as a spatial region where strain energy accumulates densely.

[0060] In a specific embodiment, regions where strain energy is densely concentrated can be identified using spatial clustering analysis methods, and these regions can be determined as energy transfer control areas.

[0061] For example, in the specific implementation process, the coordinates of the end units of the energy transfer sequence are first extracted, and clustering is performed using the spatial density clustering algorithm DBSCAN. Specific parameter settings are shown in the following example: neighborhood radius. Set to 5mm, minimum number of clusters The cluster is divided into 5 units, and the spatial location of the cluster center as the energy transfer control area is determined by the degree of concentration of the clustered units.

[0062] Based on the spatial correspondence between the energy transfer control region and the geometric singularity target region, the dominant constraint mode of the rubber pad compression deformation is determined, and the preliminary simulation deformation results are incrementally corrected according to the dominant constraint mode to output the final compression deformation characteristic simulation results.

[0063] In implementation, determining the dominant constraint mode for the compression deformation of the rubber pad includes: The spatial distribution of the energy transfer control region in the finite element mesh model is mapped to the spatial range of the geometric singularity target region, and the spatial topological mapping relationship between regions is established. Specifically, the spatial coordinates of the determined energy transfer control area are matched with the grid cells in the geometric singularity target area using a three-dimensional spatial mapping method, thereby establishing an accurate spatial topological mapping relationship.

[0064] It should be noted that the spatial location topological mapping relationship refers to the geometric mapping relationship between the spatial location of the energy transfer control region and the location of the internal unit of the geometric singularity target region.

[0065] Specifically, the process of establishing the spatial location topological mapping relationship between the regions includes: Using the geometric boundary of the geometric singularity target region as a spatial reference, determine the relative coordinates of the energy transfer control region within or at the edge of the geometric singularity target region; In a specific embodiment, a local spatial coordinate system is first defined for the geometrically singular target region. For example, the geometric center of the region is selected as the origin O, the Z-axis is along the thickness direction of the model, and the X-axis and Y-axis are respectively in the length and width directions to establish a local rectangular coordinate system.

[0066] Furthermore, if the spatial center coordinates of the energy transfer control region are... Then relative coordinates The definition is as follows: ; In the formula, This represents the position coordinates of the center O of the geometric singularity target region in the global coordinate system of the model.

[0067] Based on the geometric constraint interference range formed by the relative coordinates in the geometric singularity target region, a spatial location topological mapping relationship is constructed to describe the constraint relationship between regions.

[0068] Specifically, the geometric constraint interference range refers to the spatial influence range of the energy transfer control region on the surrounding geometric singularity region during the compression loading process; in a specific embodiment, the interference range is defined as a spherical space with a radius of 5mm to 10mm, centered on the spatial center coordinates of the energy transfer control region.

[0069] Furthermore, if the coordinates of the center of a certain element within the geometrically singular target region are... Satisfy the following formula: ; This unit is considered to be constrained by the energy transfer control region; where, The radius of the interference range is 7.5 mm in this embodiment.

[0070] Based on the physical damping effect of the energy transfer control region on the deformation path of the geometric singularity target region in the spatial location topological mapping relationship, the dominant constraint mode of the rubber pad compression deformation is determined.

[0071] It is understandable that the physical damping effect refers to the suppression of displacement vector deflection in the geometrically singular region by the energy transfer control region.

[0072] In practice, the physical damping effect is quantified by calculating the displacement coordination gradient between the displacement vector of each grid cell within the interference range and the principal energy transfer direction vector. , can be defined as: ; In the formula, This represents the displacement vector of the i-th mesh element in the preliminary simulation deformation results. This represents the main direction vector of energy transfer.

[0073] Furthermore, the physical damping effect data of all elements in the geometric singularity region are statistically analyzed, and the dominant constraint mode of the rubber pad compression deformation is determined by the spatial distribution characteristics of the element set where the physical damping effect of the element is greater than a preset threshold (e.g., 30%). If the damping effect of most elements is concentrated in the ring-shaped region at the edge of the model, then the dominant constraint mode is determined to be the ring-shaped constraint mode at the edge.

[0074] Specifically, the final output simulation results of the pressure transformer characteristics include: Based on the topology of the grid cells within the geometric singularity target region, the topological response weights of the energy transfer control region to the geometric singularity target region under the dominant constraint mode are analyzed. In practical implementation, the topological response weight is defined as the relative contribution of the element damping effect within the overall interference range, and the weight calculation method is expressed as follows: ; In the formula, represents the topological response weight of the i-th element, and N represents the total number of elements affected by the damping effect.

[0075] Based on the topological response weights, the local constraint increment of the energy transfer control region on the compressive deformation of the geometric singularity target region is quantitatively calculated; In practice, the local constraint increment represents the displacement correction caused by energy transfer path constraints, and is calculated using the following formula: ; In the formula, This represents the displacement correction increment of the i-th element. This represents the displacement scalar value of the element in the preliminary simulation deformation results. This represents the correction factor, which is obtained through prior calibration using a rubber material compression test, and its value ranges from 0.1 to 0.3.

[0076] Based on the local constraint increment, the compressive stress response data corresponding to the preliminary simulation deformation results are corrected, and the final compressive stress characteristic simulation results are output.

[0077] It should be noted that the correction is to compensate for the stiffness matrix being too stiff at geometric singularities caused by mesh distortion in the standard finite element algorithm. By introducing the displacement reduction caused by the physical damping effect, the final output displacement field cloud map is made closer to the real physical response of the rubber pad under extreme compressive stress conditions.

[0078] Specifically, the correction of the pressure transformer response data involves performing the following vector superposition operation on the initial displacements of each element to obtain the corrected final displacement. : ; in, To obtain the corrected final compressive displacement data, the corrected displacement data of each element was remapped onto the mesh model using finite element simulation analysis software and presented as a contour plot; for example... Figure 4 As shown, the corrected displacement and stress field data of the entire rubber pad are finally generated and output, thus obtaining simulation results of the compressive deformation characteristics that are closer to the actual application conditions.

[0079] Some of the data in the above formula are calculated by removing dimensions and taking their numerical values. The formula is the closest to the real situation obtained by software simulation of a large amount of collected data. The preset parameters and preset thresholds in the formula are set by those skilled in the art according to the actual situation or obtained through simulation of a large amount of data.

[0080] The above embodiments are only used to illustrate the technical methods of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical methods of the present invention without departing from the spirit and scope of the technical methods of the present invention.

Claims

1. A simulation analysis method for the compressive deformation characteristics of a rubber pad, characterized in that, include: A finite element mesh model is constructed based on the three-dimensional geometric parameters and initial material parameters of the rubber pad, and the target region with geometric singularity potential with displacement gradient mutation potential is determined according to the spatial topological connection relationship of the mesh elements in the finite element mesh model. An initial trial load is applied to the finite element mesh model, and the displacement path curvature distribution of the mesh elements in the geometric singularity target region during the loading process is extracted. Using this as a constraint, the initial material parameters are spatially redistributed to construct a local material constitutive relation with gradient correction characteristics. Based on the local material constitutive relation, the finite element mesh model is subjected to compression deformation analysis to obtain preliminary simulation deformation results. Based on the strain energy accumulation order of mesh elements in the geometric singularity target region in the preliminary simulation deformation results, the energy transfer control region is determined. Based on the spatial correspondence between the energy transfer control region and the geometric singularity target region, the dominant constraint mode of the rubber pad compression deformation is determined, and the preliminary simulation deformation results are incrementally corrected according to the dominant constraint mode to output the final compression deformation characteristic simulation results.

2. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 1, characterized in that, The process of determining the geometric singularity target region includes: Based on the finite element mesh model, a topological connection network reflecting the continuity of geometric constraints is constructed according to the shared nodes and shared edges between mesh elements; In the topological interconnection network, the set of units in which geometric constraints undergo directional abrupt changes during topological propagation is identified as the geometric inducing feature of displacement gradient evolution; Based on the spatial aggregation state of the unit set in the finite element mesh model, the geometric singularity target region with displacement gradient mutation potential is determined.

3. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 2, characterized in that, The construction of the topological connectivity network reflecting the continuity of geometric constraints includes: Using the geometric adjacency relationship of mesh cells as constraints, multi-directional topological connection paths between cells are generated; Based on the continuity constraint of the relative spatial orientation characteristics of the elements in the topological connection path, the topological connection path is screened to obtain a topological connection network for predicting the evolution of displacement gradient.

4. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 1, characterized in that, The construction of local material constitutive relations with gradient correction features includes: During the initial trial loading process, the spatial trajectory of the displacement of the mesh element in the geometric singularity target area is extracted in real time with time step, and the curvature distribution of the displacement path is calculated. The displacement path curvature distribution is used as a weighting factor and mapped to the spatial distribution matrix of the initial material parameters to generate a local material constitutive relation constrained by the displacement path curvature.

5. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 4, characterized in that, The calculation logic for the curvature distribution of the displacement path is as follows: During the continuous loading phase, the coordinate evolution sequence of the displacement trajectory of the mesh element in the geometric singularity target area is recorded in three-dimensional space; Based on the spatial deflection vector of the coordinate evolution sequence between adjacent loading steps, a displacement path curvature distribution is formed to describe the degree of bending of the displacement path.

6. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 1, characterized in that, The process of determining the energy transfer control region includes: In the process of compressive deformation analysis based on local material constitutive relations, the strain energy evolution records of each mesh element in the geometric singularity target region at different loading stages are obtained; Based on the relationship between the spatial location and the order of occurrence of strain energy in the loading stage, an energy transfer sequence reflecting the dominant propagation direction of strain energy is constructed. The energy transfer control region is determined based on the spatial convergence location of the energy transfer sequence in the finite element mesh model.

7. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 6, characterized in that, The construction of the energy transfer sequence reflecting the dominant propagation direction of strain energy includes: In the strain energy evolution record, identify the spatially connected grid cell sequence that first reaches the preset threshold and continues to expand to the neighborhood; Based on the spatial extension direction of the mesh element sequence in the finite element mesh model, an energy transfer sequence is formed to characterize the dominant propagation direction of strain energy.

8. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 1, characterized in that, The dominant constraint mode for determining the compression deformation of the rubber pad includes: The spatial distribution of the energy transfer control region in the finite element mesh model is mapped to the spatial range of the geometric singularity target region, and the spatial topological mapping relationship between regions is established. Based on the physical damping effect of the energy transfer control region on the deformation path of the geometric singularity target region in the spatial location topological mapping relationship, the dominant constraint mode of the rubber pad compression deformation is determined.

9. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 8, characterized in that, The process of establishing the spatial location topological mapping relationship between the regions includes: Using the geometric boundary of the geometric singularity target region as a spatial reference, determine the relative coordinates of the energy transfer control region within or at the edge of the geometric singularity target region; Based on the geometric constraint interference range formed by the relative coordinates in the geometric singularity target region, a spatial location topological mapping relationship is constructed to describe the constraint relationship between regions.

10. The simulation analysis method for the compressive deformation characteristics of the rubber pad according to claim 8, characterized in that, The final simulation results of the pressure transformer characteristics output include: Based on the topology of the grid cells within the geometric singularity target region, the topological response weights of the energy transfer control region to the geometric singularity target region under the dominant constraint mode are analyzed. Based on the topological response weights, the local constraint increment of the energy transfer control region on the compressive deformation of the geometric singularity target region is quantitatively calculated; Based on the local constraint increment, the compressive stress response data corresponding to the preliminary simulation deformation results are corrected, and the final compressive stress characteristic simulation results are output.

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