Brain tissue constitutive parameter identification method based on non-uniaxial stress state test
By establishing finite element models for nonaxial tensile and compression tests and constructing stress state transformation relationships, the problem of nonuniform deformation interference in brain tissue experiments was solved, accurate constitutive model parameter identification was achieved, and the reliability of brain injury research was improved.
Patent Information
- Application Number
- CN202511560210.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-29
- Publication Date
- 2026-03-17
AI Technical Summary
Existing technologies cannot effectively eliminate interference from non-uniform deformation in brain tissue experiments, and lack methods to convert non-uniaxial test data into standard uniaxial stress state data, resulting in inaccurate identification of constitutive model parameters and affecting the reliability of pediatric brain injury research.
By establishing finite element models of non-uniaxial tensile and compression tests, stress state transformation relationships are constructed, and multi-objective optimization algorithms are used to correct experimental data deviations, thereby realizing the conversion of non-uniaxial data to uniaxial data and accurately characterizing the mechanical behavior of brain tissue.
This effectively reduces testing errors, improves the accuracy of constitutive model parameter identification, and provides a reliable mechanical model basis for research on brain injury in children.
Smart Images
Figure CN121683309A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of injury biomechanics, and in particular to a method for parameter identification of a hyperelastic constitutive model using the results of non-uniaxial tensile and compression tests of brain tissue. Background Technology
[0002] Children, due to their weak self-protection awareness, face a high risk of brain injury from falls or traffic accidents. Finite element simulation technology, as an important tool for studying the mechanisms of brain injury in children, relies heavily on the accurate characterization of the mechanical properties of brain tissue for its accuracy. Currently, it is necessary to obtain the true stress-strain response of brain tissue through multi-condition mechanical testing to determine the constitutive model parameters. However, the unique properties of brain tissue make it difficult to conduct conventional uniaxial tensile / compression tests: significant necking occurs during tension, while lateral expansion deformation occurs during compression due to clamp friction. These non-ideal deformation states prevent the experimental data from directly reflecting the true mechanical response under uniaxial stress, severely limiting the accurate identification of constitutive model parameters.
[0003] The core dilemma facing existing technologies lies in two aspects: firstly, the inability to eliminate non-uniform deformation interference during the experimental process; and secondly, the lack of effective methods to convert non-uniaxial test data into standard uniaxial stress state data that can be used for parameter identification. This technological bottleneck directly affects the accuracy of brain tissue biomechanical models, thereby limiting the reliability of pediatric brain injury research. To address these issues, existing technologies urgently need improvement. Summary of the Invention
[0004] The purpose of this invention is to solve the problems mentioned in the background art, and to propose a method for parameter identification of hyperelastic constitutive models using the results of non-uniaxial tensile and compression tests of brain tissue, which has the advantages of reducing experimental data errors and accurately characterizing the mechanical behavior of brain tissue.
[0005] The technical solution adopted by this invention to solve its technical problem is: A method for parameter identification of a hyperelastic constitutive model using the results of nonaxial tensile and compression tests on brain tissue includes the following steps; S1. Preliminary processing of tensile and compression test data to obtain pseudo-true stress-elongation curves from the test data; S2. The hyperelastic constitutive model is calibrated using pseudo-real stress-elongation curves to obtain a set of temporary hyperelastic constitutive model parameters; S3. Establish a finite element model under non-standard uniaxial tensile / compression test conditions, such as... Figure 2 As shown; S4. Using the temporary hyperelastic constitutive model parameters obtained in S2 and the nonaxial tensile / compression test finite element model established in S3, the conversion relationship between the real stress-elongation curve and the engineering stress-elongation curve under the nonaxial test conditions is obtained. S5. Establish a finite element model under strict uniaxial tension / compression conditions; S6. Input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model established in S3 and S5 to obtain the conversion relationship between the real stress-elongation curve under strict uniaxial stress and the real stress-elongation curve under non-uniaxial working conditions. S7. Using the conversion relationship obtained in S4, process the force-displacement test data obtained under non-uniaxial test conditions. The engineering stress is obtained by dividing the force by the initial surface area of the brain tissue test sample; the elongation is obtained by dividing the sum of the displacement and the original length of the brain tissue test sample by the original length; calculate the engineering stress-elongation curve using the conversion relationship obtained in S4 to obtain the true stress-elongation curve of brain tissue under non-uniaxial test conditions. S8. Convert the true stress-elongation curve obtained in S7 under non-uniaxial conditions into a true stress-elongation curve under uniaxial stress state suitable for calibrating the parameters of the hyperelastic constitutive model using the transformation relationship obtained in S6. S9. Using the actual stress-elongation curve results from S8, calibrate the hyperelastic constitutive model to obtain hyperelastic constitutive model parameters that can accurately characterize the response of brain tissue.
[0006] Furthermore, the specific steps of step S1 are as follows: S11. The engineering stress-elongation curve is calculated from the force-displacement curve obtained by the experiment. The tensile force and tensile displacement obtained by the tensile test are positive values, and the compression force and compression displacement obtained by the compression test are negative values. The engineering stress is obtained by dividing the force by the initial cross-sectional area of the specimen, and the elongation is calculated by dividing the sum of the displacement and the original length of the specimen by the original length of the specimen. S12. Obtain the pseudo-true stress-elongation curve through the engineering stress-elongation curve, where the pseudo-true stress is calculated by multiplying the engineering stress and the elongation.
[0007] Furthermore, the specific steps of step S3 are as follows: S31. Establish a geometric model of the brain tissue sample based on the actual external dimensions and shape of the experimental sample; S32. Establish a simplified geometric model of the fixture; S33. Mesh the geometric model of the brain tissue sample and establish a finite element model of the brain tissue sample using solid elements. S34. Mesh the simplified fixture geometry model and use solid elements to build a finite element model of the fixture. S35. Using the finite element model of the brain tissue sample and the finite element model of the clamp established in S33 and S34, establish a non-uniaxial tensile finite element model. S36. Using the finite element model of the brain tissue sample and the finite element model of the clamp established in S33 and S34, establish a non-uniaxial compression finite element model.
[0008] Furthermore, the specific steps of step S4 are as follows: S41. Input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model under the non-standard uniaxial tension / compression test conditions described in S3 to perform non-uniaxial tension and compression simulation.
[0009] S42. Obtain the force-displacement response results of the model in the non-uniaxial tensile simulation.
[0010] S43. Process the force-displacement response results described in S42 to obtain the tensile engineering stress-elongation curve, wherein the tensile engineering stress is obtained by dividing the force by the initial cross-sectional area of the finite element model of the brain tissue sample; the elongation is obtained by dividing the sum of the tensile displacement and the original length of the finite element model of the brain tissue sample by the original length. S44. Obtain the force-displacement response results of the model in the non-uniaxial compression simulation; S45. Process the force-displacement response results described in S44 to obtain the compression stress-elongation curve, wherein the compression stress is obtained by dividing the force by the initial cross-sectional area of the finite element model of the brain tissue sample; the elongation is obtained by dividing the sum of the compression displacement and the original length of the finite element model of the brain tissue sample by the original length.
[0011] S46. Obtain the true stress-elongation response results of the model in the non-uniaxial tensile simulation. Select a cluster of meshes located at the core of the model to obtain the true tensile stress. The elongation is obtained by dividing the sum of the tensile displacement and the original length of the finite element model of the brain tissue sample by the original length. S47. Obtain the true stress-elongation response results of the model in the non-uniaxial compression simulation. Select a cluster of meshes located at the core of the model to obtain the true compressive stress. The elongation is obtained by dividing the sum of the compressive displacement and the original length of the finite element model of the brain tissue sample by the original length. S48. Based on the formula between engineering stress and actual stress under strict uniaxial stress state, a relationship between actual stress and engineering stress under non-uniaxial stress state is proposed. Multi-objective optimization is used to obtain the values of unknown constant parameters in the formula, and the conversion relationship between actual stress and engineering stress under non-uniaxial stress state is established.
[0012] Furthermore, the specific steps of step S5 are as follows: S51. Establish a geometric model of the brain tissue sample based on the actual external dimensions and shape of the experimental sample; S52. Mesh the geometric model of the brain tissue sample and establish a finite element model of the brain tissue sample using solid elements. S53. Input the parameters of the temporary hyperelastic constitutive model in S2 into the finite element model of the brain tissue sample established in S52, apply a load to the surface of the finite element model of the brain tissue sample, and allow the cross section to deform freely to establish a uniaxial tensile finite element model and a uniaxial compressive finite element model.
[0013] Furthermore, the specific steps of step S6 are as follows: S61. Input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model under the strict uniaxial tension / compression condition described in S5 to perform uniaxial tension and compression simulation. S62. Obtain the true stress-elongation response results of the model in uniaxial tension and compression simulations; S63. Based on the non-uniaxial tensile true stress-elongation curve and non-uniaxial compressive true stress-elongation curve obtained in S4, and the uniaxial tensile true stress-elongation curve and uniaxial compressive true stress-elongation curve obtained in S62, a scaling relationship between the two sets of curves is established using multi-objective optimization, and a conversion relationship is established between the true stress-elongation curve under strict uniaxial stress and the true stress-elongation curve under non-uniaxial working conditions.
[0014] Compared with existing technologies, the beneficial effects of this invention are as follows: By establishing finite element models under non-uniaxial and uniaxial stress states and constructing multi-level transformation relationships, this invention converts non-ideal test data into standard uniaxial stress state data. This reduces errors caused by test conditions and uneven deformation of brain tissue, allowing for the acquisition of the true mechanical response of brain tissue under these test conditions. Consequently, constitutive model parameters that accurately characterize the mechanical behavior of brain tissue are obtained. Through the hyperelastic constitutive model, the mechanical behavior of children's brain tissue can be accurately characterized, thus providing a research foundation for the study of childhood brain injury. Attached Figure Description
[0015] Figure 1 This is the overall technical roadmap of the present invention; Figure 2 This is a diagram of the finite element model of tension and compression under non-uniaxial working conditions established in this invention; Figure 3 This is a diagram of the finite element model of tension and compression under uniaxial working conditions established in this invention; Figure 4 This invention is used to obtain the mesh location of the true stress in tensile and compression simulations. Detailed Implementation
[0016] The technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. It should be noted that similar reference numerals and letters in the following drawings indicate similar items; therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. Furthermore, in the description of this application, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0017] In existing technologies, the mechanical property testing of brain tissue often results in distorted true stress data due to non-uniaxial deformation of the sample. Traditional non-uniaxial tensile or compression tests struggle to accurately capture the true stress-strain response of brain tissue. For example, during tension, sample necking, or during compression, lateral expansion caused by clamp friction makes the test data unable to reflect the uniaxial stress state. Existing methods rely on idealized test conditions, but the inherent characteristics of brain tissue cause actual experiments to deviate from theoretical assumptions, directly affecting the accuracy of constitutive model parameter identification.
[0018] To address the aforementioned issues, the inventors discovered a systematic deviation between non-uniaxial test data and the theoretical uniaxial state. By analyzing non-ideal factors such as necking and friction in tensile and compression tests, they realized the need to establish a mapping relationship between test conditions and the theoretical state. Furthermore, they proposed using a finite element model to simulate non-uniaxial and uniaxial working conditions, and establishing a conversion relationship between the two stress states through multi-objective optimization, thereby correcting the test data deviation.
[0019] like Figures 1 to 4 As shown, a method for parameter identification of a hyperelastic constitutive model using the results of nonaxial tensile and compression tests of brain tissue includes the following steps; S1. Preliminary processing of tensile and compression test data to obtain pseudo-true stress-elongation curves from the test data; S2. The hyperelastic constitutive model is calibrated using pseudo-real stress-elongation curves to obtain a set of temporary hyperelastic constitutive model parameters; S3. Establish a finite element model under non-standard uniaxial tensile / compression test conditions, such as... Figure 2 As shown; S4. Using the temporary hyperelastic constitutive model parameters obtained in S2 and the nonaxial tensile / compression test finite element model established in S3, the conversion relationship between the real stress-elongation curve and the engineering stress-elongation curve under the nonaxial test conditions is obtained. S5. Establish a finite element model under strict uniaxial tension / compression conditions, such as Figure 3 As shown; S6. Input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model established in S3 and S5 to obtain the conversion relationship between the real stress-elongation curve under strict uniaxial stress and the real stress-elongation curve under non-uniaxial working conditions. S7. Using the conversion relationship obtained in S4, process the force-displacement test data obtained under non-uniaxial test conditions. The engineering stress is obtained by dividing the force by the initial surface area of the brain tissue test sample; the elongation is obtained by dividing the sum of the displacement and the original length of the brain tissue test sample by the original length; calculate the engineering stress-elongation curve using the conversion relationship obtained in S4 to obtain the true stress-elongation curve of brain tissue under non-uniaxial test conditions. S8. Convert the true stress-elongation curve obtained in S7 under non-uniaxial conditions into a true stress-elongation curve under uniaxial stress state suitable for calibrating the parameters of the hyperelastic constitutive model using the transformation relationship obtained in S6. S9. Using the actual stress-elongation curve results from S8, calibrate the hyperelastic constitutive model to obtain hyperelastic constitutive model parameters that can accurately characterize the response of brain tissue.
[0020] Among them, the pseudo-true stress-elongation curve refers to an approximate true stress curve obtained by multiplying engineering stress and elongation, used for preliminary calibration of the constitutive model. The finite element model under non-standard uniaxial tensile / compression test conditions refers to a three-dimensional solid model including fixture contact and sample deformation, which can be implemented using solid element mesh generation methods, used to simulate stress distribution under actual test conditions. The transformation relationship refers to the stress state mapping function established through multi-objective optimization, which can be implemented by combining finite element simulation results with optimization algorithms, used to correct errors caused by non-ideal test conditions.
[0021] Specifically, experimental data, after preprocessing, are converted into pseudo-true stress curves for preliminary parameter calibration. Non-uniaxial tensile and compressive finite element models are established, and temporary parameters are input for simulation to obtain response curves under different stress states. By comparing the simulation results of non-uniaxial true stress and engineering stress, the conversion relationship between engineering stress and true stress is established; by comparing the simulated true stress response of non-uniaxial and uniaxial simulations, the conversion relationship between non-uniaxial true stress and uniaxial true stress is established. Actual experimental data, after being corrected by this relationship, is converted into equivalent uniaxial stress state data, which is ultimately used to accurately calibrate the parameters of the hyperelastic constitutive model.
[0022] Compared to existing technologies, which directly use non-uniaxial test data to obtain real stress for parameter identification, leading to parameter errors, this method constructs a stress state transformation system through finite element simulation. Traditional techniques ignore the differences between test conditions and theoretical models; this approach establishes a two-way mapping relationship to eliminate systematic errors. Conventional parameter identification relies on ideal test conditions; this method overcomes the limitations of test conditions by using numerical simulation to expand the applicability of the data.
[0023] Through the above technical solution, this application effectively eliminates stress distribution distortion caused by non-uniaxial stress states in brain tissue testing, converting non-ideal test data into equivalent uniaxial stress states. This method improves the accuracy of constitutive model parameter identification, enabling the hyperelastic model to more realistically reflect the mechanical properties of brain tissue and providing a reliable simulation basis for brain injury mechanism research.
[0024] Furthermore, the specific steps of step S1 are as follows: S11. The engineering stress-elongation curve is calculated from the force-displacement curve obtained by the experiment. The tensile force and tensile displacement obtained by the tensile test are positive values, and the compression force and compression displacement obtained by the compression test are negative values. The engineering stress is obtained by dividing the force by the initial cross-sectional area of the specimen, and the elongation is calculated by dividing the sum of the displacement and the original length of the specimen by the original length of the specimen. S12. Obtain the pseudo-true stress-elongation curve from the engineering stress-elongation curve. The pseudo-true stress is calculated by multiplying the engineering stress and the elongation.
[0025] The engineering stress-elongation curve is specifically calculated by dividing the test force by the initial cross-sectional area of the specimen to obtain the engineering stress, and by dividing the sum of the displacement and the original length of the specimen by the original length to obtain the elongation. This curve can intuitively reflect the apparent mechanical response of the material under non-uniaxial testing conditions, but it does not consider the influence of cross-sectional area changes during deformation. The pseudo-true stress-elongation curve is a modified stress-deformation relationship curve calculated by multiplying the engineering stress by the elongation, specifically by multiplying the engineering stress by the corresponding elongation value. This curve can provide input data for subsequent model parameter calibration.
[0026] Specifically, in the experimental data processing stage, the engineering stress and elongation are first calculated based on the force and displacement data recorded in the tensile and compression tests. For example, when the original cross-sectional area of the specimen is 10 square millimeters, if the measured tensile force is 5 Newtons, the engineering stress is 0.5 MPa; if the original length of the specimen is 20 millimeters and the tensile displacement is 2 millimeters, the elongation is 1.1. Compression test data is directional and presents negative values; for example, a compression force of -3 Newtons corresponds to an engineering stress of -0.3 MPa. Subsequently, the engineering stress at each data point is multiplied by the corresponding elongation to generate a pseudo-true stress-elongation curve, providing the input data basis for the subsequent calibration of hyperelastic constitutive model parameters.
[0027] Compared to existing technologies, traditional methods typically use the actual stress-elongation curves converted from force-displacement data obtained under non-uniaxial testing conditions for model calibration, neglecting the changes in cross-sectional area of the specimen during deformation and the influence of testing conditions on the actual stress state. This new method, by introducing a new mapping relationship, can more accurately reflect the actual stress state of the material under non-uniaxial testing conditions, effectively reducing stress calculation errors caused by specimen necking or lateral expansion.
[0028] Through the above technical solution, this application has achieved preliminary correction of the mechanical response data of brain tissue under non-uniaxial test conditions, solved the problem of stress calculation deviation caused by neglecting specimen deformation and test conditions in traditional methods, and provided a reliable data basis for the high-precision calibration of subsequent hyperelastic constitutive model parameters.
[0029] Furthermore, the specific steps of step S3 are as follows: S31. Establish a geometric model of the brain tissue sample based on the actual external dimensions and shape of the experimental sample; S32. Establish a simplified geometric model of the fixture; S33. Mesh the geometric model of the brain tissue sample and establish a finite element model of the brain tissue sample using solid elements. S34. Mesh the simplified fixture geometry model and use solid elements to build a finite element model of the fixture. S35. Using the finite element model of the brain tissue sample and the finite element model of the clamp established in S33 and S34, establish a non-uniaxial tensile finite element model. S36. Using the finite element model of the brain tissue sample and the finite element model of the clamp established in S33 and S34, establish a non-uniaxial compression finite element model.
[0030] Specifically, under non-uniaxial tensile and compression test conditions, the interaction between brain tissue samples and the fixture causes the stress distribution to deviate from the ideal uniaxial state. By establishing a geometric model of the brain tissue that includes the actual sample size, the initial morphology of the sample during the test can be accurately reflected; at the same time, simplifying the geometry of the fixture can avoid the impact of complex contact conditions on simulation efficiency. Meshing the brain tissue and fixture using solid elements can simulate the deformation response of the material in three-dimensional space. By combining the finite element model of the brain tissue sample with the finite element model of the fixture, a complete simulation environment for non-uniaxial tensile and compression tests can be constructed, thus providing a computational basis for establishing subsequent stress transformation relationships.
[0031] Furthermore, the specific steps of step S4 are as follows: S41. Input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model under the non-standard uniaxial tension / compression test conditions described in S3 to perform non-uniaxial tension and compression simulation.
[0032] S42. Obtain the force-displacement response results of the model in the non-uniaxial tensile simulation.
[0033] S43. Process the force-displacement response results described in S42 to obtain the tensile engineering stress-elongation curve, wherein the tensile engineering stress is obtained by dividing the force by the initial area of the finite element model of the brain tissue sample; the elongation is obtained by dividing the sum of the tensile displacement and the original length of the finite element model of the brain tissue sample by the original length.
[0034] S44. Obtain the force-displacement response results of the model in the non-uniaxial compression simulation.
[0035] S45. Process the force-displacement response results described in S44 to obtain the compression stress-elongation curve, wherein the compression stress is obtained by dividing the force by the initial area of the finite element model of the brain tissue sample; the elongation is obtained by dividing the sum of the compression displacement and the original length of the finite element model of the brain tissue sample by the original length.
[0036] S46. Obtain the true stress-elongation response results of the model in the non-uniaxial tensile simulation. To ensure that the true stress output in the non-uniaxial tensile simulation is uniaxial stress, select a cluster of meshes located at the core of the model to obtain the true tensile stress, such as... Figure 4 As shown, the elongation is obtained by dividing the sum of the tensile displacement and the original length of the finite element model of the brain tissue sample by the original length.
[0037] S47. Obtain the true stress-elongation response results of the model in the non-uniaxial compression simulation. To ensure that the true stress output in the non-uniaxial tension simulation is uniaxial stress, a cluster of meshes located at the core of the model is selected to obtain the true compressive stress. The elongation is obtained by dividing the sum of the compressive displacement and the original length of the finite element model of the brain tissue sample by the original length.
[0038] S48. Based on the formula between engineering stress and actual stress under strict uniaxial stress state, a relationship between actual stress and engineering stress under non-uniaxial stress state is proposed. Multi-objective optimization is used to obtain the values of unknown constant parameters in the formula, thereby establishing the conversion relationship between actual stress and engineering stress under non-uniaxial stress state.
[0039] Specifically, in non-uniaxial tensile simulation, tensile force-displacement response data can be obtained by inputting temporary constitutive model parameters and running the finite element model. The tensile engineering stress is calculated by dividing the tensile force by the initial cross-sectional area of the brain tissue sample, and the elongation is obtained by dividing the sum of the tensile displacement and the original length of the sample by the original length. The true stress is obtained by selecting the mesh stress output value of the core region of the model to avoid interference from the non-uniaxial stress state caused by mesh deformation. In non-uniaxial compression simulation, the same method is used to process the compression force-displacement data to obtain the engineering stress and true stress under compression conditions. Subsequently, based on the theoretical relationship between engineering stress and true stress under uniaxial stress conditions, a correction term is introduced to construct a conversion formula under non-uniaxial conditions. The correction coefficient is calibrated using a multi-objective optimization algorithm, ultimately establishing the conversion relationship between true stress and engineering stress under non-uniaxial stress conditions.
[0040] Compared with existing technologies, current methods typically assume that experimental data meet uniaxial stress conditions, neglecting errors caused by fixture constraints and non-uniform sample deformation. This approach, however, establishes a non-uniaxial finite element model to simulate the complex stress state in actual experiments. Combined with a multi-objective optimization algorithm, it quantifies the impact of non-uniaxial effects, effectively eliminating the interference of experimental condition deviations on data conversion. This application can accurately establish the quantitative relationship between real stress and engineering stress under non-uniaxial testing conditions, providing a reliable data foundation for subsequent constitutive model parameter calibration and solving the technical problem of the failure of the uniaxial stress state assumption due to non-uniform deformation of brain tissue samples.
[0041] Furthermore, the specific steps of step S5 are as follows: S51. Establish a geometric model of the brain tissue sample based on the actual external dimensions and shape of the experimental sample.
[0042] S52. Mesh the geometric model of the brain tissue sample and establish a finite element model of the brain tissue sample using solid elements.
[0043] S53. Input the temporary hyperelastic constitutive model parameters in S2 into the finite element model of the brain tissue sample established in S52, apply a load to the surface of the finite element model of the brain tissue sample, and allow the cross-sectional area to deform freely to establish a uniaxial tensile finite element model and a uniaxial compressive finite element model.
[0044] The actual external dimensions and shape refer to a digital model constructed by measuring the three-dimensional geometric features of actual brain tissue samples. Data can be acquired using 3D scanning or microscopic imaging techniques to ensure consistency between the geometric model and the actual sample's morphology. Solid elements refer to the finite element type used to simulate the mechanical behavior of a three-dimensional continuum. Specifically, hexahedral elements can be used for meshing, accurately describing the volumetric deformation characteristics of brain tissue under uniaxial loads. Temporary hyperelastic constitutive model parameters refer to material property data obtained through preliminary calibration using pseudo-realistic stress-elongation curves. These parameters may include coefficients from the hyperelastic constitutive model and are used to predict the nonlinear mechanical response of brain tissue in uniaxial simulations. Load application refers to simulating the mechanical environment of uniaxial tension or compression through boundary conditions. Specifically, displacement loads can be applied to the model's end faces while allowing free deformation of the cross-section to achieve a uniaxial stress state.
[0045] Specifically, a finite element model of brain tissue is established based on the geometric features of real samples, and a mesh is created using solid elements to capture three-dimensional deformation behavior. Temporary constitutive parameters are input into the model, and axial loads are applied to the end faces while lateral constraints are removed, allowing the cross-sectional area of the model to change freely during tension or compression, thus simulating the deformation process under strict uniaxial stress. This model avoids stress distribution deviations caused by clamp friction or necking effects in non-uniaxial tests, providing an accurate simulation data basis for subsequent parameter calibration.
[0046] Compared with existing technologies, traditional methods often ignore the deviation between simulation results and actual mechanical responses caused by boundary condition constraints in uniaxial simulations. This method effectively eliminates the interference of non-uniaxial stress components by accurately restoring the geometry of the sample and removing lateral constraints, making the simulation results more consistent with real uniaxial test conditions.
[0047] Furthermore, the specific steps of step S6 are as follows: S61. Input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model under the strict uniaxial tension / compression condition described in S5 to perform uniaxial tension and compression simulation.
[0048] S62. Obtain the true stress-elongation response results of the model in uniaxial tension and compression simulation.
[0049] S63. Based on the non-uniaxial tensile true stress-elongation curve and non-uniaxial compressive true stress-elongation curve obtained in S4, and the uniaxial tensile true stress-elongation curve and uniaxial compressive true stress-elongation curve obtained in S62, a scaling relationship between the two sets of curves is established using multi-objective optimization, thereby establishing the transformation relationship between the true stress-elongation curve under strict uniaxial stress and the true stress-elongation curve under non-uniaxial working conditions.
[0050] Compared to existing technologies, traditional methods directly equate the true stress obtained from non-uniaxial test data to the true stress under uniaxial stress conditions for parameter calibration, ignoring errors caused by fixture constraints and uneven sample deformation. In contrast, this approach, by constructing a scaling transformation relationship, effectively separates test system errors from inherent material properties, preserving the true mechanical response of brain tissue while eliminating interference factors introduced by experimental condition limitations.
[0051] Through the above technical solution, this application achieves a reliable conversion from non-uniaxial test data to uniaxial stress state, solving the problem that uniaxial stress-strain relationships cannot be directly obtained due to experimental limitations, and significantly improving the accuracy of parameter identification for hyperelastic constitutive models. The established scaling conversion relationship can be applied to both tensile and compressive load conditions simultaneously, ensuring the consistency of the constitutive model's characterization under different stress states, and providing a reliable mechanical model foundation for subsequent brain injury simulation.
[0052] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of protection claimed by the present invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.
Claims
1. A method for parameter identification of a hyperelastic constitutive model using brain tissue non-axial tension and compression test results, characterized in that, The method comprises the following steps: S1, preliminary processing of test data of tensile test and compression test, obtaining pseudo true stress-elongation rate curve through test data; S2, calibrating hyperelastic constitutive model through pseudo true stress-elongation rate curve, obtaining a set of temporary hyperelastic constitutive model parameters; S3, establishing finite element model under non-standard uniaxial tensile / compression test condition, as shown in FIG. 2; S4, obtaining conversion relationship between true stress-elongation rate curve and engineering stress-elongation rate curve under non-uniaxial test condition by using temporary hyperelastic constitutive model parameters obtained in S2 and finite element model established in S3; S5, establishing finite element model under strict uniaxial tensile / compression condition; S6, inputting temporary hyperelastic constitutive model parameters obtained in S2 into finite element model established in S3 and S5, obtaining conversion relationship between true stress-elongation rate curve under non-uniaxial condition and true stress-elongation rate curve under strict uniaxial stress state; S7, processing force-displacement test data obtained under non-uniaxial test condition by using conversion relationship obtained in S4, wherein engineering stress is obtained by dividing force by initial surface area of brain tissue test sample, elongation rate is obtained by dividing sum of displacement and original length of brain tissue test sample by original length, and engineering stress-elongation rate curve is calculated through conversion relationship obtained in S4 to obtain true stress-elongation rate curve of brain tissue under non-uniaxial test condition; S8, converting true stress-elongation rate curve under non-uniaxial condition obtained in S7 into true stress-elongation rate curve under uniaxial stress state suitable for calibrating hyperelastic constitutive model parameters by using conversion relationship obtained in S6; S9, calibrating hyperelastic constitutive model by using true stress-elongation rate curve result in S8, obtaining hyperelastic constitutive model parameters capable of accurately characterizing brain tissue response.
2. The method of claim 1, wherein the method is characterized by: The specific steps of the step S1 are as follows: S11, calculating engineering stress-elongation rate curve through force-displacement curve obtained through test, wherein tensile force and tensile displacement obtained through tensile test are positive values, compression test force and compression displacement obtained through compression test are negative values, engineering stress is obtained by dividing force by initial cross-sectional area of test piece, and elongation rate is obtained by dividing sum of displacement and original length of test piece by original length of test piece; S12, obtaining pseudo true stress-elongation rate curve through engineering stress-elongation rate curve, wherein pseudo true stress is calculated by multiplying engineering stress and elongation rate.
3. The method of claim 2, wherein the method is characterized by: The specific steps of the step S3 are as follows: S31, establishing geometric model of brain tissue sample according to true shape size and shape of test sample; S32, establishing simplified jig geometric model; S33, performing mesh division on brain tissue sample geometric model, and using solid element to establish finite element model of brain tissue sample; S34, performing mesh division on simplified jig geometric model, and using solid element to establish finite element model of jig; S35, establishing non-uniaxial tensile finite element model by using finite element model of brain tissue sample and finite element model of jig established in S33 and S34. S36, using the finite element model of the brain tissue sample and the finite element model of the clamp established in S33 and S34, a non-uniaxial compression finite element model is established.
4. The method of claim 3, wherein the method is characterized by: The specific steps of the step S4 are as follows: S41, input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model under the non-standard uniaxial tension / compression test condition in S3 to perform non-uniaxial tension and compression simulation; S42, obtain the force-displacement response results of the model in the non-uniaxial tension simulation; S43, process the force-displacement response results in S42 to obtain a tension engineering stress-elongation rate curve, wherein the tension engineering stress is obtained by dividing the force by the initial cross-sectional area of the brain tissue sample finite element model; and the elongation rate is obtained by dividing the sum of the tension displacement and the original length of the brain tissue sample finite element model by the original length; S44, obtain the force-displacement response results of the model in the non-uniaxial compression simulation; S45, process the force-displacement response results in S44 to obtain a compression engineering stress-elongation rate curve, wherein the compression engineering stress is obtained by dividing the force by the initial cross-sectional area of the brain tissue sample finite element model; and the elongation rate is obtained by dividing the sum of the compression displacement and the original length of the brain tissue sample finite element model by the original length; S46, obtain the true stress-elongation rate response results of the model in the non-uniaxial tension simulation, select a cluster of grids located at the most core position of the model to obtain the tension true stress, and the elongation rate is obtained by dividing the sum of the tension displacement and the original length of the brain tissue sample finite element model by the original length; S47, obtain the true stress-elongation rate response results of the model in the non-uniaxial compression simulation, select a cluster of grids located at the most core position of the model to obtain the compression true stress, and the elongation rate is obtained by dividing the sum of the compression displacement and the original length of the brain tissue sample finite element model by the original length; S48, based on the formula between the engineering stress and the true stress under the strict uniaxial stress state, a relationship formula between the true stress and the engineering stress under the non-uniaxial stress state is proposed, and a multi-objective optimization is used to obtain the numerical value of the unknown constant parameter in the formula, and a conversion relationship between the true stress and the engineering stress under the non-uniaxial stress state is established.
5. The method of claim 4, wherein the method is characterized by: The specific steps of the step S5 are as follows: S51, a geometric model of the brain tissue sample is established according to the true shape size and shape of the test sample; S52, the brain tissue sample geometric model is meshed, and a brain tissue sample finite element model is established using solid elements; S53, input the temporary hyperelastic constitutive model parameters in S2 into the brain tissue sample finite element model established in S52, apply a load on the surface of the brain tissue sample finite element model, and allow the cross section to deform freely, to establish a uniaxial tension finite element model and a uniaxial compression finite element model.
6. The method of claim 5, wherein the method is characterized by: The specific steps of the step S6 are as follows: S61, input the temporary hyperelastic constitutive model parameters obtained in S2 into the finite element model under the strict uniaxial tension / compression working condition in S5 to perform uniaxial tension and compression simulation; S62, obtain the true stress-elongation rate response results of the model in the uniaxial tension and compression simulation; S63, according to the non-axial tension real stress-elongation curve and the non-axial compression real stress-elongation curve obtained in S4 and the uniaxial tension real stress-elongation curve and the uniaxial compression real stress-elongation curve obtained in S62, a scaling relationship between the two groups of curves is established by using multi-objective optimization, and a conversion relationship between the real stress-elongation curve under the strict uniaxial stress state and the real stress-elongation curve under the non-uniaxial working condition is established.