Method and system for inverting material shear constitutive relation based on solid round rod torsion
By using the torsion inversion method for solid round bars, a polynomial model is established and the algorithm for solving the coefficients is optimized, which solves the problems of complexity and high cost in the inversion of material constitutive relations in the existing technology, and realizes a simple and efficient material shear constitutive relation inversion.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-11
- Publication Date
- 2026-04-14
AI Technical Summary
Existing methods for inverting material constitutive relations require pre-setting the constitutive relations of the material, which are mathematically complex, difficult to calibrate parameters, and costly to conduct experiments. In particular, thin-walled cylindrical specimens are difficult to process and have low computational efficiency.
The torsion inversion method of solid round bars is adopted. By obtaining experimental torque-torsion angle curve data, a polynomial model of shear stress-shear strain and torque-torsion angle is established. The polynomial coefficients are solved by optimization algorithm to obtain the shear constitutive relation of the material.
It requires no pre-defined constitutive relations, has a simple mathematical form, is applicable to different materials, has low experimental costs, high computational efficiency, and strong applicability, making it suitable for the study of shear properties of engineering materials.
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Figure CN121862268A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of constitutive relation inversion technology, and more specifically, to a method and system for inverting material shear constitutive relations based on the torsion of a solid round bar. Background Technology
[0002] Constitutive relations of materials are fundamental for structural design and strength verification in practical applications, and their accuracy depends on the development of experimental and theoretical methods. Existing inversion methods often require the assumption that the material possesses a certain form of constitutive relation. Furthermore, due to the complexity of material mechanical behavior, traditional constitutive relations often require complex mathematical expressions, which are not only costly to learn but also generally suffer from difficulties in use, such as complex parameter calibration methods and low computational efficiency. In addition, obtaining the shear properties of materials often requires specially processed specimens such as thin-walled cylinders, which are relatively difficult to manufacture and have high experimental costs.
[0003] Therefore, there is an urgent need for a method and system based on the torsion inversion of material shear constitutive relations using solid circular bars to solve the above-mentioned technical problems. Summary of the Invention
[0004] The purpose of this invention is to provide a method and system for inverting the material shear constitutive relation based on the torsion of a solid circular bar, so as to improve the above-mentioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:
[0005] Firstly, this application provides a method for inverting material shear constitutive relations based on the torsion of a solid circular bar, including:
[0006] Obtain the experimental torque-torsion angle curve data, length, and radius of the solid round bar specimen in the pure torsion test;
[0007] Based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, a mathematical model was established. By defining the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial, a mathematical model based on polynomial form was obtained.
[0008] Based on the mathematical model based on polynomial form, the coefficient relationship is derived to obtain the conversion relationship between polynomial coefficients. The polynomial coefficients refer to the polynomials of shear stress-shear strain relationship and torque-torsion angle relationship.
[0009] Based on the conversion relationship between the experimental torque-torsion angle curve data and the polynomial coefficients, the parameters are optimized, and the coefficients of the torque-torsion angle relationship polynomial are solved by the optimization algorithm to obtain the optimized torque polynomial coefficients.
[0010] Constitutive coefficients are calculated based on the optimized torque polynomial coefficients and the conversion relationship between polynomial coefficients. Shear constitutive relation analysis is then performed using the calculated constitutive relation coefficients to obtain the shear constitutive relation of the inverted material.
[0011] Secondly, this application also provides a system for inverting material shear constitutive relations based on the torsion of a solid circular bar, comprising:
[0012] The acquisition unit is used to acquire the experimental torque-torsion angle curve data, length, and radius of the solid round bar specimen in the pure torsion test;
[0013] The construction unit is used to establish a mathematical model based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, and to obtain a mathematical model based on polynomial form by defining the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial.
[0014] The conversion unit is used to derive the coefficient relationship based on the mathematical model based on polynomial form to obtain the conversion relationship between polynomial coefficients, wherein the polynomial coefficients refer to the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial.
[0015] The optimization unit is used to optimize parameters based on the conversion relationship between the experimental torque-torsion angle curve data and polynomial coefficients, and to solve the coefficients of the torque-torsion angle relationship polynomial through the optimization algorithm to obtain the optimized torque polynomial coefficients.
[0016] The calculation unit is used to calculate constitutive coefficients based on the optimized torque polynomial coefficients and the conversion relationship between the polynomial coefficients, and to perform shear constitutive relation analysis through the calculated constitutive relation coefficients to obtain the shear constitutive relation of the inverted material.
[0017] The beneficial effects of this invention are as follows:
[0018] First, the constitutive relation inversion method provided by this invention does not require pre-setting the constitutive relation of the material and is applicable to different materials. Second, this invention uses polynomial expansion to describe the constitutive relation, which is simple in mathematical form and very easy to use. Finally, this invention uses a solid round bar torsion experiment to invert the shear properties of the material, which is easier to process and has lower experimental costs than thin-walled cylindrical samples.
[0019] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description
[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0021] Figure 1 This is a schematic diagram of the method for inverting material shear constitutive relations based on the torsion of a solid round bar, as described in an embodiment of the present invention.
[0022] Figure 2 This is a schematic diagram of the system structure based on the torsional inversion of material shear constitutive relations using a solid circular bar, as described in an embodiment of the present invention.
[0023] Figure 3 This is a schematic diagram comparing the torque-torsion angle curves obtained from the pure torsion experiment and the inversion of the 2A12 aluminum alloy solid round bar in an embodiment of the present invention.
[0024] Figure 4 This is a schematic diagram of the shear stress-shear strain curve of 2A12 aluminum alloy obtained by inversion in an embodiment of the present invention.
[0025] Figure 5 This is a schematic diagram comparing the torque-torsion angle curves obtained from the pure torsion experiment and the inversion of a solid round bar of nylon 6 (PA6) in an embodiment of the present invention.
[0026] Figure 6 The image shows the shear stress-shear strain curve of nylon 6 (PA6) aluminum alloy obtained by inversion in an embodiment of the present invention.
[0027] In the diagram: 701, Acquisition Unit; 702, Construction Unit; 703, Conversion Unit; 704, Optimization Unit; 705, Calculation Unit. Detailed Implementation
[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention 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 the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.
[0029] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.
[0030] Example 1:
[0031] This embodiment provides a method for inverting the material shear constitutive relation based on the torsion of a solid round bar.
[0032] See Figure 1 , Figure 3 and Figure 4 The figure shows that the method includes steps S1, S2, S3, S4 and S5.
[0033] Step S1: Obtain the experimental torque-torsion angle curve data, length and radius of the solid round bar specimen in the pure torsion test;
[0034] It is understandable that the pure torsion test of the solid round bar specimen in this step uses angle control to perform a quasi-static pure torsion test on the solid round bar specimen to obtain the experimental torque-torsion angle curve.
[0035] This embodiment selects a common material (aluminum alloy, grade 2A12) for a pure torsion test. In this embodiment, the gauge length of the solid round 2A12 aluminum alloy specimen is... The length of the clamping sections at both ends is 60mm. All are 35mm, radius The thickness is 3mm, and the loading rate for the quasi-static pure torsion test is... .
[0036] Pure torsion testing requires precise alignment of the upper and lower clamps of the testing machine to avoid axial deformation during loading. For materials without a significant rate effect, the loading rate can be selected within a relatively wide range; for materials with a significant rate effect, the loading rate should be slow enough, corresponding to quasi-static loading.
[0037] It should be noted that the theoretical derivation in step S3 of this invention is based on the classical solid round bar torsion theory. The validity of this theory depends on the following assumptions: (1) The deformation of the rod satisfies the plane section assumption, that is, the cross section remains a plane and the radius remains a straight line, which has high accuracy in the small and medium strain range; (2) The material is macroscopically continuous, uniform and isotropic; (3) The loading process is quasi-static and the mechanical response of the material does not depend on the loading rate.
[0038] Therefore, the method described in this invention is particularly applicable to inverting the shear constitutive relations of engineering materials that conform to the above assumptions, such as, but not limited to: various metallic materials (such as the 2A12 aluminum alloy in this embodiment), homogeneous engineering plastics, polymer materials, ceramic materials, etc.
[0039] For materials that do not fully satisfy the above assumptions (such as orthotropic composite materials or hyperelastic materials that undergo large geometric deformation), those skilled in the art can adjust the theoretical derivation in step S3 by adopting corresponding modified theories (such as nonlinear geometric relationships or anisotropic mechanical theories) based on the basic ideas of this invention.
[0040] Step S2: Based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, a mathematical model is established. By defining the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial, a mathematical model based on polynomial form is obtained.
[0041] It is understandable that this step achieves efficient conversion from macroscopic experimental data to microscopic constitutive parameters by establishing a dual polynomial model of shear stress-shear strain and torque-torsion angle. This method employs a generalized polynomial expansion, avoiding the pre-defined dependence on specific constitutive relations inherent in traditional methods, thus significantly improving applicability. Through rigorous theoretical derivation, coefficient conversion relationships are established, and parameter inversion is performed using optimization algorithms, ultimately obtaining accurate material shear constitutive curves. In this step, step S2 includes steps S21, S22, and S23.
[0042] Step S21: Based on the experimental torque-torsion angle curve data and the length and radius of the solid round bar specimen, define the shear stress-shear strain relationship. By using a polynomial function to describe the shear stress and shear strain relationship, obtain the shear stress-shear strain relationship polynomial.
[0043] Step S22: Based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, and the shear stress-shear strain polynomial, define the torque-torsion angle relationship. By describing the relationship between torque and torsion angle using a polynomial function, obtain the torque-torsion angle relationship polynomial.
[0044] Step S23: Use the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial as the mathematical model based on the polynomial form.
[0045] It is understood that steps S21, S22, and S23 detail the process by which step S2 uses the shear stress-shear strain polynomial and the torque-torsion angle polynomial to describe the shear constitutive behavior and macroscopic torsional behavior of the material, respectively. In this invention, the following generalized polynomial expansion is selected:
[0046]
[0047]
[0048] in, The distance from the center of the circular bar cross section is Shear stress at the point, The distance from the center of the circular bar cross section is Shear strain at the point, For the coefficients of the shear stress-shear strain relationship model, For the torque of the round bar, For the torsion angle of the round bar, These are the coefficients of the torque-torsion angle relationship model. The index is the number of the expansion, such as the first one. item, Let be the number of terms in the expansion. The advantage of choosing this form is that it... The power term can flexibly describe the smooth transition of a material from elastic to plastic and has high fitting accuracy.
[0049] However, those skilled in the art should understand that the core ideas of this invention are not limited to the specific ones described above. The power polynomial. The "mathematical model" mentioned in step S2 can be any functional form that can describe the nonlinear behavior of the material, as long as step S3 can derive the shear stress-shear strain relationship model (e.g., based on the selected functional form and the torsion theory of circular bars) ) and the torque-torsion angle relationship model (e.g. The mathematical conversion relationship between the coefficients can be obtained.
[0050] For example, the mathematical model may also be, but is not limited to:
[0051] Standard power polynomial: Its corresponding .
[0052] Other power function series: for example, the Ramberg-Osgood form or its modified form.
[0053] Other function bases that include exponential, logarithmic, or hyperbolic functions.
[0054] Step S3: Based on the mathematical model based on polynomial form, the coefficient relationship is derived to obtain the conversion relationship between polynomial coefficients. The polynomial coefficients refer to the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial.
[0055] Understandably, this step establishes a complete analytical transfer path, making it possible to invert material constitutive parameters from macroscopic experimental data. Its innovation lies in transforming a complex mechanical integral problem into a concise polynomial coefficient matching problem, significantly reducing computational complexity. Furthermore, this derivation framework has good universality; as long as the basic theoretical assumptions are met, it can be applied to various engineering materials. In this step, step S3 includes steps S31, S32, and S33.
[0056] Step S31: Perform shear strain distribution processing based on the mathematical model based on polynomial form. By applying the circular bar torsion theory to define the relationship between shear strain and torsion angle and length of solid circular bar specimen, the shear strain distribution expression is obtained.
[0057] It is understandable that this step is based on the theory of torsion of a circular bar, and derives the mathematical conversion relationship between the coefficients of the shear stress-shear strain polynomial and the coefficients of the torque-torsion angle polynomial.
[0058] For a solid round bar, the distance from the center of the circular cross-section is... Shear strain at the point relative to the two ends of the member , pole length The relationships (mathematical conversion relationships between the coefficients of polynomials) are as follows:
[0059]
[0060] Step S32: Based on the shear strain distribution expression and the shear stress-shear strain relationship polynomial, derive the torque expression and obtain the torque polynomial expression through integration.
[0061] It is understandable that the torque of the round bar in this step... It is the integral of the shear stress on the circular cross section, as shown below:
[0062]
[0063] Substitution The expression is as follows:
[0064]
[0065] right After integration, the torque polynomial expression is obtained, as shown below:
[0066]
[0067] Among them, length ,radius All of these are geometric parameters of a solid round rod, and are known physical quantities. The differential symbol, Pi is the mathematical constant of a circle.
[0068] Step S33: Based on the torque polynomial expression and the torque-torsion angle relationship polynomial, perform coefficient matching processing. By comparing the conversion relationship between the polynomial coefficients of the shear stress-shear strain relationship coefficient and the torque-torsion angle relationship coefficient, obtain the conversion relationship between the polynomial coefficients.
[0069] It is understandable that this step will integrate to obtain the torque polynomial expression and the torque-torsion angle relationship polynomial. By comparison, the polynomial coefficients can be obtained. and The conversion relationships between them are as follows:
[0070]
[0071]
[0072] Step S4: Optimize the parameters based on the conversion relationship between the experimental torque-torsion angle curve data and the polynomial coefficients. Solve the coefficients of the torque-torsion angle relationship polynomial using the optimization algorithm to obtain the optimized torque polynomial coefficients.
[0073] Understandably, this step first establishes an optimization objective function, aiming to minimize the sum of squared residuals between each data point on the experimental torque-torsion angle curve and the calculated value from the polynomial model. Specifically, the objective function is defined as the sum of squared differences between the experimental torque value and the theoretical torque value, ensuring that the inversion process has a clear mathematical optimization objective. Based on this objective function, this invention employs a hybrid optimization strategy to balance robustness and accuracy in the solution. First, a genetic algorithm (GA) is used to perform a global search on the polynomial coefficients, leveraging its powerful global exploration capability to avoid getting trapped in local optima. Then, the optimal solution obtained by the genetic algorithm is used as the initial value, and a sequential quadratic programming algorithm (SQP) is employed for a locally accurate search to further improve the accuracy of parameter solving. In this step, step S4 includes steps S41, S42, and S43.
[0074] Step S41: Based on the experimental torque-torsion angle curve data and the mathematical model based on polynomial form, define the objective function by minimizing the sum of squared residuals between the experimental torque value and the theoretical torque value.
[0075] It is understood that this step is based on the experimental torque-torsion angle curve, and the coefficients of the torque-torsion angle relationship polynomial are determined by an optimization algorithm. The coefficients of the shear stress-shear strain relationship polynomial are calculated according to the mathematical conversion relationship, thereby obtaining the shear constitutive relationship of the material.
[0076] Number of terms in the expansion The selection principle is: while ensuring the fitted curve is smooth and does not overfit, gradually increase the [value]. The value of is calculated until the sum of squared residuals of the objective function converges to below a preset threshold. In this embodiment, the number of terms in the expansion is... Set it to 10.
[0077] The process of determining the expansion coefficients through optimization algorithms specifically aims to minimize the sum of squared residuals between the data points on the experimentally obtained torque-torsion angle curve and the theoretical torque value calculated by the polynomial model. This objective function can be expressed by the following equation:
[0078]
[0079] in, Let the value of the objective function be minimized. The total number of experimental data points. For the first Torque values at each experimental data point To make the first Torsion angle at each experimental data point Substituting into the torque polynomial expansion The theoretical torque value was then calculated, where, The total number of experimental data points
[0080] Step S42: Perform global optimization search processing according to the optimization objective function. Use a preset genetic algorithm to perform a global search on the coefficients of the torque-torsion angle relationship polynomial to obtain preliminary optimization coefficients.
[0081] Understandably, this step first uses a genetic algorithm (GA) to process the polynomial coefficients. A global search is performed to find a set of initial values close to the optimal solution. The genetic algorithm in this step does not rely on the gradient information of the objective function, can handle non-differentiable or discontinuous optimization problems, and is suitable for constitutive inversion of various material types. Meanwhile, its parallel search characteristics significantly improve computational efficiency, making it particularly suitable for multi-parameter optimization problems. Through global exploration, this method ensures the reliability of the inversion results and avoids optimization failures caused by improper initial value selection.
[0082] Step S43: Based on the preliminary optimization coefficients and the optimization objective function, perform local optimization and refinement processing. Use a preset sequential quadratic programming algorithm to perform a local precise search on the preliminary optimization coefficients to obtain the optimized torque polynomial coefficients.
[0083] It is understandable that, to improve the solution accuracy, this step uses the optimal solution obtained by the genetic algorithm as the initial value, and employs a Sequential Quadratic Programming (SQP) algorithm for a locally precise search until the objective function value converges. The comparison diagram of the torque-torsion angle curves obtained from the pure torsion experiment and the inversion of 2A12 aluminum alloy in this embodiment is shown below. Figure 3 As shown.
[0084] The hybrid optimization strategy combining genetic algorithm (GA) and sequential quadratic programming (SQP) employed in this embodiment is a preferred implementation. Its advantage lies in the fact that the global search capability of the genetic algorithm effectively avoids getting trapped in local optima, while sequential quadratic programming enables efficient local exact search, thus balancing robustness and accuracy. However, this step is not limited to this specific algorithm combination. The core of this step lies in solving the objective function. To determine the coefficients of the torque-torsion angle relationship polynomial. Any numerical algorithm capable of solving this type of nonlinear least squares or parameter optimization problem can be used to implement this invention.
[0085] For example, alternative optimization algorithms include, but are not limited to:
[0086] Other global optimization algorithms include Particle Swarm Optimization (PSO), Simulated Annealing, and Differential Evolution.
[0087] Gradient descent algorithms include Levenberg-Marquardt (LM) algorithms, trust-region methods, interior-point methods, and conjugate gradient methods.
[0088] Step S5: Perform constitutive coefficient calculation based on the optimized torque polynomial coefficients and the conversion relationship between polynomial coefficients, and perform shear constitutive relation analysis using the calculated constitutive relation coefficients to obtain the shear constitutive relation of the inverted material.
[0089] Understandably, this step achieves a direct conversion from macroscopic mechanical tests to microscopic constitutive parameters, avoiding the complex iterative calculation process in traditional methods. By establishing a complete coefficient conversion chain, the mathematical rigor and computational efficiency of the inversion process are ensured. Furthermore, this method has good applicability to various engineering materials, providing a standardized analytical tool for the study of material shear properties. In this step, step S5 includes steps S51 and S52.
[0090] Step S51: Perform constitutive coefficient calculation based on the optimized torque polynomial coefficients and the conversion relationship between polynomial coefficients. Calculate the coefficients of the shear stress-shear strain relationship polynomial through mathematical conversion relationships to obtain the constitutive coefficients of the inverted material.
[0091] To obtain the optimal torque polynomial coefficients Then, according to the conversion formula The shear constitutive polynomial was calculated. coefficient , and use them as constitutive relation coefficients for inverted materials.
[0092] This step enables the rapid and accurate acquisition of the constitutive coefficients of materials, providing reliable input for subsequent engineering applications. This concise and efficient conversion process achieves a seamless transition from macroscopic experiments to microscopic parameters, demonstrating the method's dual advantages in both engineering practicality and theoretical rigor.
[0093] Step S52: Generate shear constitutive relations based on the constitutive coefficients of the inverted material. By substituting the constitutive coefficients of the inverted material into the mathematical model based on polynomial form, a complete shear stress-shear strain relationship curve is generated, and the shear constitutive relations of the inverted material are obtained.
[0094] It is understandable that this step will ultimately result in constitutive coefficients. Substituting the polynomial based on the shear stress-shear strain relationship, the shear stress-shear strain curve of the material can be obtained, thus completing the entire inversion process. The shear stress-shear strain curve corresponding to the inverted shear constitutive relation is shown in the figure below. Figure 4 As shown.
[0095] Example 2:
[0096] like Figure 2 As shown, this embodiment provides a system for inverting material shear constitutive relations based on the torsion of a solid circular bar. See [link to documentation]. Figure 2 The system includes an acquisition unit 701, a construction unit 702, a conversion unit 703, an optimization unit 704, and a calculation unit 705.
[0097] The acquisition unit 701 is used to acquire the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen in the pure torsion test;
[0098] The construction unit 702 is used to perform mathematical model building based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, and to obtain a mathematical model based on polynomial form by defining the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial.
[0099] The conversion unit 703 is used to perform coefficient relationship derivation processing based on the mathematical model based on polynomial form to obtain the conversion relationship between polynomial coefficients, wherein the polynomial coefficients refer to the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial.
[0100] The optimization unit 704 is used to optimize the parameters based on the conversion relationship between the experimental torque-torsion angle curve data and the polynomial coefficients, and to solve the coefficients of the torque-torsion angle relationship polynomial through the optimization algorithm to obtain the optimized torque polynomial coefficients.
[0101] The calculation unit 705 is used to perform constitutive coefficient calculation based on the optimized torque polynomial coefficients and the conversion relationship between the polynomial coefficients, and to perform shear constitutive relation analysis through the calculated constitutive relation coefficients to obtain the shear constitutive relation of the inverted material.
[0102] Example 3:
[0103] like Figure 5 and Figure 6 As shown, this invention is also applicable to non-metallic materials. This embodiment uses a solid round bar specimen of nylon 6 (PA6) as an example. The experimental curves exhibit nonlinear characteristics different from those of metals (e.g., a longer elastic phase and significant strain hardening). This embodiment first repeats steps S1-S5 of Example 1. In step S5, according to the Nylon 6 material... The smoothness of the curve can be flexibly adjusted by selecting an appropriate number of terms. By optimizing the solution in step S5 and converting the coefficients in step S4, the nylon 6 material can be obtained. Shear constitutive relation.
[0104] In this embodiment, the gauge length of the solid nylon 6 round bar specimen used is... The length of the clamping sections at both ends is 14.5mm. All are 20mm, radius The thickness is 1.5 mm. The loading rate for the quasi-static pure torsion test is... Repeat steps S1-S5 in Example 1, expanding the number of terms. The value is set to 8. The comparison diagram of the torque-torsion angle curves obtained from the pure torsion experiment and the inversion of Nylon 6 in this embodiment is shown below. Figure 5 As shown. The inverse shear constitutive relation, and its shear stress-shear strain curve are shown in the figure. Figure 6 As shown.
[0105] Example 3 further demonstrates that the inversion method provided by the present invention does not depend on specific material types and has wide applicability and practicality.
[0106] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here.
[0107] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
[0108] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for inverting material shear constitutive relations based on the torsion of a solid circular bar, characterized in that, include: Obtain the experimental torque-torsion angle curve data, length, and radius of the solid round bar specimen in the pure torsion test; Based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, a mathematical model was established. By defining the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial, a mathematical model based on polynomial form was obtained. Based on the mathematical model based on polynomial form, the coefficient relationship is derived to obtain the conversion relationship between polynomial coefficients. The polynomial coefficients refer to the polynomials of shear stress-shear strain relationship and torque-torsion angle relationship. Based on the conversion relationship between the experimental torque-torsion angle curve data and the polynomial coefficients, the parameters are optimized, and the coefficients of the torque-torsion angle relationship polynomial are solved by the optimization algorithm to obtain the optimized torque polynomial coefficients. Constitutive coefficients are calculated based on the optimized torque polynomial coefficients and the conversion relationship between polynomial coefficients. Shear constitutive relation analysis is then performed using the calculated constitutive relation coefficients to obtain the shear constitutive relation of the inverted material.
2. The method for inverting material shear constitutive relations based on the torsion of a solid circular bar according to claim 1, characterized in that... Based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, a mathematical model was established. This involved defining polynomials for the shear stress-shear strain relationship and the torque-torsion angle relationship, including: Based on the experimental torque-torsion angle curve data and the length and radius of the solid round bar specimen, the shear stress-shear strain relationship was defined and processed. By using a polynomial function to describe the shear stress and shear strain relationship, the polynomial of the shear stress-shear strain relationship was obtained. Based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, and the shear stress-shear strain polynomial, the torque-torsion angle relationship is defined and processed. By describing the relationship between torque and torsion angle using a polynomial function, the torque-torsion angle relationship polynomial is obtained. The shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial are used as the mathematical model based on the polynomial form.
3. The method for inverting material shear constitutive relations based on the torsion of a solid circular bar according to claim 1, characterized in that... The derivation of coefficient relationships based on the polynomial-based mathematical model includes: Based on the mathematical model based on polynomial form, the shear strain distribution is processed, and by applying the circular bar torsion theory, the relationship between shear strain and torsion angle and length of solid circular bar specimen is defined to obtain the shear strain distribution expression; The torque expression is derived based on the shear strain distribution expression and the shear stress-shear strain relationship polynomial, and then the torque expression is obtained through integration, resulting in the torque polynomial expression. Based on the torque polynomial expression and the torque-torsion angle relationship polynomial, coefficient matching is performed. By comparing the conversion relationship between the polynomial coefficients of the shear stress-shear strain relationship coefficient and the torque-torsion angle relationship coefficient, the conversion relationship between the polynomial coefficients is obtained.
4. The method for inverting material shear constitutive relations based on the torsion of a solid circular bar according to claim 1, characterized in that... Based on the experimental torque-torsion angle curve data and the conversion relationship between polynomial coefficients, the parameters are optimized, including: Based on the experimental torque-torsion angle curve data and the mathematical model based on polynomial form, the objective function is defined by minimizing the sum of squared residuals between the experimental torque value and the theoretical torque value. A global optimization search is performed based on the objective function. The coefficients of the torque-torsion angle relationship polynomial are searched globally using a preset genetic algorithm to obtain preliminary optimization coefficients. Based on the preliminary optimization coefficients and the optimization objective function, local optimization and refinement processing is performed. The preliminary optimization coefficients are then locally precisely searched using a preset sequential quadratic programming algorithm to obtain the optimized torque polynomial coefficients.
5. The method for inverting material shear constitutive relations based on the torsion of a solid circular bar according to claim 1, characterized in that... Constitutive coefficients are calculated based on the optimized torque polynomial coefficients and the conversion relationship between polynomial coefficients. Shear constitutive relation analysis is then performed using the calculated constitutive relation coefficients, including: Constitutive coefficients are calculated based on the optimized torque polynomial coefficients and the conversion relationship between polynomial coefficients. The coefficients of the shear stress-shear strain relationship polynomial are calculated through mathematical conversion relationships to obtain the constitutive coefficients of the inverted material. Shear constitutive relations are generated based on the constitutive relations coefficients of the inverted material. By substituting the constitutive relations coefficients of the inverted material into a mathematical model based on polynomial form, a complete shear stress-shear strain relationship curve is generated, and the shear constitutive relations of the inverted material are obtained.
6. A system for inverting material shear constitutive relations based on the torsion of a solid circular bar, characterized in that, include: The acquisition unit is used to acquire the experimental torque-torsion angle curve data, length, and radius of the solid round bar specimen in the pure torsion test; The construction unit is used to establish a mathematical model based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, and to obtain a mathematical model based on polynomial form by defining the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial. The conversion unit is used to derive the coefficient relationship based on the mathematical model based on polynomial form to obtain the conversion relationship between polynomial coefficients, wherein the polynomial coefficients refer to the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial. The optimization unit is used to optimize parameters based on the conversion relationship between the experimental torque-torsion angle curve data and polynomial coefficients, and to solve the coefficients of the torque-torsion angle relationship polynomial through the optimization algorithm to obtain the optimized torque polynomial coefficients. The calculation unit is used to calculate constitutive coefficients based on the optimized torque polynomial coefficients and the conversion relationship between the polynomial coefficients, and to perform shear constitutive relation analysis through the calculated constitutive relation coefficients to obtain the shear constitutive relation of the inverted material.
7. The system for inverting material shear constitutive relations based on torsion of a solid circular bar according to claim 6, characterized in that, The building unit includes: The first construction subunit is used to define the shear stress-shear strain relationship based on the experimental torque-torsion angle curve data and the length and radius of the solid round bar specimen. The shear stress-shear strain relationship polynomial is obtained by describing the shear stress and shear strain relationship in the form of a polynomial function. The second construction subunit is used to define the torque-torsion angle relationship based on the experimental torque-torsion angle curve data, the length and radius of the solid round bar specimen, and the shear stress-shear strain relationship polynomial. By describing the relationship between torque and torsion angle in polynomial function form, the torque-torsion angle relationship polynomial is obtained. The third construction subunit is used to take the shear stress-shear strain relationship polynomial and the torque-torsion angle relationship polynomial as the mathematical model based on the polynomial form.
8. The system for inverting material shear constitutive relations based on torsion of a solid circular bar according to claim 6, characterized in that, The conversion unit includes: The first conversion sub-unit is used to process the shear strain distribution according to the mathematical model based on the polynomial form. By applying the circular bar torsion theory, the relationship between shear strain and torsion angle and length of solid circular bar specimen is defined to obtain the shear strain distribution expression. The second conversion subunit is used to derive the torque expression based on the shear strain distribution expression and the shear stress-shear strain relationship polynomial, and obtain the torque expression through integration, thus obtaining the torque polynomial expression. The third conversion subunit is used to perform coefficient matching processing based on the torque polynomial expression and the torque-torsion angle relationship polynomial. By comparing the conversion relationship between the polynomial coefficients of the shear stress-shear strain relationship coefficient and the torque-torsion angle relationship coefficient, the conversion relationship between the polynomial coefficients is obtained.
9. The system for inverting material shear constitutive relations based on the torsion of a solid circular bar according to claim 6, characterized in that, The optimization unit includes: The first optimization subunit is used to perform objective function definition processing based on the experimental torque-torsion angle curve data and the mathematical model based on polynomial form. The optimization objective function is defined by minimizing the sum of squared residuals between the experimental torque value and the theoretical torque value. The second optimization subunit is used to perform global optimization search processing according to the optimization objective function. It uses a preset genetic algorithm to perform a global search on the coefficients of the torque-torsion angle relationship polynomial to obtain preliminary optimization coefficients. The third optimization subunit is used to perform local optimization and refinement processing based on the preliminary optimization coefficients and the optimization objective function. It uses a preset sequential quadratic programming algorithm to perform a local precise search on the preliminary optimization coefficients to obtain the optimized torque polynomial coefficients.
10. The system for inverting material shear constitutive relations based on the torsion of a solid circular bar according to claim 6, characterized in that, The computing unit includes: The first calculation subunit is used to perform constitutive coefficient calculation based on the optimized torque polynomial coefficients and the conversion relationship between polynomial coefficients. It calculates the coefficients of the shear stress-shear strain relationship polynomial through mathematical conversion relationship to obtain the constitutive relationship coefficients of the inverted material. The second calculation sub-unit is used to generate shear constitutive relations based on the constitutive relations coefficients of the inverted material. By substituting the constitutive relations coefficients of the inverted material into the mathematical model based on polynomial form, a complete shear stress-shear strain relationship curve is generated, and the shear constitutive relations of the inverted material are obtained.