A method for performance prediction and design of negative poisson's ratio tubular structure based on geometric evolution

Abstract

This invention discloses a method for predicting and designing the performance of a negative Poisson's ratio tubular structure based on geometric evolution. The performance prediction method includes the following steps: establishing a comprehensive correction model based on the initial effective height, effective height, perimeter, total number of cells, axial number of cells, arbitrary rib width, arbitrary major and minor axis lengths of the elliptical cavity, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure; obtaining the rib width, major axis length, and minor axis length of the elliptical cavity; determining the major-to-minor axis ratio based on the major and minor axis lengths; and determining the effective Poisson's ratio based on the comprehensive correction model and the rib width and major-to-minor axis ratio. The comprehensive correction model, combining the thickness nonlinearity compensation coefficient and the physical compaction saturation limit, accurately reveals the intrinsic analytical relationship between geometric parameters and the effective Poisson's ratio, improving the prediction efficiency and accuracy of the effective Poisson's ratio.

Description

Technical Field

[0001] This invention relates to the field of pipe technology, and in particular to a method for predicting and designing the performance of negative Poisson's ratio tubular structures based on geometric evolution. Background Technology

[0002] Orthogonal elliptical lattice cylindrical structures exhibit excellent negative Poisson's ratio effects under axial compression, showing broad application prospects in engineering energy absorption and lightweight protection. However, in practical engineering applications and metamaterial design, current technologies for evaluating the performance of such structures mainly rely on finite element numerical simulation methods and ideal theoretical model prediction methods. Although numerical simulation can intuitively reproduce the stress characteristics and complex deformation evolution processes of structures, it is inefficient. Ideal theoretical model prediction methods can display global parameters and are more efficient, but they suffer from significant prediction bias.

[0003] Therefore, existing technologies still need improvement and development. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a method for predicting and designing the performance of negative Poisson's ratio tubular structures based on geometric evolution, in order to address the aforementioned deficiencies in the prior art.

[0005] The technical solution adopted by this invention to solve the technical problem is as follows: A method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution, comprising the following steps: Based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, a comprehensive correction model is established; wherein, the tubular structure forms elliptical holes, the elliptical holes include vertical elliptical holes and horizontal elliptical holes, each unit cell includes two vertical elliptical holes and two horizontal elliptical holes, the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the circumferential direction, and the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the axial direction; Obtain the rib width of the tubular structure and the length of the major and minor axes of the elliptical holes; The ratio of the major axis to the minor axis is determined based on the length of the major axis and the length of the minor axis. Based on the comprehensive correction model, the effective Poisson's ratio is determined according to the rib width and the ratio of major to minor axis.

[0006] The aforementioned method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution includes establishing a comprehensive correction model based on the initial effective height, effective height, perimeter, total number of cells, axial number of cells, arbitrary rib width, arbitrary major and minor axis lengths of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure. This model includes: A correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, and thickness nonlinear compensation coefficient of tubular structure. A comprehensive correction model is established based on the physical compaction saturation limit and the correction model.

[0007] The aforementioned method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution includes establishing a correction model based on the initial effective height, effective height, perimeter, total number of cells, axial number of cells, arbitrary rib width, arbitrary major and minor axis lengths of elliptical holes, and thickness nonlinear compensation coefficients of the tubular structure. This model includes: The equivalent long axis length is determined based on the long axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent short axis length is determined based on the short axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent residual bow height is determined based on the equivalent major axis length and the equivalent minor axis length. A correction model is established based on the initial effective height, the effective height, the perimeter, the total number of unit cells, the axial number of unit cells, the equivalent residual bow height, the equivalent major axis length, and the equivalent minor axis length.

[0008] The aforementioned method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution, wherein the equivalent residual bow height is: ; The equivalent major axis length is: ; The equivalent minor axis length is: ; in, Indicates the equivalent residual arch height. Indicates the equivalent major axis length. Indicates the length of the major axis. This represents the thickness nonlinearity compensation coefficient. Indicates rib width. Indicates the equivalent minor axis length. Indicates the length of the minor axis.

[0009] The aforementioned method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution, wherein the modified model is: ; ; ; in, This represents the corrected equivalent Poisson's ratio. Indicates the corrected surface porosity. This indicates the corrected axial compression ratio. Indicates the total number of unit cells. Indicates the effective height. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the initial effective height.

[0010] A design method for negative Poisson's ratio tubular structures based on geometric evolution, comprising the following steps: Based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, a comprehensive correction model is established; wherein, the tubular structure forms elliptical holes, the elliptical holes include vertical elliptical holes and horizontal elliptical holes, each unit cell includes two vertical elliptical holes and two horizontal elliptical holes, the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the circumferential direction, and the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the axial direction; Determine the target Poisson's ratio and constraints for the tubular structure; wherein the constraints include: the rib width of the elliptical hole is greater than or equal to the minimum rib width, and the major axis length of the elliptical hole is greater than or equal to the minimum major axis. Under constraints, the objective evaluation function is solved to obtain the rib width, major axis length, and minor axis length; wherein, the objective evaluation function is: , Represents the objective evaluation function. Indicates the length of the major axis. Indicates the length of the minor axis. Indicates the effective Poisson ratio. The target Poisson's ratio is represented; the effective Poisson's ratio is determined based on a comprehensive correction model, according to the rib width and the ratio of the major axis to the minor axis; the ratio of the major axis to the minor axis is determined based on the length of the major axis and the length of the minor axis. Based on the rib width, the major axis length, and the minor axis length, a negative Poisson's ratio tubular structure based on geometric evolution is prepared.

[0011] The aforementioned design method for negative Poisson's ratio tubular structures based on geometric evolution, wherein solving the objective evaluation function under constraints to obtain the major axis length and minor axis length includes: A numerical optimization algorithm is used to solve the objective evaluation function to obtain the rib width, major axis length, and minor axis length; wherein, the numerical optimization algorithm includes gradient descent or genetic algorithm.

[0012] The aforementioned design method for negative Poisson's ratio tubular structures based on geometric evolution includes establishing a comprehensive correction model based on the initial effective height, effective height, perimeter, total number of units, axial number of units, arbitrary rib width, arbitrary major and minor axis lengths of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure. This model includes: A correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, and thickness nonlinear compensation coefficient of tubular structure. A comprehensive correction model is established based on the physical compaction saturation limit and the correction model.

[0013] The aforementioned design method for negative Poisson's ratio tubular structures based on geometric evolution includes establishing a correction model based on the initial effective height, effective height, perimeter, total number of units, axial number of units, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, and thickness nonlinear compensation coefficient of the tubular structure. This model includes: The equivalent long axis length is determined based on the long axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent short axis length is determined based on the short axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent residual bow height is determined based on the equivalent major axis length and the equivalent minor axis length. A correction model is established based on the initial effective height, the effective height, the perimeter, the total number of unit cells, the axial number of unit cells, the equivalent residual bow height, the equivalent major axis length, and the equivalent minor axis length.

[0014] The aforementioned geometric evolution-based negative Poisson's ratio tubular structure design method, wherein the equivalent residual bow height is: ; The equivalent major axis length is: ; The equivalent minor axis length is: ; in, Indicates the equivalent residual arch height. Indicates the equivalent major axis length. Indicates the length of the major axis. This represents the thickness nonlinearity compensation coefficient. Indicates rib width. Indicates the equivalent minor axis length. Indicates the length of the minor axis; The corrected model is as follows: ; ; ; in, This represents the corrected equivalent Poisson's ratio. Indicates the corrected surface porosity. This indicates the corrected axial compression ratio. Indicates the total number of unit cells. Indicates the effective height. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the initial effective height.

[0015] Beneficial effects: By combining the thickness nonlinearity compensation coefficient and the physical compaction saturation limit, a comprehensive correction model is established. The comprehensive correction model accurately reveals the intrinsic analytical relationship between geometric parameters and effective Poisson's ratio, thereby improving the prediction efficiency and accuracy of effective Poisson's ratio. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the unit cell structure in an embodiment of the present invention.

[0017] Figure 2 This is a schematic diagram of the unfolded tubular structure in an embodiment of the present invention.

[0018] Figure 3 This is a schematic diagram of the tubular structure in an embodiment of the present invention.

[0019] Figure 4 This is a top view of the tubular structure in an embodiment of the present invention.

[0020] Figure 5 This is the equivalent Poisson ratio phase diagram in the embodiments of the present invention.

[0021] Figure 6 This is a comparison and verification diagram of the accuracy of different models in the embodiments of the present invention with a rib width of 1.5mm and a major axis of 16mm.

[0022] Figure 7 This is a comparison and verification diagram of the accuracy of different models in the embodiments of the present invention with a rib width of 1mm and a major axis of 16mm.

[0023] Figure 8This is a flowchart of the method for predicting the performance of a negative Poisson's ratio tubular structure based on geometric evolution, as described in this invention. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0025] Please also refer to Figures 1-8 This invention provides some embodiments of a method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution.

[0026] like Figure 8 As shown in the figure, the method for predicting the performance of a negative Poisson's ratio tubular structure based on geometric evolution according to an embodiment of the present invention includes the following steps: Step S100: Based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of the elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, a comprehensive correction model is established; wherein, the tubular structure forms elliptical holes, the elliptical holes include vertical elliptical holes and horizontal elliptical holes, each unit cell includes two vertical elliptical holes and two horizontal elliptical holes, the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the circumferential direction, and the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the axial direction; Step S200: Obtain the rib width of the tubular structure and the length of the major axis and minor axis of the elliptical hole; Step S300: Determine the ratio of the major axis to the minor axis based on the length of the major axis and the length of the minor axis; Step S400: Based on the comprehensive correction model, determine the effective Poisson's ratio according to the rib width and the ratio of major to minor axis.

[0027] Specifically, a comprehensive correction model for the tubular structure is first established. The major-minor axis ratio is determined based on the major and minor axis lengths of the elliptical aperture. Finally, based on the comprehensive correction model, the effective Poisson's ratio is determined according to the rib width and the major-minor axis ratio. By combining the thickness nonlinearity compensation coefficient and the physical compaction saturation limit, a comprehensive correction model is established. This model accurately reveals the intrinsic analytical relationship between geometric parameters and the effective Poisson's ratio, improving the prediction efficiency and accuracy of the effective Poisson's ratio.

[0028] The tubular structure can be made of metallic materials, which typically have a high modulus of elasticity. Multiple elliptical holes are formed within the tubular structure, creating a matrix and evenly distributed throughout. Based on their orientation, the elliptical holes are classified as vertical or horizontal. The major axis of the vertical elliptical holes is aligned with the axial direction of the tubular structure, while the minor axis of the horizontal elliptical holes is also aligned with the axial direction. The vertical and horizontal elliptical holes are the same size; their major and minor axes are equal. Axially, the major and minor axes of the vertical and horizontal elliptical holes are on the same straight line. Circumferentially, the minor and major axes of the vertical and horizontal elliptical holes are at the same horizontal level.

[0029] like Figure 1 and Figure 2 As shown, the elliptical holes are arranged in a repeating pattern, forming repeating units, i.e., unit cells. Each unit cell contains two vertical elliptical holes and two horizontal elliptical holes. The geometric parameters involved in the unit cell include: total number of unit cells, number of axial unit cells, unit cell length, major axis of the elliptical holes, minor axis of the elliptical holes, and the distance between two adjacent elliptical holes. For ease of description of the geometric parameters, a tubular structure is unfolded into a planar representation. The distance between the centers of two adjacent vertical elliptical holes is taken as the unit cell length. L That is, the unit cell space constraint scale (also known as pitch), the distance between the centers of two adjacent horizontal elliptical holes is also . L The major axis length of the elliptical hole is... The minor axis length of the elliptical hole is The minimum distance between the endpoint of the major axis of the vertical elliptical hole and the endpoint of the minor axis of the adjacent horizontal elliptical hole is taken as the spacing between two adjacent elliptical holes, i.e., the rib width. The minimum distance between the endpoint of the major axis of the horizontal elliptical hole and the endpoint of the minor axis of the adjacent vertical elliptical hole is also... The geometric parameters in each unit cell satisfy the following relationship: L = a + b +2 t ,0< b < a ; 0 < L ; 0 < t The ratio of the major axis to the minor axis is... λ = a / b Based on the comprehensive correction model, according to the rib width t and the ratio of major axis to minor axis λ The effective Poisson's ratio can be determined.

[0030] Step S100 specifically includes: Step S110: Based on the initial effective height, effective height, perimeter, total number of cells, axial number of cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, and thickness nonlinear compensation coefficient of the tubular structure, establish a correction model; Step S120: Based on the physical compaction saturation limit and the correction model, establish a comprehensive correction model.

[0031] Specifically, arbitrary rib width, arbitrary major axis length, and arbitrary minor axis length can form multiple sets of rib width, major axis length, and minor axis length, and each set of rib width, major axis length, and minor axis length satisfies the following relationship: L = a + b +2 t ,0< b < a ; 0 < L ; 0 < t This relationship allows for verification of the rib width, major axis length, and minor axis length for each group. If the verification fails, for example, regarding the rib width... t If the value is ≤0, the subsequent process is terminated, thereby avoiding invalid calculations that have no physical meaning.

[0032] Under the ideal closed model, the hole is completely closed, and the nominal Poisson's ratio of the cylindrical structure with an elliptical hole lattice is... It is determined by only two dimensionless geometric parameters, namely surface porosity. With axial compression ratio ,like Figure 5 As shown. Figure 6 and Figure 7 As shown by the gray dashed line, the nominal Poisson's ratio is: ; ; ; in, Indicates the nominal Poisson ratio. Indicates surface porosity. Indicates the axial compression ratio. Indicates the total number of unit cells. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the initial effective height. a Indicates the length of the major axis. b Indicates the length of the minor axis.

[0033] To characterize the morphology of the solid in the later stage of closure, the residual arch height is derived based on the assumption of curvature continuity during the compression closure process. On this basis, the macroscopic equivalent axial compression ratio and surface porosity are solved simultaneously. Based on these two factors, the equivalent Poisson's ratio is determined, and a peanut-shaped closure model is established. The cavity is not completely closed, but rather resembles a peanut. Figure 6 and Figure 7 As shown by the red dashed line, the equivalent Poisson's ratio is: ; ; ; ; in, Indicates the equivalent Poisson ratio. This represents the macroscopic equivalent surface porosity. This represents the macroscopic equivalent axial compression ratio. Indicates the total number of unit cells. Indicates the effective height. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the initial effective height. a Indicates the length of the major axis. b Indicates the length of the minor axis. Indicates the residual bow height.

[0034] Step S110 specifically includes: Step S111: Determine the equivalent long axis length based on the long axis length, the rib width, and the thickness nonlinear compensation coefficient; Step S112: Determine the equivalent short axis length based on the short axis length, the rib width, and the thickness nonlinear compensation coefficient; Step S113: Determine the equivalent residual bow height based on the equivalent major axis length and the equivalent minor axis length; Step S114: Establish a correction model based on the initial effective height, the effective height, the perimeter, the total number of unit cells, the axial number of unit cells, the equivalent residual bow height, the equivalent major axis length, and the equivalent minor axis length.

[0035] Specifically, the equivalent Poisson's ratio based on pure geometric theory is not affected by thickness interference, requiring the use of thickness nonlinearity compensation coefficients to compensate for the major and minor axis lengths, thus obtaining a modified model. Because the equivalent Poisson's ratio based on pure geometric theory does not fully consider the compaction effect caused by line contact, its prediction results exhibit severe non-physical divergence. It is necessary to introduce a physical compaction saturation limit truncation to effectively constrain the prediction results, thus obtaining a comprehensive modified model (such as...). Figure 6 and Figure 7(As shown by the blue solid line). When establishing the comprehensive modified model based on the physical compaction saturation limit and the modified model, a smoothing truncation function based on Softplus logic is used. This function drives Poisson's ratio to exhibit a natural parabolic asymptotic characteristic as it approaches the physical limit. S8, S9, S10, S11, S17, S18, S21, S22, and S25 are different data obtained from simulation, and these simulation data are close to the comprehensive modified model.

[0036] The corrected equivalent Poisson's ratio is: ; ; ; in, This represents the corrected equivalent Poisson's ratio. Indicates the corrected surface porosity. This indicates the corrected axial compression ratio. Indicates the total number of unit cells. Indicates the effective height. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the equivalent residual arch height. Indicates the initial effective height. Indicates the equivalent major axis length. This indicates the equivalent minor axis length.

[0037] When compensating for the major and minor axis lengths, the equivalent major axis length is calculated based on the nonlinear compensation coefficients for the major axis length, rib width, and thickness; the equivalent minor axis length is calculated based on the nonlinear compensation coefficients for the minor axis length, rib width, and thickness. The equivalent major axis length is: ; The equivalent minor axis length is: ; in, Indicates the equivalent major axis length. Indicates the length of the major axis. This represents the thickness nonlinearity compensation coefficient. Indicates rib width. Indicates the equivalent minor axis length. Indicates the length of the minor axis.

[0038] Specifically, effective kinematic reduction is performed on the major and minor axes, and the lengths of the major and minor axes are compensated based on the thickness nonlinearity compensation coefficient. The constraint interference of the solid wall thickness and the rigid core at the intersection on the pure rotational deformation mode of the star cell is dynamically stripped.

[0039] After compensation, the aspect ratio changes, and so does the equivalent Poisson's ratio. Under the constraint of the physical densification saturation limit, the equivalent Poisson's ratio is saturated and corrected to obtain the corrected equivalent Poisson's ratio. Since the aspect ratio differs with different rib widths, the equivalent Poisson's ratio also differs. At smaller aspect ratios, the corrected equivalent Poisson's ratio is close to the uncorrected equivalent Poisson's ratio. As the aspect ratio increases, the corrected equivalent Poisson's ratio approaches the physical densification saturation limit. The physical densification saturation limit is related to material properties. Taking steel as an example, the physical densification saturation limit can be configured to -1.05 (e.g., ...). Figure 6 and Figure 7 (The lower limit of the correction is shown).

[0040] Based on the embodiments of the performance prediction method for negative Poisson's ratio tubular structures based on geometric evolution, the present invention provides some embodiments of the design method for negative Poisson's ratio tubular structures based on geometric evolution.

[0041] The design method of this invention includes the following steps: Step T100: Based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of the elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, a comprehensive correction model is established; wherein, the tubular structure forms elliptical holes, the elliptical holes include vertical elliptical holes and horizontal elliptical holes, each unit cell includes two vertical elliptical holes and two horizontal elliptical holes, the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the circumferential direction, and the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the axial direction; Step T200: Determine the target Poisson's ratio and constraints of the tubular structure; wherein, the constraints include: the rib width of the elliptical hole is greater than or equal to the minimum rib width, and the major axis length of the elliptical hole is greater than or equal to the minimum major axis. Step T300: Solve the objective evaluation function under constraints to obtain the rib width, major axis length, and minor axis length; wherein, the objective evaluation function is: , Represents the objective evaluation function. Indicates the length of the major axis. Indicates the length of the minor axis. Indicates the effective Poisson ratio. The target Poisson's ratio is represented; the effective Poisson's ratio is determined based on a comprehensive correction model, according to the rib width and the ratio of the major axis to the minor axis; the ratio of the major axis to the minor axis is determined based on the length of the major axis and the length of the minor axis. Step T400: Based on the rib width, the major axis length, and the minor axis length, prepare a negative Poisson's ratio tubular structure based on geometric evolution.

[0042] Specifically, a comprehensive correction model is first established, and based on this model, the objective evaluation function is solved under constraints to obtain multiple sets of rib widths, major axis lengths, and minor axis lengths. From these multiple sets, one set is selected, and a negative Poisson's ratio tubular structure based on geometric evolution is fabricated. When selecting a set of rib widths, major axis lengths, and minor axis lengths, secondary screening and optimization of the secondary weight requirements for "porosity (lightweight requirements)" or "limit strain stroke" need to be performed in conjunction with the specific engineering project. When fabricating the negative Poisson's ratio tubular structure based on geometric evolution, further selection of the height H and thickness T (e.g., ...) is also required. Figure 3 and Figure 4 (As shown). The minimum major axis is L / 2, and the minimum rib width is... t min Determined based on the manufacturing process.

[0043] Step T100 includes: Step T110: Based on the initial effective height, effective height, perimeter, total number of cells, axial number of cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, and thickness nonlinearity compensation coefficient of the tubular structure, establish a correction model; Step T120: Based on the physical compaction saturation limit and the correction model, establish a comprehensive correction model.

[0044] Specifically, arbitrary rib width, arbitrary major axis length, and arbitrary minor axis length can form multiple sets of rib width, major axis length, and minor axis length, and each set of rib width, major axis length, and minor axis length satisfies the following relationship: L = a + b +2 t ,0< b < a ; 0 < L ; 0 < t Under this premise, a comprehensive correction model is established by combining the residual bow height, thickness nonlinearity compensation coefficient, and physical compaction saturation limit.

[0045] Step T110 includes: Step T111: Determine the equivalent long axis length based on the long axis length, the rib width, and the thickness nonlinear compensation coefficient; Step T112: Determine the equivalent short axis length based on the short axis length, the rib width, and the thickness nonlinear compensation coefficient; Step T113: Determine the equivalent residual bow height based on the equivalent major axis length and the equivalent minor axis length; Step T114: Establish a correction model based on the initial effective height, the effective height, the perimeter, the total number of unit cells, the axial number of unit cells, the equivalent residual bow height, the equivalent major axis length, and the equivalent minor axis length.

[0046] The equivalent major axis length is determined based on the major axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent minor axis length is determined based on the minor axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent residual bow height is: ; The equivalent major axis length is: ; The equivalent minor axis length is: ; in, Indicates the equivalent residual arch height. Indicates the equivalent major axis length. Indicates the length of the major axis. This represents the thickness nonlinearity compensation coefficient. Indicates rib width. Indicates the equivalent minor axis length. Indicates the length of the minor axis; The corrected model is as follows: ; ; ; in, This represents the corrected equivalent Poisson's ratio. Indicates the corrected surface porosity. This indicates the corrected axial compression ratio. Indicates the total number of unit cells. Indicates the effective height. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the initial effective height.

[0047] Step T300 includes: Step T310: Use a numerical optimization algorithm to solve the target evaluation function to obtain the rib width, major axis length and minor axis length; wherein, the numerical optimization algorithm includes gradient descent method or genetic algorithm.

[0048] Specifically, a numerical optimization algorithm can be used to solve the objective evaluation function and obtain multiple sets of rib widths, major axis lengths, and minor axis lengths.

[0049] This application starts from the underlying deformation geometry of lattice structures and introduces a residual bow height parameter into the model to quantify the correction of the axial effective height shortening by the residual opening. Simultaneously, this application innovatively introduces a nonlinear thickness penalty mechanism based on rib width to compensate for the nonlinear erosion of the hole geometry by rigid boundaries. Based on this, combined with a physical compaction saturation truncation criterion, a comprehensive correction and prediction algorithm with global parameter applicability and physical self-consistency is constructed. This method transforms the complex geometric nonlinear deformation mechanism into a standardized algorithm solution process, which can not only accurately predict the macroscopic equivalent Poisson's ratio of the structure in the full parameter space, but also completely eliminates the singularity divergence of purely theoretical formulas. It provides an efficient and reliable computational tool for the performance evaluation and parametric reverse design of tubular lattice structures, greatly reducing the trial-and-error and computational costs in the R&D process.

[0050] This application breaks away from the purely mathematical assumption in traditional ideal analytical models that holes can shrink to a point line without volume, and introduces a residual bow height characteristic parameter into the geometric evolution path. This parameter is used to accurately characterize the residual opening shape that inevitably exists in real solid components in the later stage of closure due to curvature continuity constraints. Incorporating the geometric boundary of the residual opening into the kinematic equations provides a reliable geometric benchmark for accurately deriving the actual height shortening and radial displacement of the unit cell during axial compression. Compared to the uncorrected ideal model, this deduction based on real spatial evolution allows the computational path of the theoretical algorithm to closely match the actual physical interference and contact laws of materials.

[0051] By deeply coupling multiple physical boundary correction mechanisms (such as nonlinear thickness penalty mechanisms and compaction saturation cutoff criteria) into the analytical algorithm, this method avoids the extreme value singularity divergence or severe prediction distortion that often occurs in traditional pure theoretical formulas when facing parameter combinations with thick stress skeletons or extreme major and minor axis ratios. The nonlinear penalty mechanism based on rib width can dynamically eliminate the physical erosion of rigid nodes on the effective closing stroke of holes, effectively overcoming the problem of geometric stiffness overestimation caused by material thickness; while the physical saturation cutoff criterion forcibly limits over-computation. The above correction algorithms cooperate and constrain each other in the solution process, completely avoiding the limitations of pure kinematic solutions, and ultimately ensuring that the entire prediction model achieves a high-precision, physically self-consistent analytical mapping between geometric variables (pitch, major and minor axes, rib width) and macroscopic equivalent negative Poisson's ratio in the full parameter space.

[0052] Furthermore, based on the fully parameter-space analytical mapping relationship constructed above, this method not only supports forward performance evaluation but also opens up a goal-driven reverse design path. Since this application transforms the relationship between geometric variables and the effective Poisson's ratio into an explicit algorithmic analytical expression, designers can directly use the target Poisson's ratio required by engineering needs as a guide to construct a target optimization function with geometric parameters as independent variables. By combining phase diagram mapping or numerical optimization algorithms, it is possible to quickly and backward lock the parameter combination (major axis, minor axis, rib width) that satisfies the target performance in the multi-dimensional design space, thereby realizing a closed-loop design from performance prediction to on-demand customization.

[0053] This application has the following technical effects: (1) Breaking through the computational bottleneck and efficiency limitation of numerical simulation: The complex parameter optimization process is transformed into a standardized analytical algorithm solution, which gets rid of the high computational cost and time cost faced by the traditional finite element trial and error method, and provides an efficient calculation tool for the parameterized reverse design of subsequent components.

[0054] (2) Revealing the analytical mapping relationship between underlying geometric parameters and macroscopic performance: It not only provides accurate performance prediction results, but also explicitly reveals the intrinsic physical mechanism and evolution law of the determination of macroscopic equivalent Poisson ratio by basic geometric parameters such as major axis, minor axis and rib width through mathematical forms such as product decoupling.

[0055] (3) High-precision prediction and physical self-consistency in the full parameter space: By innovatively introducing residual bow height correction, nonlinear thickness compensation mechanism and physical saturation cutoff criterion, the singularity of pure theoretical formula diverging to negative infinity under extreme geometric parameters is completely eliminated, ensuring that the prediction results are highly consistent with the physical response of the real component.

[0056] (4) Achieving target-driven structural customization: Traditional methods can only proceed through forward trial and error, while this invention, relying on the established high-precision analytical mapping relationship, successfully opens up the reverse calculation path from "target Poisson's ratio" to "underlying geometric parameters". Engineers only need to input the required target performance, and the optimal cell size combination can be quickly and accurately obtained through algorithms or phase diagram contour lines. This truly on-demand customization is different from the traditional trial-and-error design process, greatly improving the efficiency of targeted R&D of metamaterials and impact-absorbing energy-absorbing components.

[0057] It should be understood that the application of the present invention is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for performance prediction of a negative Poisson's ratio tubular structure based on geometric evolution, characterized by, Including the following steps: Based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, a comprehensive correction model is established; wherein, the tubular structure forms elliptical holes, the elliptical holes include vertical elliptical holes and horizontal elliptical holes, each unit cell includes two vertical elliptical holes and two horizontal elliptical holes, the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the circumferential direction, and the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the axial direction; Obtain the rib width of the tubular structure and the length of the major and minor axes of the elliptical holes; The ratio of the major axis to the minor axis is determined based on the length of the major axis and the length of the minor axis. Based on the comprehensive correction model, the effective Poisson's ratio is determined according to the rib width and the ratio of major to minor axis.

2. The method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution according to claim 1, characterized in that, A comprehensive correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major and minor axis lengths of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, including: A correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, and thickness nonlinear compensation coefficient of tubular structure. A comprehensive correction model is established based on the physical compaction saturation limit and the correction model.

3. The method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution according to claim 2, characterized in that, The correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of the elliptical hole, and thickness nonlinear compensation coefficient of the tubular structure, including: The equivalent long axis length is determined based on the long axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent short axis length is determined based on the short axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent residual bow height is determined based on the equivalent major axis length and the equivalent minor axis length. A correction model is established based on the initial effective height, the effective height, the perimeter, the total number of unit cells, the axial number of unit cells, the equivalent residual bow height, the equivalent major axis length, and the equivalent minor axis length.

4. The method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution according to claim 3, characterized in that, The equivalent residual bow height is: ； The equivalent major axis length is: ； The equivalent minor axis length is: ； in, Indicates the equivalent residual arch height. Indicates the equivalent major axis length. Indicates the length of the major axis. This represents the thickness nonlinearity compensation coefficient. Indicates rib width. Indicates the equivalent minor axis length. Indicates the length of the minor axis.

5. The method for predicting the performance of negative Poisson's ratio tubular structures based on geometric evolution according to claim 4, characterized in that, The corrected model is as follows: ； ； ； in, This represents the corrected equivalent Poisson's ratio. Indicates the corrected surface porosity. This indicates the corrected axial compression ratio. Indicates the total number of unit cells. Indicates the effective height. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the initial effective height.

6. A design method for negative Poisson's ratio tubular structures based on geometric evolution, characterized in that, Including the following steps: Based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, a comprehensive correction model is established; wherein, the tubular structure forms elliptical holes, the elliptical holes include vertical elliptical holes and horizontal elliptical holes, each unit cell includes two vertical elliptical holes and two horizontal elliptical holes, the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the circumferential direction, and the vertical elliptical holes and horizontal elliptical holes are alternately arranged in the axial direction; Determine the target Poisson's ratio and constraints for the tubular structure; wherein the constraints include: the rib width of the elliptical hole is greater than or equal to the minimum rib width, and the major axis length of the elliptical hole is greater than or equal to the minimum major axis. Under constraints, the objective evaluation function is solved to obtain the rib width, major axis length, and minor axis length; wherein, the objective evaluation function is: , Represents the objective evaluation function. Indicates the length of the major axis. Indicates the length of the minor axis. Indicates the effective Poisson ratio. The target Poisson's ratio is represented; the effective Poisson's ratio is determined based on a comprehensive correction model, according to the rib width and the ratio of the major axis to the minor axis; the ratio of the major axis to the minor axis is determined based on the length of the major axis and the length of the minor axis. Based on the rib width, the major axis length, and the minor axis length, a negative Poisson's ratio tubular structure based on geometric evolution is prepared.

7. The design method for negative Poisson's ratio tubular structures based on geometric evolution according to claim 6, characterized in that, The process of solving the objective evaluation function under constraints to obtain the major axis length and minor axis length includes: A numerical optimization algorithm is used to solve the objective evaluation function to obtain the rib width, major axis length, and minor axis length; wherein, the numerical optimization algorithm includes gradient descent or genetic algorithm.

8. The design method for negative Poisson's ratio tubular structures based on geometric evolution according to any one of claims 6 to 7, characterized in that, A comprehensive correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major and minor axis lengths of elliptical holes, thickness nonlinearity compensation coefficient, and physical compaction saturation limit of the tubular structure, including: A correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of elliptical holes, and thickness nonlinear compensation coefficient of tubular structure. A comprehensive correction model is established based on the physical compaction saturation limit and the correction model.

9. The design method for negative Poisson's ratio tubular structures based on geometric evolution according to claim 8, characterized in that, The correction model is established based on the initial effective height, effective height, perimeter, total number of unit cells, axial number of unit cells, arbitrary rib width, arbitrary major axis length and arbitrary minor axis length of the elliptical hole, and thickness nonlinear compensation coefficient of the tubular structure, including: The equivalent long axis length is determined based on the long axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent short axis length is determined based on the short axis length, the rib width, and the thickness nonlinear compensation coefficient. The equivalent residual bow height is determined based on the equivalent major axis length and the equivalent minor axis length. A correction model is established based on the initial effective height, the effective height, the perimeter, the total number of unit cells, the axial number of unit cells, the equivalent residual bow height, the equivalent major axis length, and the equivalent minor axis length.

10. The design method for negative Poisson's ratio tubular structures based on geometric evolution according to claim 9, characterized in that, The equivalent residual bow height is: ； The equivalent major axis length is: ； The equivalent minor axis length is: ； in, Indicates the equivalent residual arch height. Indicates the equivalent major axis length. Indicates the length of the major axis. This represents the thickness nonlinearity compensation coefficient. Indicates rib width. Indicates the equivalent minor axis length. Indicates the length of the minor axis; The corrected model is as follows: ； ； ； in, This represents the corrected equivalent Poisson's ratio. Indicates the corrected surface porosity. This indicates the corrected axial compression ratio. Indicates the total number of unit cells. Indicates the effective height. Indicates the perimeter. Indicates the number of axial unit cells. Indicates the initial effective height.

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