WO2022193477A1 - 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法 - Google Patents

大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法 Download PDF

Info

Publication number
WO2022193477A1
WO2022193477A1 PCT/CN2021/104141 CN2021104141W WO2022193477A1 WO 2022193477 A1 WO2022193477 A1 WO 2022193477A1 CN 2021104141 W CN2021104141 W CN 2021104141W WO 2022193477 A1 WO2022193477 A1 WO 2022193477A1
Authority
WO
WIPO (PCT)
Prior art keywords
notch
metamaterial
unit cell
kirigami
square
Prior art date
Application number
PCT/CN2021/104141
Other languages
English (en)
French (fr)
Inventor
王毅强
杜琛
亢战
Original Assignee
大连理工大学
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by 大连理工大学 filed Critical 大连理工大学
Priority to US17/639,522 priority Critical patent/US20230185999A1/en
Publication of WO2022193477A1 publication Critical patent/WO2022193477A1/zh

Links

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/17—Mechanical parametric or variational design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/06—Multi-objective optimisation, e.g. Pareto optimisation using simulated annealing [SA], ant colony algorithms or genetic algorithms [GA]

Definitions

  • the invention belongs to the field of metamaterials, and relates to a kirigami metamaterial with adjustable auxetic properties under large stretching amount and a structure design method thereof.
  • Kirigami metamaterials are a class of mechanical metamaterials that obtain specific equivalent mechanical properties through the orderly (periodic, gradient, irregular) arrangement of notches on the sheet structure. waste and fast load response.
  • auxetic kirigami metamaterial undergoes lateral expansion and deformation under the longitudinal tensile load, and this auxetic characteristic can be expressed as the negative value of the ratio of the average lateral deformation to the longitudinal elongation.
  • the existing auxetic kirigami metamaterials are designed and obtained based on artificial experience or repeated trial-and-error methods, and the included notch arrangements have the form of mirror symmetry, chiral symmetry or antichiral symmetry.
  • auxetic kirigami metamaterials undergo unstable out-of-plane buckling deformation when the elongation exceeds a certain proportion (usually less than 10%) of the sample size, resulting in the inability to maintain the specified auxetic properties. This is due to the small out-of-plane stiffness of the thin-film structure on the one hand, and the reduced out-of-plane stiffness of the local area due to the preset notch and notch layout.
  • the existing auxetic kirigami metamaterials are prone to generate high strain (or high stress) under large stretches, resulting in the failure or even destruction of the matrix material. cause negative effects. These two performance deficiencies limit the practical application of kirigami metamaterials.
  • the present invention provides an auxetic kirigami metamaterial and a design method for realizing a kirigami metamaterial with adjustable auxetic properties under a large amount of stretching.
  • the kirigami metamaterial can achieve adjustable auxetic properties and obtain good deformation recoverability when subjected to a tensile load to generate a large amount of stretching, and has the advantages of simple preparation process and application to a variety of matrix materials.
  • the kirigami metamaterial 1 is composed of a plurality of square unit cells 2 arranged in an orderly manner, and the orderly arrangement refers to: a plurality of square unit cells.
  • the cells 2 are arranged periodically, gradiently or irregularly in the kirigami metamaterial 1, and the corresponding kirigami metamaterial 1 has uniform auxetic properties, gradient auxetic properties and specified non-uniform auxetic properties, respectively.
  • Said one square unit cell 2 has a side length L and a thickness t, which consists of a 1/4 square domain 3 and the other three obtained by mirroring the 1/4 square domain along the x-axis/y-axis 6 inside the unit cell respectively.
  • 1/4 square field composition Two notches 5 with the same shape are preset in the 1/4 square domain 3, and the two notches 5 satisfy rotational symmetry along the center of the 1/4 square domain.
  • the layout of all notches 5 satisfies the antichiral symmetry along the center point of the unit cell.
  • All the notches 5 in the one 1/4 square field 3 have a uniform width w, and one notching tip 4 of one of the notches 5 is located at one vertex 11 of the 1/4 square field, and the other notches
  • the tip 4 is in the shape of a circular arc with a radius of w/2 and is located inside the 1/4 square field.
  • Said one notch 5 is a slender three-segment broken line type, starting from a vertex 11 of a 1/4 square domain, and consists of three parts: a straight notch first section 7, a notch middle section 8 and a notch end section 9.
  • the lengths of the center lines 10 of the first section 7, the middle section 8 and the end section 9 of the notch are L 1 , L 2 and L 3 respectively; 4.
  • the included angle of the bottom boundary of the square domain 3 is ⁇ 1
  • the middle section 8 of the notch is parallel to the y-axis
  • the relative angle between the middle section 8 of the notch 8 and the end section 9 of the notch is ⁇ 2
  • ⁇ 2 is always located in the middle section of the notch 8
  • the range of the geometric parameters used to describe the configuration of a square unit cell 2 is as follows: the variation range of the parameter t/L is 0.0033-0.0167, which can be selected according to the design requirements and the selected matrix material and manufacturing technology. Determine the size L and thickness t of a unit cell; the variation range of the parameter L 1 /L is 0.33-0.44; the variation range of the parameter L 2 /L is 0.08-0.39; the variation range of the parameter L 3 /L is 0.10-0.29; The variation range of parameter ⁇ 1 is 0°-11.5°; the variation range of parameter ⁇ 2 is 60°-160°; the variation range of parameter w/L is 0.001-0.033. All parameters can take on the endpoints of the range of variation.
  • the center line 10 of the first section 7 of the notch overlaps with the boundary of the 1/4 square domain 3.
  • the width of the first section 7 of the notch is w/2, which is at the symmetry axis of the unit cell with other
  • the first notch section 7 in the 1/4 square area constitutes a notch first section with a width w.
  • the base material of the kirigami metamaterial 1 can be selected from metal or high molecular polymer (rubber, PET or PVC).
  • the kirigami metamaterial can be manufactured by knife engraving, laser cutting, water cutting or 3D printing technology.
  • a design method for a kirigami metamaterial with adjustable auxetic properties under a large amount of stretching the steps of which are as follows:
  • a square unit cell 2 is selected as the design domain, and periodic boundary conditions are imposed on its boundary to simulate the real deformation of the unit cell in the metamaterial, and at the same time save the cost of calculation and analysis and shorten the design cycle.
  • preset an artificially specified number of free-curve notches 20 take the arrangement position, shape and length of free-curve notches 20 as design variables, and take the length and maximum curvature of free-curve notches 20 as constraints.
  • an optimization algorithm of gradient, intelligence or a combination of the two is used to update the design variables, optimize the position, shape and length of the notch, obtain the unit cell configuration with specified auxetic properties, and complete the heuristic design of the unit cell configuration.
  • Finite element analysis is performed on the unit cell to obtain its deformation during loading.
  • the linear buckling analysis of the unit cell is carried out, and the low-order modes obtained by the analysis are introduced into the finite element model as initial geometric defects, and the nodal coordinates are modified.
  • the nonlinear finite element method is used to solve the deformation response under tensile load, and the auxetic characteristic value is calculated, fully considering the influence of complex out-of-plane buckling deformation on the auxetic characteristic.
  • step S2 Perform geometric reconstruction and parameter modeling on the optimization results obtained in step S1, and obtain auxetic properties under different geometric parameters, as follows:
  • the free curve notch 20 in the optimized unit cell configuration is reconstructed into a three-segment broken line notch 22, which not only facilitates parameter description, but also helps to improve the preparation accuracy of kirigami metamaterials;
  • the length and distribution angle of each line segment in the mouth 22 are used as parameters to describe the unit cell configuration 23 including the three-segment broken-line notch 22 after geometric reconstruction. Carry out parameter learning, traverse all notch parameters within the specified parameter range, and obtain the corresponding unit cell auxetic performance.
  • step S3 Arrange the multiple parameterized unit cells obtained in step S2 in a periodic, gradient or irregular form to construct a kirigami metamaterial, as follows:
  • Select multiple unit cells described by the same notch parameters for periodic arrangement to construct a kirigami metamaterial with uniform auxetic properties select multiple unit cells described by different notch parameters for gradient or irregular arrangement to construct gradient or A kirigami metamaterial specifying non-uniform auxetic properties.
  • the description method of the centerline 10 of the curvilinear notch 20 in step S1 includes but is not limited to B-spline interpolation function, non-uniform rational B-spline interpolation function or analytic curve function description.
  • nonlinear finite element method described in step S1 includes but is not limited to the Newton-Raphson method or the improved arc length method; the optimization algorithm includes but is not limited to nonlinear sequential quadratic programming algorithm (gradient algorithm) and genetic algorithm. Algorithms (Intelligent Algorithms).
  • the kirigami metamaterial provided by the present invention can always obtain a specified auxetic characteristic value between 5-50% of the tensile amount under the action of a unidirectional tensile load whose tensile amount does not exceed 50% of the sample size, By modifying the notch parameters, a variety of auxetic characteristics change trends that can be adjusted with the amount of stretching can be realized.
  • the kirigami metamaterial provided by the present invention may include a plurality of unit cells arranged periodically, gradient or irregularly, and obtain auxetic properties of uniform distribution, gradient change and specified non-uniform distribution, respectively.
  • the present invention has obvious advantages in structural design, application range and application prospect.
  • Fig. 1 is a kind of kirigami metamaterial provided by the present invention and the included unit cell configuration; wherein, Fig. 1(a) is the configuration diagram of the kirigami metamaterial, Fig. 1(b) is the configuration diagram of the unit cell, Figure 1(c) is a top view of a 1/4 square domain in a unit cell;
  • Fig. 2 is the structural deformation of a unit cell shown in Fig. 1 in a tensile state, wherein Fig. 2(a) is a structural deformation of a unit cell with a tensile amount of 10%; Fig. 2(b) is a Figure 2(c) shows the structural deformation of a single cell at 30% stretching;
  • Figure 3 is a top view of the unit cell configuration described by different geometric parameters; among them, Figure 3(a) is a unit cell configuration with a minimum auxetic characteristic of -0.27 when the stretching amount is less than 50%; Figure 3(b) is the unit cell configuration with a minimum auxetic characteristic of -0.94 when the stretching amount is less than 50%; Figure 3(c) is a unit cell with a minimum auxetic characteristic of -1.90 when the stretching amount is less than 50% structure;
  • Figure 4 is the auxetic properties and elongation curves of the kirigami metamaterial unit cells described by different geometric parameters
  • Figure 5 is a kirigami metamaterial containing different unit cell arrangements;
  • Figure 5(a) is a top view of a kirigami metamaterial containing multiple periodically arranged unit cells;
  • Figure 5(b) is a graph containing multiple gradient arrangements
  • Figure 5(c) is a top view of a kirigami metamaterial containing multiple irregularly arranged unit cells;
  • Figure 6 is a schematic diagram of the modeling of a notch in a 1/4 square domain in the structural optimization design of the design process; among them, Figure 6(a) is a schematic diagram of the center line of the notch described by a non-uniform rational B-spline curve; Figure 6 (b) is the top view of the 1/4 square area including the above-mentioned one notch;
  • Figure 7 is a schematic diagram of the geometric reconstruction in the design process
  • Figure 7(a) is a top view of the unit cell configuration obtained by structural optimization, including a curved notch
  • Figure 7(b) is the unit cell configuration after geometric reconstruction.
  • Type top view including multi-segment polyline type notches;
  • Fig. 8 is a flow chart of the design method of the kirigami metamaterial provided by the present invention.
  • 1 kirigami metamaterial 2 square unit cell; 3 1/4 square domain constituting the square unit cell; 4 notch tip; 5 notch; 6 x-axis/y-axis inside the unit cell; 7 notch first segment ; 8 The middle section of the notch; 9 The end section of the notch; 10 The center line of the notch; 11 The vertex of the 1/4 square domain; 12 The uniaxial tensile load; Metamaterial unit cell configuration; 18 control points for free-form notch modeling; 19 control point connecting lines; 20 free-form notch; 21 unit cell geometric model; 22 three-segment broken line notch; 23 unit cell type.
  • the present invention provides a kirigami metamaterial with adjustable auxetic properties under a large stretching amount.
  • the kirigami metamaterial 1 is composed of a plurality of ordered Arranged square unit cells 2 are formed, which can be formed by a plurality of square unit cells 2 arranged in an orderly (periodic, gradient or irregular) manner.
  • Said one square unit cell 2 has a side length of L and a thickness of t, which consists of a 1/4 square domain 3 and the other obtained by mirroring the 1/4 square domain along the x-axis/y-axis 6 inside the unit cell. It consists of three 1/4 square fields.
  • the one 1/4 square domain 3 is preset with two three-segment broken-line notches with the same shape, and the two notches 5 satisfy rotational symmetry along the center of the 1/4 square domain.
  • the layout of all notches in the unit cell 2 satisfies the antichiral symmetry along the center point of the unit cell.
  • the notch 5 in the 1/4 square domain 3 has a uniform width w, and its shape is an elongated three-segment broken line as shown in Fig. 1(c) and Fig. 7(b). Wherein, one notch tip is located at one vertex 11 of the 1/4 square domain 3, and the other notch tip 4 is in the shape of an arc, and the radius of the arc is w/2.
  • the notch 5 is composed of a notch first section 7 , a notch middle section 8 and a notch end section 9 .
  • a notch 5 of the square unit cell 2 shown in Figure 1(b) is described by the following notch parameters: the lengths of the centerlines 10 of the first , middle and end segments of the notch are: L1 is 11.0 mm, L2 is 7.6 mm and L 3 is 4.7 mm; the angle ⁇ 1 between the first section of the notch and the bottom boundary of the 1/4 square domain 3 is 0°, and the width w/2 is 0.2 mm; the middle section of the notch and the end of the notch are clamped The angle ⁇ 2 is 113°, and the width w between the middle section and the end of the notch is 0.4 mm.
  • the thickness t of the square unit cell 2 is much smaller than the side length L, and its internal notch layout weakens the stiffness of the local area, making the unit cell unstable under load, resulting in out-of-plane deformation.
  • This out-of-plane deformation is fully considered in the design process, so that the unit cell can reach 3% of the unit cell length L along the x-direction under the action of the x-direction uniaxial tensile load 12 as shown in FIG. 2 .
  • obvious out-of-plane buckling deformation occurs due to instability, which leads to auxetic deformation. Under a larger stretching amount, the auxetic properties of the unit cell are stable at the specified value.
  • the deformation of the kirigami metamaterial unit cell provided by the present invention and the auxetic properties caused by the deformation are mainly determined by the above-mentioned geometric parameters of the unit cell.
  • different unit cell configurations can be obtained, and the auxetic properties in the range of -0.2 to -1.9 and different types of auxetic deformation trends (stationary type, monotonically decreasing type and pre-existing deformation) can be obtained. rising after falling).
  • the combination of geometric parameters of different notch can be obtained as shown in Figure 3
  • the unit cell configuration 15 shown in Figure 3(a), the geometric parameters of the notch are: the length of the notch center line 10 of the first notch 7, the middle 8 and the end 9 of the notch, respectively. are: L 1 is 12.0 mm, L 2 is 8.5 mm, and L 3 is 7.0 mm; the angle ⁇ 1 between the first section 7 of the notch and the bottom boundary of the 1/4 square domain 3 is 0°; the middle section 8 of the notch and the The included angle ⁇ 2 of the mouth end section 9 is 90°.
  • the stable auxetic characteristic curve shown in Figure 4 is achieved, and the minimum auxetic characteristic in tensile deformation is -0.27.
  • the geometric parameters of the notch are: the lengths of the center line 10 of the first notch 7, the middle 8 and the end 9 of the notch are: L 1 is 11.0 mm, L 2 is 4.0 mm, and L 3 is 8.3 mm; the angle ⁇ 1 between the first section 7 of the notch and the bottom boundary of the 1/4 square domain 3 is 0°; the middle section 8 of the notch and the end of the notch are 0°.
  • the included angle ⁇ 2 of the segment 9 is 160°.
  • the monotonically decreasing auxetic characteristic curve shown in Figure 4 is realized, and the minimum auxetic characteristic in tensile deformation is -0.94;
  • the geometric parameters of the notch are: the length of the center line 10 of the first notch section 7, the notch middle section 8 and the notch end section 9 are: L 1 is 13.0 mm, L 2 is 11.5 mm, and L 3 is 3.4 mm; the angle ⁇ 1 between the first section 7 of the notch and the bottom boundary of the 1/4 square domain 3 is 0°; the middle section 8 of the notch and the end section 9 of the notch are clamped The angle ⁇ 2 is 66°.
  • the curve of the auxetic characteristic of the first falling and then rising type as shown in Fig. 4 is realized, and the minimum auxetic characteristic in the tensile deformation reaches -1.90.
  • the auxetic kirigami metamaterial of the present invention is composed of a variety of unit cells with different notch parameters according to a specific period, gradient or irregular arrangement, and obtains the auxetic properties of uniform distribution, gradient change and specified non-uniform distribution respectively.
  • the kirigami metamaterial shown in Fig. 5(a) contains a plurality of unit cells 14 periodically arranged along the x-axis and y-axis, with uniform auxetic properties; the kirigami metamaterial shown in Fig. 5(b) is provided.
  • the material contains unit cells 15, 16, and 17 that are gradiently arranged along the x-axis and periodically arranged along the y-axis, and have auxetic properties with gradient changes along the x-direction;
  • the provided kirigami metamaterial shown in Figure 5(c) contains Unit cells 14, 15, 16 and 17, which are irregularly arranged along the x and y axes, have auxetic properties that are non-uniform in all directions.
  • the kirigami metamaterial described in this embodiment is prepared by laser cutting by selecting the high molecular polymer material PET as the base material.
  • This embodiment also provides a design method for the above-mentioned kirigami metamaterial.
  • the design flow chart is shown in Figure 8, and the detailed steps are as follows:
  • step S1 a heuristic design of the unit cell configuration is obtained under the condition of fully considering the out-of-plane deformation by using the structure optimization technology. specific:
  • a geometric model of a periodic square unit cell 21 is established as the optimization design domain.
  • Two free-curve notches 20 are preset in a 1/4 square domain of the square unit cell 21 , and the center line of each notch is described by a non-uniform rational B-spline interpolation function.
  • finite element analysis is performed on the unit cell.
  • a periodic boundary condition is imposed on the boundary of the unit cell, that is, the displacement difference of the corresponding points on the opposite boundary of the square unit cell is equal, so as to simulate the real deformation of the unit cell in the metamaterial while saving the calculation cost and shortening the design cycle; and use the modal scale
  • the factorial method scales and superimposes multiple linear buckling modes, which are introduced into the analytical configuration as initial geometric imperfections to simulate machining imperfections and allow for possible out-of-plane buckling deformations.
  • the Newton-Raphson method in nonlinear analysis is considered to complete the deformation analysis of the above unit cell under the tensile load along the x direction.
  • the 18 coordinates of each notch control point in the 1/4 square domain are selected as the design variables, the specified auxetic properties under different stretches are taken as the optimization objective, and the maximum length and maximum curvature of the notch are selected as constraint.
  • the structure optimization process includes two steps: the first step uses the multi-island genetic algorithm in the intelligent algorithm to search for the overall optimization in the design space, and obtains the spatial coordinates of the control point close to the optimal solution; the second step uses the gradient algorithm in the The nonlinear sequential quadratic programming algorithm completes local optimization in the design space near the optimal solution obtained in the first step, obtains the optimal position of the notch control point, and finally completes the free-curve unit cell structure as shown in Figure 7(a). The inspired design of the Type 21.
  • Step S2 performing geometric reconstruction and parameter modeling on the optimized configuration obtained in the selected step S1, specifically:
  • the free curve notch is equivalent to the multi-segment polyline notch, and the length of each straight segment and the laying angle of each straight segment in the multi-segment polyline are selected as geometric description parameters.
  • the optimized configuration of the unit cell shown in Fig. 7(a) is geometrically reconstructed, and a parametric model including a three-segment broken-line notch as shown in Fig. 7(b) is obtained.
  • the traversal parameters are within the specified range, and the interval value is completed.
  • Step S3 constructing kirigami metamaterials including different unit cell arrangements, specifically:
  • the kirigami metamaterial can contain multiple periodic unit cells described by the same geometric parameters to achieve uniform auxetic properties, and its internal arrangement is shown in Figure 5(a); the kirigami metamaterial can contain different geometric parameters along a certain direction.
  • the described multiple unit cells realize the auxetic properties of gradient change, and their internal arrangement is shown in Fig. 5(b); kirigami metamaterials can also contain irregularly arranged multiple cells described by different geometric parameters along various directions.
  • a single unit cell achieves non-uniform auxetic properties, and its internal arrangement is shown in Figure 5(c).

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Geometry (AREA)
  • Evolutionary Computation (AREA)
  • General Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Artificial Intelligence (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Prostheses (AREA)
  • Paper (AREA)

Abstract

一种大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法，剪纸超材料（1）由多个有序排布的方形单胞（2）构成，多个方形单胞（2）在剪纸超材料（1）内周期性、梯度性或非规则性排布，对应的剪纸超材料（1）分别具有均匀拉胀特性、梯度拉胀特性和指定非均匀拉胀特性。其设计方法为：首先，采用结构优化方法，充分考虑面外变形约束，得到单胞构型（23）的启发式设计。其次，对上述步骤得到的优化结果进行几何重构与参数建模，并获得不同几何参数下的拉胀特性。最后，根据特定的排布顺序对多种单胞构型（23）进行排布，构造剪纸超材料（1）。本方法通过修改剪口（5）参数，能够随拉伸量大小调节拉胀特性。

Description

大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法 技术领域
本发明属于超材料领域，涉及一种在大拉伸量下具有可调节拉胀特性的剪纸超材料及其结构体设计方法。
 背景技术
剪纸超材料是在薄片结构上，通过剪口的有序（周期、梯度、非规则）排布，获得特定等效力学性能的一类力学超材料，具有易制造性、大延展性、减少材料浪费和快速的载荷响应等优点。
拉胀剪纸超材料在受到纵向拉伸载荷作用下产生横向膨胀变形，这种拉胀特性可表示为横向变形平均值与纵向伸长量比值的负值。目前，已有的拉胀剪纸超材料是基于人工经验或者采用反复试错方法设计获得，包含的剪口排布具有镜像对称、手性对称或反手性对称形式。
上述的拉胀剪纸超材料在伸长量超过样件尺寸一定比例（通常小于10%）时，发生不稳定的面外屈曲变形，导致无法保持指定的拉胀特性。这一方面是由于薄片结构具有很小的面外刚度，另一方面是由于预置剪口以及剪口布局降低了局部区域的面外刚度。同时，已有的拉胀剪纸超材料在大拉伸量下，还易产生高应变（或高应力），导致基体材料失效甚至破坏，对超材料的可靠性、变形可恢复性和等效性能造成负面影响。这两方面的性能缺陷限制了剪纸超材料的实际应用。
因此，提供一种拉胀剪纸超材料，实现随拉伸量可调节的满足特定变化规律的拉胀特性，同时具有变形可恢复性，是剪纸超材料领域亟待解决的技术问题，对剪纸超材料的推广应用具有重要意义。
 技术问题
针对上述技术不足，本发明提供了一种拉胀剪纸超材料，及用于实现在大拉伸量下，具有可调节拉胀特性的剪纸超材料的设计方法。该剪纸超材料在受到拉伸载荷产生大拉伸量下，能够实现可调节的拉胀特性，并且获得良好的变形可恢复性，同时兼具制备工艺简单、适用于多种基体材料的优点。
 技术解决方案
一种大拉伸量下具有可调节拉胀特性的剪纸超材料，所述剪纸超材料1由多个有序排布的方形单胞2构成，所述有序排布指：多个方形单胞2在剪纸超材料1内周期性、梯度性或非规则性排布，对应的剪纸超材料1分别具有均匀拉胀特性、梯度拉胀特性和指定非均匀拉胀特性。
所述的一个方形单胞2边长L、厚度t，由一个1/4方形域3和由该1/4方形域分别沿着单胞内部的x轴/y轴6镜像得到的另外三个1/4方形域组成。所述的一个1/4方形域3中预置两条形状相同的剪口5，两条剪口5之间满足沿该1/4方形域中心旋转对称。在一个完整的方形单胞2中，所有剪口5的布局满足沿单胞中心点反手性对称。
所述的一个1/4方形域3中的所有剪口5均具有均匀宽度w，其中一条剪口5的一个剪口尖端4位于所述1/4方形域的一个顶点11，另一个剪口尖端4呈圆弧状，其半径为w/2，位于所述1/4方形域内部。所述的一条剪口5为细长的三段折线型，从1/4方形域一个顶点11起，由直线型的剪口首段7、剪口中段8和剪口末段9三部分组成，并由以下剪口参数描述：剪口首段7、中段8和末段9的中心线10的长度分别为L 1、L 2和L 3；所述剪口首段7与所述1/4方形域3底部边界夹角为θ 1，剪口中段8与y轴平行，剪口中段8与剪口末段9的相对夹角为θ 2，且θ 2始终位于所述剪口的中段8靠近单胞边界的一侧。
进一步的，所述的用于描述一个方形单胞2构型的几何参数取值范围如下：参数t/L的变化范围为0.0033-0.0167，可根据设计需求以及选用的基体材料与制造技术，选定一个单胞的尺寸L及厚度t；参数L 1/L的变化范围为0.33-0.44；参数L 2/L的变化范围为0.08-0.39；参数L 3/L的变化范围为0.10-0.29；参数θ 1的变化范围为0°-11.5°；参数θ 2的变化范围为60°-160°；参数w/L的变化范围为0.001-0.033。所有参数均可取变化范围的端点值。当θ 1=0°时，剪口首段7的中心线10与1/4方形域3的边界重叠，此时剪口首段7的宽度为w/2，在单胞对称轴处与其他1/4方形域内的剪口首段7组成宽度为w的剪口首段。
进一步的，所述剪纸超材料1的基体材料可选用金属或高分子聚合物（橡胶、PET或PVC）。针对所述的基体材料，所述剪纸超材料可采用刀刻、激光切割、水切割或3D打印技术制造。
一种大拉伸量下具有可调节拉胀特性的剪纸超材料的设计方法，其步骤如下：
S1.采用结构优化方法，充分考虑面外变形约束，得到单胞构型的启发式设计，具体如下：
首先，选用一个方形单胞2作为设计域，在其边界施加周期性边界条件，模拟所述单胞在超材料的真实变形，同时节约计算分析成本，缩短设计周期。其次，预置人为指定数量的自由曲线型剪口20，将自由曲线型剪口20的排布位置、形状和长度作为设计变量，将自由曲线型剪口20的长度及最大曲率作为约束条件。进而，选用梯度、智能或两者结合的优化算法更新设计变量，优化剪口的位置、形状和长度，获得指定拉胀特性的单胞构型，完成单胞构型的启发式设计。
所述迭代优化过程中：对单胞进行有限元分析以获取其在加载过程中的变形。首先对单胞进行线性屈曲分析，并将分析得到的低阶模态作为初始几何缺陷引入到有限元模型中，修改节点坐标。选用非线性有限元方法求解在拉伸载荷下的变形响应，并计算拉胀特性值，充分考虑复杂的面外屈曲变形对拉胀特性的影响。
S2.对步骤S1得到的优化结果进行几何重构与参数建模，并获得不同几何参数下的拉胀特性，具体如下：
将优化的单胞构型中的自由曲线型剪口20重构为三段折线型剪口22，除便于参数描述外，还有助于提升剪纸超材料的制备精度；采用三段折线型剪口22中各线段的长度及分布角度作为参数，描述几何重构后包含三段折线型剪口22的单胞构型23。开展参数学习，在指定的参数范围区间内遍历所有剪口参数，获得相应的单胞拉胀性能。
S3. 对步骤S2得到的多个参数化单胞按照周期、梯度或非规则的形式进行排布，构造剪纸超材料，具体如下：
选用多个采用相同剪口参数描述的单胞进行周期排列，构造具有均匀拉胀特性的剪纸超材料；选用多个采用不同剪口参数描述的单胞进行梯度或非规则排列，构造具有梯度或指定非均匀拉胀特性的剪纸超材料。
进一步的，步骤S1中曲线型剪口20的中心线10的描述方法包括但不限于B样条插值函数、非均匀有理B样条插值函数或解析曲线函数描述。
进一步的，步骤S1中所述的非线性有限元方法包括但不限于Newton-Raphson法或改进弧长法；所述的优化算法包括但不限于非线性序列二次规划算法（梯度算法）和遗传算法（智能算法）。
 有益效果
（1）本发明提供的剪纸超材料在拉伸量不超过样件尺寸50%的单向拉伸载荷作用下，始终能够在5-50%拉伸量之间获得指定的拉胀特性值，还可通过修改剪口参数，实现多种随拉伸量大小可调节的拉胀特性变化趋势。
（2）设计过程中充分考虑了面外屈曲变形，使得所述剪纸超材料能够合理地利用这些面外屈曲变形显著减小面内应力，从而获得在大拉伸量下的变形恢复特性。
（3）本发明提供的剪纸超材料可包含周期、梯度或非规则排布的多个单胞，分别获得了均匀分布、梯度变化和指定非均匀分布的拉胀特性。与已有的剪纸超材料相比，本发明在结构设计、使用范围和应用前景具有明显优势。
 附图说明
图1是本发明提供的一种剪纸超材料及包含的单胞构型；其中，图1（a）是该剪纸超材料的构型图，图1（b）是单胞的构型图，图1（c）是单胞中的一个1/4方形域的俯视图；
图2是图1所示的一个单胞在拉伸状态下的结构变形，其中，图2（a）是一个单胞在拉伸量为10%的结构变形；图2（b）是一个单胞在拉伸量为20%的结构变形；图2（c）是一个单胞在拉伸量为30%的结构变形；
图3是不同几何参数描述的单胞构型俯视图；其中，图3（a）是在拉伸量小于50%时，拉胀特性最小值为-0.27的单胞构型；图3（b）是在拉伸量小于50%时，拉胀特性最小值为-0.94的单胞构型；图3（c）是在拉伸量小于50%时，拉胀特性最小值为-1.90的单胞构型；
图4是采用不同几何参数描述的剪纸超材料单胞的拉胀特性与伸长量曲线；
图5是包含不同单胞排布方式的剪纸超材料；其中，图5（a）是包含多个周期排布单胞的剪纸超材料俯视图；图5（b）是包含多个梯度排布单胞的剪纸超材料俯视图；图5（c）是包含多个非规则排布单胞的剪纸超材料俯视图；
图6是在设计流程的结构优化设计中，1/4方形域内一条剪口的建模示意图；其中，图6（a）是采用非均匀有理B样条曲线描述剪口中心线示意图；图6（b）是包含上述一条剪口的1/4方形域俯视图；
图7是在设计流程的几何重构示意图；其中，图7（a）是结构优化得到的单胞构型俯视图，包含曲线型剪口；图7（b）是几何重构后的单胞构型俯视图，包含多段折线型剪口；
图8 是本发明提供的剪纸超材料设计方法流程图。
图中：1 剪纸超材料；2 方形单胞；3 构成方形单胞的1/4方形域；4 剪口尖端；5 剪口；6 单胞内部的x轴/y轴；7 剪口首段；8 剪口中段；9 剪口末段；10 剪口中心线；11 1/4方形域的顶点；12 单向拉伸载荷；13 面外屈曲变形；14-17均表示不同参数组合的剪纸超材料单胞构型；18 自由曲线型剪口建模所用控制点；19 控制点连接线；20 自由曲线型剪口；21 单胞几何模型；22 三段折线型剪口；23 单胞构型。
 本发明的实施方式
为了充分说明本发明，下面结合附图和实施例做进一步的详细说明。应当理解，这里所描述的具体实施例仅仅用来解释本发明，但是并不用于限定本发明。参见图1（a）以及图5（a）-（c），本发明提供的一种大拉伸量下具有可调节拉胀特性的剪纸超材料，所述剪纸超材料1由多个有序排布的方形单胞2构成，其可由多个有序（周期、梯度或非规则）排布的方形单胞2构成。
所述的一个方形单胞2边长为L、厚度为t，其由一个1/4方形域3与由该1/4方形域沿着单胞内部的x轴/y轴6镜像得到的另外三个1/4方形域组成。所述的一个1/4方形域3中预置两个形状相同的三段折线型剪口，两条剪口5之间满足沿1/4方形域中心旋转对称。在一个完整的方形单胞2中，所述的一个单胞2内所有剪口的布局满足沿单胞中心点反手性对称。如图1（b）所示，方形单胞2边长为L=30.0mm、厚度为t=0.3mm。
所述的一个1/4方形域3中的剪口5具有均匀宽度w，其形状为如图1（c）和图7（b）所示的细长三段折线。其中，一个剪口尖端位于所述1/4方形域3的一个顶点11，另一个剪口尖端4呈圆弧状，圆弧半径为w/2。所述剪口5由剪口首段7、剪口中段8和剪口末段9组成。
图1（b）中所示方形单胞2的一条剪口5由以下剪口参数描述：剪口首段、中段和末段的中心线10的长度分别为：L 1为11.0 mm、L 2为7.6 mm和L 3为4.7 mm；剪口首段与所述1/4方形域3底部边界夹角θ 1为0°，宽度w/2为0.2mm；剪口中段与剪口末段夹角θ 2为113°，剪口中段与末端宽度w为0.4mm。
所述方形单胞2厚度t远小于边长L的结构特性且其内部剪口布局，对局部区域的刚度造成了削弱，使得单胞在受载时不稳定从而产生面外变形。在设计过程中充分考虑这种面外变形，使得所述单胞在受到如图2所示的x向单向拉伸载荷12作用下，在沿x方向达到单胞长度L的3%的伸长量后就因失稳产生了明显的面外屈曲变形，并导致拉胀变形出现。在更大拉伸量下，所述单胞的拉胀特性稳定在指定数值，当伸长量为单胞长度L的10%、20%、30%时，得到的拉胀特性值均为-0.7，产生如图2（a）-（c）所示的变形，包括如图2所示的面外屈曲变形13。
本发明所提供的剪纸超材料单胞的变形及由变形产生的拉胀特性主要由上述单胞几何参数决定。在参数范围内通过不同几何参数的组合，能够得到不同的单胞构型，获得在-0.2到-1.9范围内的拉胀特性及不同类型的拉胀变形趋势（平稳型、单调下降型和先下降后上升型）。作为优选，在所述单胞的几何参数边长L=30.0mm、厚度t=0.3mm、剪口宽度w=0.4mm不变的情况下，选用不同剪口几何参数组合得到如图3所示的不同类型的单胞构型：
（1）如图3（a）所示的单胞构型15，其剪口几何参数为：剪口首段7、剪口中段8和剪口末段9的剪口中心线10的长度分别为：L 1为12.0 mm、L 2为8.5 mm和L 3为7.0 mm；剪口首段7与所述1/4方形域3底部边界夹角θ 1为0°；剪口中段8与剪口末段9的夹角θ 2为90°。实现了如图4所示的平稳型拉胀特性变化曲线，在拉伸变形中的最小拉胀特性为-0.27。
（2）如图3（b）所示的单胞构型16，其剪口几何参数为：剪口首段7、剪口中段8和剪口末段9的中心线10的长度分别为：L 1为11.0 mm、L 2为4.0 mm和L 3为8.3 mm；剪口首段7与所述1/4方形域3底部边界夹角θ 1为0°；剪口中段8与剪口末段9的夹角θ 2为160°。实现了如图4所示的单调下降型拉胀特性变化曲线，在拉伸变形中的最小拉胀特性为-0.94；
（3）如图3所示的单胞构型17，其剪口几何参数为：剪口首段7、剪口中段8和剪口末段9的中心线10的长度分别为：L 1为13.0 mm、L 2为11.5 mm和L 3为3.4 mm；剪口首段7与所述1/4方形域3底部边界夹角θ 1为0°；剪口中段8与剪口末段9夹角θ 2为66°。实现了如图4所示的先下降后上升型拉胀特性变化曲线，在拉伸变形中的最小拉胀特性达到-1.90。
本发明所述拉胀剪纸超材料由不同剪口参数的多种单胞按照特定的周期、梯度或非规则排布规律构成，分别获得了均匀分布、梯度变化和指定非均匀分布的拉胀特性。如图5（a）所示的剪纸超材料包含多个沿x轴和y轴方向均周期排布的单胞14，具有均匀拉胀特性；提供的如图5（b）所示的剪纸超材料包含沿x轴梯度排布、沿y轴周期排布的单胞15、16和17，具有沿x方向梯度变化的拉胀特性；提供的如图5（c）所示的剪纸超材料包含沿x轴和y轴不规则排布的单胞14、15、16和17，具有沿各个方向都是非均匀的拉胀特性。
本实施例中所述的剪纸超材料，选用高分子聚合物材料PET作为基体材料，采用激光切割制备。
本实施例还提供用于上述剪纸超材料的设计方法，设计流程图如图8所示，其详细步骤如下：
步骤S1，采用结构优化技术，在充分考虑面外变形条件下，得到单胞构型的启发式设计。具体的：
首先，建立一个周期方形单胞21的几何模型作为优化设计域。在方形单胞21的一个1/4方形域内预置两个自由曲线型剪口20，每一条剪口的中心线都采用非均匀有理B样条插值函数进行描述。使用连接线19顺序连接控制点18构成曲线控制多边形，并选取非均匀有理B样条插值函数阶数为2阶，进而通过对控制点坐标进行插值获得具有自由曲线形状的剪口中心线10；进而，采用线偏移技术，将每条剪口中心线10沿每点处的法线方向两侧各自偏移0.2mm，形成如图6（b）所示的细长自由曲线型剪口20，其中剪口尖端为圆弧形状；最终，将包含剪口的1/4区域沿着x轴和y轴镜像，得到具有反手性对称的完整单胞几何模型。
在优化设计过程中，对单胞进行有限元分析。在单胞边界上施加周期性边界条件，即方形单胞相对边界上对应点的位移差相等，以模拟单胞在超材料中的真实变形同时节约计算成本，缩短设计周期；并使用模态比例因子方法将多阶线性屈曲模态进行缩比和叠加，作为初始几何缺陷引入到分析构型中，用以模拟加工缺陷，允许可能出现的面外屈曲变形。进而，考虑采用非线性分析中的Newton-Raphson方法完成对上述单胞在受到沿x方向拉伸载荷作用下的变形分析。
在结构优化中，选择1/4方形域的每个剪口控制点18坐标作为设计变量，将在不同拉伸量下的指定拉胀特性作为优化目标，选择剪口的最大长度和最大曲率作为约束。结构优化过程包括两步：第一步利用智能类算法中的多岛遗传算法，在设计空间内整体寻优，得到接近最优解的控制点的空间坐标；第二步利用梯度类算法中的非线性序列二次规划算法在第一步得到的优化解附近的设计空间中完成局部寻优，获得剪口控制点的最优位置，最终完成如图7（a）的自由曲线型单胞构型21的启发式设计。
步骤S2，对所选步骤S1中得到的优化构型进行几何重构和参数建模，具体为：
将自由曲线型剪口等效为多段折线型剪口，并选取多段折线中各直线段的长度及各直线段的铺设角度作为几何描述参数。本发明实施例中对如图7（a）所示的单胞优化构型进行几何重构，得到了如图7（b）所示的包含三段折线型剪口的参数模型。
遍历所有几何参数，获得相应的拉胀特性。作为优选，遍历参数是在指定的范围内，间隔取值完成的。
步骤S3，构造包含不同单胞排布形式的剪纸超材料，具体为：
剪纸超材料可包含采用相同几何参数描述的多个周期单胞，实现了均匀拉胀特性，其内部排布如图5（a）所示；剪纸超材料可包含沿某一方向采用不同几何参数描述的多个单胞，实现了梯度变化的拉胀特性，其内部排布如图5（b）所示；剪纸超材料还可包含沿各个方向采用不同几何参数描述的非规则排布的多个单胞，实现了非均匀拉胀特性，其内部排布如图5（c）所示。
以上所述实施例仅表达本发明的实施方式，但并不能因此而理解为对本发明专利的范围的限制，应当指出，对于本领域的技术人员来说，在不脱离本发明构思的前提下，还可以做出若干变形和改进，这些均属于本发明的保护范围。本实施例中未明确的各组成部分均可用现有技术加以实现。

Claims (7)

  1. 一种大拉伸量下具有可调节拉胀特性的剪纸超材料，其特征在于，所述剪纸超材料(1)由多个有序排布的方形单胞(2)构成，所述有序排布指：多个方形单胞(2)在剪纸超材料(1)内周期性、梯度性或非规则性排布，对应的剪纸超材料(1)分别具有均匀拉胀特性、梯度拉胀特性和指定非均匀拉胀特性；
    所述的一个方形单胞(2)边长L、厚度t，由一个1/4方形域(3)和由该1/4方形域分别沿着单胞内部的x轴/y轴(6)镜像得到的另外三个1/4方形域组成；所述的一个1/4方形域(3)中预置两条形状相同的剪口(5)，两条剪口(5)之间满足沿该1/4方形域中心旋转对称；在一个完整的方形单胞(2)中，所有剪口(5)的布局满足沿单胞中心点反手性对称；
    所述的一个1/4方形域(3)中的所有剪口(5)均具有均匀宽度w，其中一条剪口(5)的一个剪口尖端4位于所述1/4方形域的一个顶点(11)，另一个剪口尖端4呈圆弧状，其半径为w/2，位于所述1/4方形域内部；所述的一条剪口(5)为细长的三段折线型，从1/4方形域一个顶点(11)起，由直线型的剪口首段(7)、剪口中段(8)和剪口末段(9)三部分组成，并由以下剪口参数描述：剪口首段(7)、中段(8)和末段(9)的中心线(10)的长度分别为L 1、L 2和L 3；所述剪口首段(7)与所述1/4方形域(3)底部边界夹角为θ 1，剪口中段(8)与y轴平行，剪口中段(8)与剪口末段(9)的相对夹角为θ 2，且θ 2始终位于所述剪口的中段(8)靠近单胞边界的一侧。
  2. 根据权利要求1所述的一种大拉伸量下具有可调节拉胀特性的剪纸超材料，其特征在于，所述的用于描述一个方形单胞(2)构型的几何参数取值范围如下：参数t/L的变化范围为0.0033-0.0167；参数L 1/L的变化范围为0.33-0.44；参数L 2/L的变化范围为0.08-0.39；参数L 3/L的变化范围为0.10-0.29；参数θ 2的变化范围为60°-160°；参数w/L的变化范围为0.001-0.033；参数θ 1的变化范围为0°-11.5°，且当θ 1=0°时，剪口首段(7)的中心线(10)与1/4方形域(3)的边界重叠，此时剪口首段(7)的宽度为w/2。
  3. 根据权利要求1所述的一种大拉伸量下具有可调节拉胀特性的剪纸超材料，其特征在于，所述剪纸超材料(1)的基体材料选用金属或高分子聚合物，采用刀刻、激光切割、水切割或3D打印技术制造。
  4. 一种权利要求1-3任一所述的大拉伸量下具有可调节拉胀特性的剪纸超材料的设计方法，其特征在于，包括以下步骤：
    S1.采用结构优化方法，充分考虑面外变形约束，得到单胞构型的启发式设计，具体如下：
    首先，选用一个方形单胞(2)作为设计域，在其边界施加周期性边界条件，模拟所述单胞在超材料的真实变形，同时节约计算分析成本，缩短设计周期；其次，预置人为指定数量的自由曲线型剪口(20)，将自由曲线型剪口(20)的排布位置、形状和长度作为设计变量，将自由曲线型剪口(20)的长度及最大曲率作为约束条件；进而，选用梯度算法、智能算法或两者结合的优化算法更新设计变量，优化剪口的位置、形状和长度，获得指定拉胀特性的单胞构型，完成单胞构型的启发式设计；
    所述迭代优化过程中：对单胞进行有限元分析以获取其在加载过程中的变形；首先对单胞进行线性屈曲分析，并将分析得到的低阶模态作为初始几何缺陷引入到有限元模型中，修改节点坐标；选用非线性有限元方法求解在拉伸载荷下的变形响应，并计算拉胀特性值，充分考虑复杂的面外屈曲变形对拉胀特性的影响； 
    S2.对步骤S1得到的优化结果进行几何重构与参数建模，并获得不同几何参数下的拉胀特性，具体如下：
    将优化的单胞构型中的自由曲线型剪口(20)重构为三段折线型剪口(22)；采用三段折线型剪口(22)中各线段的长度及分布角度作为参数，描述几何重构后包含三段折线式剪口(22)的单胞构型(23)；开展参数学习，在指定的参数范围区间内遍历所有剪口参数，获得相应的单胞拉胀性能；
    S3.对步骤S2得到的多个参数化单胞按照周期、梯度或非规则的形式进行排布，构造剪纸超材料，具体如下：
    选用多个采用相同剪口参数描述的单胞进行周期排列，构造具有均匀拉胀特性的剪纸超材料；选用多个采用不同剪口参数描述的单胞进行梯度或非规则排列，构造具有梯度或指定非均匀拉胀特性的剪纸超材料。
  5. 一种权利要求4所述的大拉伸量下具有可调节拉胀特性的剪纸超材料的设计方法，其特征在于，步骤S1中所述曲线型剪口(20)的描述方法采用B样条插值函数、非均匀有理B样条插值函数或解析曲线函数描述。
  6. 一种权利要求4所述的大拉伸量下具有可调节拉胀特性的剪纸超材料的设计方法，其特征在于，步骤S1中所述的非线性有限元方法包括Newton-Raphson法或改进弧长法。
  7. 一种权利要求4所述的大拉伸量下具有可调节拉胀特性的剪纸超材料的设计方法，其特征在于，步骤S1中所述的梯度算法包括非线性序列二次规划算法，智能算法包括遗传算法。
PCT/CN2021/104141 2021-03-16 2021-07-02 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法 WO2022193477A1 (zh)

Priority Applications (1)

Application Number Priority Date Filing Date Title
US17/639,522 US20230185999A1 (en) 2021-03-16 2021-07-02 Kirigami metamaterial with tunable auxetic property under large tensions and its design method

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
CN202110278090.0A CN112949136B (zh) 2021-03-16 2021-03-16 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法
CN202110278090.0 2021-03-16

Publications (1)

Publication Number Publication Date
WO2022193477A1 true WO2022193477A1 (zh) 2022-09-22

Family

ID=76229372

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/CN2021/104141 WO2022193477A1 (zh) 2021-03-16 2021-07-02 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法

Country Status (3)

Country Link
US (1) US20230185999A1 (zh)
CN (1) CN112949136B (zh)
WO (1) WO2022193477A1 (zh)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116416878A (zh) * 2023-03-22 2023-07-11 大连理工大学 一种大拉伸量下无图像失真的柔性led点阵屏

Families Citing this family (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112949136B (zh) * 2021-03-16 2022-03-29 大连理工大学 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法
CN114161437B (zh) * 2021-11-29 2023-09-15 大连理工大学 一种流体管道中爬行的软体机器人及其设计方法
CN114582445B (zh) * 2022-03-10 2024-06-21 湖南大学 一种超材料的优化方法、系统及设备
CN116432330B (zh) * 2022-12-23 2024-03-19 华中科技大学 功能梯度拉胀超材料填充的多尺度壳体设计方法及设备

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2961625A1 (en) * 2016-06-02 2017-12-02 The Royal Institution For The Advancement Of Learning/Mcgill University Bistable auxetics
CN108591810A (zh) * 2018-05-15 2018-09-28 大连理工大学 一种高拉伸强度的可调带隙机械超材料
CN112045990A (zh) * 2020-09-10 2020-12-08 西安交通大学 具有压剪耦合特性的手性拉胀超构材料结构及其制备方法
CN112307663A (zh) * 2020-11-06 2021-02-02 西北工业大学 具有预定负泊松比特性的手性超材料结构的设计方法
CN112490681A (zh) * 2020-11-24 2021-03-12 中国人民解放军空军工程大学 三维剪纸超材料可调吸波体及其设计方法
CN112949136A (zh) * 2021-03-16 2021-06-11 大连理工大学 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2015109359A1 (en) * 2014-01-24 2015-07-30 Rmit University Structured porous metamaterial
CN111950095B (zh) * 2020-07-09 2024-02-23 中山大学 一种具有可调泊松比和热膨胀系数的三维多胞结构
CN112049886B (zh) * 2020-09-10 2022-02-11 西安交通大学 具有拉扭耦合特性的手性拉胀超构材料结构及其制备方法

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CA2961625A1 (en) * 2016-06-02 2017-12-02 The Royal Institution For The Advancement Of Learning/Mcgill University Bistable auxetics
CN108591810A (zh) * 2018-05-15 2018-09-28 大连理工大学 一种高拉伸强度的可调带隙机械超材料
CN112045990A (zh) * 2020-09-10 2020-12-08 西安交通大学 具有压剪耦合特性的手性拉胀超构材料结构及其制备方法
CN112307663A (zh) * 2020-11-06 2021-02-02 西北工业大学 具有预定负泊松比特性的手性超材料结构的设计方法
CN112490681A (zh) * 2020-11-24 2021-03-12 中国人民解放军空军工程大学 三维剪纸超材料可调吸波体及其设计方法
CN112949136A (zh) * 2021-03-16 2021-06-11 大连理工大学 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116416878A (zh) * 2023-03-22 2023-07-11 大连理工大学 一种大拉伸量下无图像失真的柔性led点阵屏
CN116416878B (zh) * 2023-03-22 2023-09-26 大连理工大学 一种大拉伸量下无图像失真的柔性led点阵屏

Also Published As

Publication number Publication date
US20230185999A1 (en) 2023-06-15
CN112949136A (zh) 2021-06-11
CN112949136B (zh) 2022-03-29

Similar Documents

Publication Publication Date Title
WO2022193477A1 (zh) 大拉伸量下具有可调节拉胀特性的剪纸超材料及其设计方法
CN110516388B (zh) 基于调和映射的曲面离散点云模型环切刀轨生成方法
CN108327287B (zh) 一种三周期极小曲面三维打印切片轮廓的快速生成方法
CN106202732B (zh) 一种渐开线直齿圆柱齿轮副的齿向修形方法及与其配套的专用参数化cad系统
CN103823649B (zh) 一种基于切片文件的三维打印均匀壁厚抽壳方法
CN111062166A (zh) 一种基于变密度法的三周期极小曲面多孔结构拓扑优化方法
CN105740953A (zh) 一种基于实数编码量子进化算法的不规则排样方法
CN111444573B (zh) 船舶对称分段模型生成方法及装置、存储介质和终端
CN115688276A (zh) 一种基于离散伴随方法的飞行器外形自动化优化方法、系统、设备、介质
CN113297776B (zh) 一种风力机叶片有限元建模与铺层方法
CN112464349A (zh) 一种单层自由曲面空间网格优化方法
CN117473655B (zh) 基于边坍缩网格优化的飞行器仿真驱动设计方法和装置
Lin et al. An improved numerical technique for simulating the growth of planar fatigue cracks
CN115985421A (zh) 一种基于微观几何模型的织物复合材料有限元建模方法
CN111444619B (zh) 一种注塑模具冷却系统在线分析方法及设备
Aung et al. Isogeometric analysis and bayesian optimization on efficient weld geometry design for remarkable stress concentration reduction
Hahmann Shape improvement of surfaces
CN116562071A (zh) 一种各向异性网格质量的判断方法
CN116049941B (zh) 装配式环桁架结构构件装配前多维度状态提取及分析方法
CN111488704A (zh) 一种排管敷设电缆外部热阻计算方法及系统
CN114693887A (zh) 一种复杂点阵结构体参数化造型方法
CN113033056B (zh) 计算流体力学与有限元分析联合仿真方法
CN106651979A (zh) 基于投影的空间曲面四边形网格剖分方法
KR100440492B1 (ko) 곡면을 평면으로 전개시키는 방법
CN112883518A (zh) 一种预测tig增材与轧制复合制造件残余应力及变形的方法

Legal Events

Date Code Title Description
121 Ep: the epo has been informed by wipo that ep was designated in this application

Ref document number: 21931061

Country of ref document: EP

Kind code of ref document: A1

NENP Non-entry into the national phase

Ref country code: DE

122 Ep: pct application non-entry in european phase

Ref document number: 21931061

Country of ref document: EP

Kind code of ref document: A1