Chiral Mechanical Metamaterial Sandwich Structure without Torsional Size Effect and Its Application

Abstract

A chiral mechanical metamaterial sandwich structure with no torsional size effect and its application. The sandwich structure includes upper and lower panels and a core layer. The core layer is made of chiral mechanical metamaterials with no torsional size effect. The specific implementation method is as follows: According to the position and rotation direction of the torsional central axis in each main direction, and based on the relative position of the center of each chiral mechanical metamaterial unit cell to the torsional central axis, the torsional unit of each unit cell in this direction is calculated. By looping through until all torsional units in the core layer are calculated, the present invention eliminates the size effect of compression / tension torsion without changing the geometric parameters of the metamaterial, enabling the chiral metamaterial to still exhibit an obvious torsional angle when having a large number of unit cells, bringing an improvement in the energy absorption performance of the sandwich structure formed by its core layer.

Description

Technical Field

[0001] The present invention relates to a technology in the field of structural materials / metamaterials, and specifically to a chiral mechanical metamaterial sandwich structure without torsional size effect and its application. Background Art

[0002] The essence of the torsional size effect of chiral mechanical metamaterials is that the compression / tension rotation of the chiral metamaterial unit cell itself is prevented from accumulating into macroscopic rotation due to the mutual cancellation between unit cells. The more unit cells there are, the more intense this mutual cancellation is and the weaker the rotation accumulation is, and thus the smaller the torsional angle reflected macroscopically, which hinders the further application of chiral mechanical metamaterials. There are few designs of chiral metamaterials considering size effect in existing literature. All of them start from the idea of weakening the mutual cancellation of rotations between unit cells. By designing new structures and inserting them between the unit cells of the original metamaterial, such as rod structures, frame structures, etc., the connection between unit cells is weakened to maintain the micro-rotation freedom of the unit cells. The results of such designs do improve the size effect of chiral mechanical metamaterials, but there are still deficiencies: First, there is still mutual cancellation after weakening the connection between unit cells, so the size effect is only alleviated and not fundamentally solved. Second, because the introduction of the new structure destroys the structural connection relationship of the original metamaterial, whether it can be equivalently replaced for the original metamaterial in terms of geometric parameters, material properties, manufacturing processes, etc. still needs further discussion. Third, in existing improved designs, only the torsional size effect of chiral mechanical metamaterials in a certain main direction is discussed, that is, only unidirectional response is considered, and no improvement design is considered for the three main directions simultaneously. Summary of the Invention

[0003] In view of the above deficiencies of the existing technology, the present invention proposes a chiral mechanical metamaterial sandwich structure without torsional size effect and its application, which can eliminate the size effect of compression / tension torsion without changing the geometric parameters of the metamaterial, enabling the chiral metamaterial to still exhibit an obvious torsional angle when having a large number of unit cells and being able to be independently designed in three main directions. Due to the improvement of the torsional performance of this metamaterial, the energy absorption performance of the sandwich structure composed of it as the core layer is improved.

[0004] The present invention is achieved through the following technical solutions:

[0005] The present invention relates to a sandwich structure for bearing loads perpendicular to the panel direction, comprising: upper and lower panels and a core layer, wherein: the core layer is made of a chiral mechanical metamaterial without torsional size effect, and the specific implementation method is as follows: according to the position and rotation direction of the torsional central axis in each main direction, and according to the relative position of the center of each chiral mechanical metamaterial unit cell to the torsional central axis, calculate the torsional unit of each unit cell in this direction, and cycle through until all the torsional units in the core layer are calculated. The deformation trend of each unit cell in the torsional unit when compressed / tensioned is consistent with the rotation direction in this direction, so that the core layer of the sandwich structure undergoes plastic deformation of compression / torsion without size effect, realizing energy absorption.

[0006] The main directions mentioned refer to the x direction, y direction, and z direction.

[0007] The rotation direction mentioned refers to left-handed, right-handed, or no rotation direction.

[0008] The torsional unit is a rod structure with different deformation displacement trends. The torsional units in the three main directions of the unit cell are geometrically connected to each other and do not affect each other in selection.

[0009] The unit cell includes: three pairs of six torsional units along the three main directions. The torsional units in each main direction include: non-rotating torsional units, right-handed torsional units, left-handed torsional units, -180° torsional units, -135° torsional units, -90° torsional units, -45° torsional units, 0° torsional units, 45° torsional units, 90° torsional units, and 135° torsional units.

[0010] The torsional unit is a rod system structure composed of an upper square frame, a lower square frame, and four rods connecting the two frames. The joints between the rods are rounded. The geometric parameters of the torsional unit include: rod diameter d, side length a of the square frame, and distance b between the upper and lower square frames.

[0011] The torsional unit achieves the effect of controlling the deformation displacement trend of the chiral mechanical metamaterial unit cell no longer interfering and canceling each other through different combinations of the rod system structure, so as to increase the overall torsion.

[0012] Technical effects

[0013] The present invention calculates the form of the torsion unit according to the position of the chiral mechanical metamaterial unit cell, and constitutes a chiral mechanical metamaterial with unique properties and no torsional size effect, which is used to form the core layer of a sandwich structure with high energy absorption performance. Compared with the prior art, without changing the relative density and structural form of the original chiral mechanical metamaterial, the present invention overcomes the size effect and greatly improves the torsional performance of the chiral mechanical metamaterial; thus, the energy absorption performance and specific energy absorption of the sandwich structure composed of the core layer are significantly improved compared with the traditional sandwich structure. Description of the Drawings

[0014] Figure 1 Schematic diagrams of the chiral mechanical metamaterial unit cell without torsional size effect and the torsion unit;

[0015] Figure 2 Schematic diagram of the overall arrangement rule of the chiral mechanical metamaterial without torsional size effect;

[0016] Figure 3 Schematic diagram of the original chiral mechanical metamaterial used in the embodiment;

[0017] Figure 4 Schematic diagrams of the RRR configuration and detailed arrangement of the chiral mechanical metamaterial without torsional size effect used in the embodiment;

[0018] Figure 5 Schematic diagrams of the NNR configuration and NLR configuration of the chiral mechanical metamaterial without torsional size effect used in the embodiment;

[0019] Figure 6 Comparison diagram of the torsional performance between the chiral mechanical metamaterial without torsional size effect and the original chiral mechanical metamaterial in the embodiment;

[0020] Figure 7 Schematic diagrams of the sandwich panel structure with the NLR configuration of the chiral mechanical metamaterial as the core material and the loading in the embodiment;

[0021] Figure 8 Force-displacement curve diagram of the sandwich panel with the NLR configuration of the chiral mechanical metamaterial as the core material under quasi-static uniaxial compression load in the embodiment;

[0022] In the figure: 1 is a chiral mechanical metamaterial unit cell, 2 is a torsion unit, 21 is a torsion unit along the x direction, 22 is a torsion unit along the y direction, 23 is a torsion unit along the z direction, 24 is an upper square frame, 25 is a lower square frame, 26 is a rod connecting the upper and lower square frames, 3 is an irrotational basic structure, 41 is a right-handed torsion unit, 42 is a left-handed torsion unit, 43 is a -180° torsion unit, 44 is a -135° torsion unit, 45 is a -90° torsion unit, 46 is a -45° torsion unit, 47 is a 0° torsion unit, 48 is a 45° torsion unit, 49 is a 90° torsion unit, 410 is a 135° torsion unit, 5 is a local chiral mechanical metamaterial, 51 is the torsion central axis of the chiral mechanical metamaterial, 52 is the center of the chiral mechanical metamaterial unit cell, 6 is a comparison diagram of the arrangement of right-handed chiral mechanical metamaterial unit cells, 7 is a comparison diagram of the arrangement of left-handed chiral mechanical metamaterial unit cells, 81 is the original right-handed structure of the chiral mechanical metamaterial (the number of unit cells in the x direction N = 1), 82 is the z-direction arrangement of the original right-handed structure of the chiral mechanical metamaterial (N = 1), 83 is the original right-handed structure of the chiral mechanical metamaterial (N = 2), 84 is the z-direction arrangement of the original right-handed structure of the chiral mechanical metamaterial (N = 2), 85 is the original right-handed structure of the chiral mechanical metamaterial (N = 3), 86 is the z-direction arrangement of the original right-handed structure of the chiral mechanical metamaterial (N = 3), 91 is the RRR configuration of the chiral mechanical metamaterial without torsional size effect (N = 1), 92 is the x-direction arrangement of the RRR configuration (N = 1), 93 is the y-direction arrangement of the RRR configuration (N = 1), 94 is the z-direction arrangement of the RRR configuration (N = 1), 95 is the RRR configuration of the chiral mechanical metamaterial without torsional size effect (N = 2), 96 is the x-direction arrangement of the RRR configuration (N = 2), 97 is the y-direction arrangement of the RRR configuration (N = 2), 98 is the z-direction arrangement of the RRR configuration (N = 2), 99 is the RRR configuration of the chiral mechanical metamaterial without torsional size effect (N = 3), 910 is the x-direction arrangement of the RRR configuration (N = 3), 911 is the y-direction arrangement of the RRR configuration (N = 3), 912 is the z-direction arrangement of the RRR configuration (N = 3), 101 is the NNR configuration of the chiral mechanical metamaterial without torsional size effect (N = 1), 102 is the NNR configuration of the chiral mechanical metamaterial without torsional size effect (N = 2), 103 is the NNR configuration of the chiral mechanical metamaterial without torsional size effect (N = 3), 111 is the NLR configuration of the chiral mechanical metamaterial without torsional size effect (N = 1), 112 is the NLR configuration of the chiral mechanical metamaterial without torsional size effect (N = 2), 113 is the NLR configuration of the chiral mechanical metamaterial without torsional size effect (N = 3), 121 is the upper panel of the sandwich structure of the chiral mechanical metamaterial without torsional size effect, 122 is the core material of the sandwich structure of the chiral mechanical metamaterial without torsional size effect, 123 is the lower panel of the sandwich structure of the chiral mechanical metamaterial without torsional size effect124 is the NLR configuration (N = 5) of a chiral mechanical metamaterial with no torsional size effect used as the core material. Detailed implementation mode

[0023] As Figure 3 , Figure 4 , Figure 5 shown, this embodiment relates to a method for realizing a chiral mechanical metamaterial with no torsional size effect. The overall shape and size of the chiral mechanical metamaterial used are consistent, that is, a cylinder with a square cross-section in the xOy plane and along the z direction. Among them, the side length L of the cross-section and the height H of the cylinder remain unchanged, and H = 3L is satisfied. The measurement of the side length and height is based on the distance between the center points of the chiral mechanical metamaterial unit cell 1. The torsional helix directions of the chiral mechanical metamaterial used in the embodiment are all right-handed, and the positions of the torsional central axes in the three main directions are all defined at the geometric centers in the corresponding directions.

[0024] The number of unit cells of the chiral mechanical metamaterial is N×N×3N = 3N 3 , where: N is the number of basic structural forms along the side length L in the x direction.

[0025] The compressive / tensile torsional performance of the chiral mechanical metamaterial is measured by the magnitude of the axial unit strain torsional angle θ of the chiral mechanical metamaterial under 1% axial strain in the z direction. Then, the torsional size effect of the chiral mechanical metamaterial can be investigated by recording the change of θ with N.

[0026] The geometric parameters of the unit cells of the chiral mechanical metamaterial are consistent, and are all: Under this setting, the volume fraction of the chiral mechanical metamaterial does not change with N and is independent of the existence of torsional size effect.

[0027] As Figure 3 shown, this is the original chiral mechanical metamaterial involved in this embodiment. The original chiral mechanical metamaterial right-handed structure (N = 1) 81 includes 28 right-handed basic structures 41. Among them: According to the z-direction arrangement of the original chiral mechanical metamaterial right-handed structure (N = 1) 82, and by the same token, extended to the x direction and the y direction, the periodic arrangement of the right-handed basic structures 41 is realized; the original chiral mechanical metamaterial right-handed structure (N = 2) 83 includes 138 right-handed basic structures 41. Among them: According to the z-direction arrangement of the original chiral mechanical metamaterial right-handed structure (N = 2) 84, and by the same token, extended to the x direction and the y direction, the periodic arrangement of the right-handed basic structures 41 is realized; the original chiral mechanical metamaterial right-handed structure (N = 3) 85 includes 138 right-handed basic structures 41. Among them: According to the z-direction arrangement of the original chiral mechanical metamaterial right-handed structure (N = 3) 86, and by the same token, extended to the x direction and the y direction, the periodic arrangement of the right-handed basic structures 41 is realized.

[0028] Figure 3Among them, the black dots in the original right-handed structure of the chiral mechanical metamaterial arranged in the z-direction (N = 1) 82, the original right-handed structure of the chiral mechanical metamaterial arranged in the z-direction (N = 2) 84, and the original right-handed structure of the chiral mechanical metamaterial arranged in the z-direction (N = 3) 86 indicate z the position of the direction torsion center axis. It can be seen that there is mutual cancellation between the displacement trends of each right-handed basic structure 41 of the original chiral mechanical metamaterial and the adjacent basic structures, thus weakening the accumulation of the displacement trend. The larger N is, the greater the cancellation is, and thus the size effect is obvious.

[0029] As Figure 4 shown, it is the RRR configuration and detailed arrangement of the chiral mechanical metamaterial without torsion size effect used in the embodiment. Among them, the RRR configuration, that is, it is defined that the rotation directions of the torsion center axes of the chiral mechanical metamaterial in the x-direction, y-direction, and z-direction are right-handed - right-handed - right-handed respectively; the basic structure styles 2 in the three main directions of the RRR configuration are all arranged according to the right-handed chiral mechanical metamaterial unit cell arrangement for reference Figure 6 for arrangement.

[0030] Specifically, taking the RRR configuration (N = 1) 91 of the chiral mechanical metamaterial without torsion size effect as an example, in the RRR configuration arranged in the x-direction (N = 1) 92, the black dot indicates the position of the torsion center axis in the x-direction. The basic structure form 21 along the x-direction is numbered as shown in the figure. Calculate the azimuth angle of the center of the basic structure form 21 along the x-direction with this torsion center axis position as the origin of the polar coordinates. Then the azimuth angles of X1,1, X1,2, X1,3, X1,4, X2,1, X2,2, X2,3, X2,4 are -108.4°, -135°, 135°, 108.4°, -71.6°, -45°, 45°, 71.6° respectively. According to the right-handed chiral mechanical metamaterial unit cell arrangement for reference Figure 6 arrange the 0° basic structure 47, -45° basic structure 46, -135° basic structure 44, -180° basic structure 43, 0° basic structure 47, 45° basic structure 48, 135° basic structure 410, and -180° basic structure 43 respectively. In the RRR configuration arranged in the y-direction (N = 1) 93, the black dot indicates the position of the torsion center axis in the y-direction. The basic structure form 22 along the y-direction is numbered as shown in the figure. Calculate the azimuth angle of the center of the basic structure form 22 along the y-direction with this torsion center axis position as the origin of the polar coordinates. Then the azimuth angles of Y1,1, Y1,2, Y1,3, Y1,4, Y2,1, Y2,2, Y2,3, Y2,4 are -108.4°, -135°, 135°, 108.4°, -71.6°, -45°, 45°, 71.6° respectively. According to the right-handed chiral mechanical metamaterial unit cell arrangement for reference Figure 6Arrange the 0° basic structure 47, -45° basic structure 46, -135° basic structure 44, -180° basic structure 43, 0° basic structure 47, 45° basic structure 48, 135° basic structure 410, and -180° basic structure 43 separately. In the RRR configuration z-direction arrangement (N = 1) 94, the black dots represent the positions of the z-direction torsion center axes. The basic structure forms 23 along the z-direction are numbered as shown in the figure. Calculate the azimuth angles of the centers of the basic structure forms 23 along the z-direction with the position of this torsion center axis as the origin of the polar coordinates. Then the azimuth angles of Z1,1, Z1,2, Z2,1, and Z2,2 are -135°, 135°, -45°, and 45° respectively, in accordance with the right-handed chiral mechanical metamaterial unit cell arrangement comparison Figure 6 Arrange the -45° basic structure 46, -135° basic structure 44, 45° basic structure 48, and 135° basic structure 410 separately.

[0031] According to the same arrangement rules, the chiral mechanical metamaterial RRR configuration (N = 2) 95 without torsional size effect is based on the RRR configuration x-direction arrangement (N = 2) 96, RRR configuration y-direction arrangement (N = 2) 97, and RRR configuration z-direction arrangement (N = 2) 98. The chiral mechanical metamaterial RRR configuration (N = 3) 99 without torsional size effect is then based on the RRR configuration x-direction arrangement (N = 3) 910, RRR configuration y-direction arrangement (N = 3) 911, and RRR configuration z-direction arrangement (N = 3) 912, realizing the design of the chiral mechanical metamaterial without torsional size effect.

[0032] Through specific actual experiments, the chiral mechanical metamaterial NNR configuration and NLR configuration without torsional size effect as shown Figure 5 are also designed according to the above rules. For the NNR configuration, that is, it is defined that the rotation directions of the torsion center axes of the chiral mechanical metamaterial in the x-direction, y-direction, and z-direction are non-rotating - non-rotating - right-handed; for the NLR configuration, that is, it is defined that the rotation directions of the torsion center axes of the chiral mechanical metamaterial in the x-direction, y-direction, and z-direction are non-rotating - left-handed - right-handed.

[0033] Specifically, the chiral mechanical metamaterial NNR configuration (N = 1) 101, chiral mechanical metamaterial NNR configuration (N = 2) 102, and chiral mechanical metamaterial NNR configuration (N = 3) 103 without torsional size effect are arranged in the z-direction in accordance with the right-handed chiral mechanical metamaterial unit cell arrangement comparison Figure 6Arrange them. In the x-direction and y-direction, use the non-rotational basic structure 3 for periodic arrangement; the NLR configurations (N = 1) 111, NLR configurations (N = 2) 112, and NLR configurations (N = 3) 113 of the chiral mechanical metamaterial without torsional size effect are arranged in the z-direction according to the right-handed chiral mechanical metamaterial unit cell arrangement comparison Figure 6 Arrange them. In the y-direction, arrange them according to the left-handed chiral mechanical metamaterial unit cell arrangement comparison Figure 7 Arrange them. In the x-direction, use the non-rotational basic structure 3 for periodic arrangement.

[0034] According to the above arrangement rules, the corresponding chiral mechanical metamaterials without torsional size effect for any N (N is a positive integer) can be generated. For example Figure 6 As shown, it is the comparison of the torsional performance between the chiral mechanical metamaterial without torsional size effect and the original chiral mechanical metamaterial in the embodiment. The unit strain torsional angle θ of the chiral mechanical metamaterials from N = 1 to N = 20 is calculated through the mechanical simulation analysis results, and the N-θ curve is plotted.

[0035] Specifically, the mechanical simulation is calculated through the commercial software ABAQUS Standard solver. The matrix material of the chiral mechanical metamaterial is set to steel (Young's modulus 210 GPa, Poisson's ratio 0.3). The model is meshed using the beam structure element B31, and the mesh resolution is 0.2. The boundary conditions of the model are set as follows: the bottom in the z-direction of the chiral mechanical metamaterial is fixed, and a displacement boundary condition is applied at the top, and the remaining boundaries are free boundaries. All models use a unified z-axis strain ε z = 1%. Material models from N = 1 to N = 20 are generated for the RRR configuration, NNR configuration, NLR configuration of the chiral mechanical metamaterial without torsional size effect and the original metamaterial respectively, and static analysis is carried out. Geometric nonlinearity is turned on in all analyses. Finally, through the coordinates of the top nodes in the z-direction of the model before and after displacement, the overall torsional angle θ0 of the model is calculated, and finally the corresponding unit strain torsional angle θ = θ0 / ε = θ0 / 1% = θ0 [° / %] is obtained.

[0036] As Figure 6 shown, for the original chiral mechanical metamaterial, as N increases, the unit strain torsional angle θ decreases in inverse proportion, that is, θ When N is large enough, θ approaches 0, and the phenomenon of the metamaterial being compressed / twisted under tension disappears. On the contrary, for the chiral mechanical metamaterial with no torsional size effect in this embodiment, as N increases, the torsional angle θ per unit strain gradually rises and remains constant. Moreover, it can be concluded that the torsional properties in the z-direction are similar among the three configurations in this embodiment, that is, the designs in the x-direction and y-direction do not affect the design in the z-direction, indicating the independence of the design in the three main directions in this embodiment. In addition to the RRR configuration, NNR configuration, and NLR configuration in this embodiment, the configurations that can be designed in the same way are: LNR configuration, LLR configuration, RNR configuration, RLR configuration, NRR configuration, LRR configuration, RRL configuration, RNL configuration, RLL configuration, LRL configuration, LNL configuration, LLL configuration, NRL configuration, NNL configuration, NLL configuration, RRN configuration, RNN configuration, RLN configuration, LRN configuration, LNN configuration, LLN configuration, NRN configuration, NNN configuration, NLN configuration, a total of 3^3 = 27 kinds. Figure 6 It shows that the torsional performance of the chiral mechanical metamaterial core layer with no torsional size effect in this embodiment has been greatly improved compared with the original chiral mechanical metamaterial.

[0037] As Figure 7 shown, it is a schematic diagram of the loading test of the sandwich structure using the chiral metamaterial of this embodiment as the core material. In the test, a quasi-static uniaxial compression was performed on the sample as Figure 7 shown. The lower panel 123 of the sandwich structure was fixed, and the pressure was vertically applied to the upper panel 121 of the sandwich structure. The core layer 122 of the sandwich structure is a chiral mechanical metamaterial 124 with the RNL configuration and no torsional size effect. The thickness of the sandwich panel is 2 mm, the thickness of the core layer is 21 mm, the size of the sandwich structure is 60 mm × 60 mm × 25 mm, and the diameter of the metamaterial rod is 0.25 mm. The matrix material of the sandwich structure is steel (Young's modulus 210 GPa, Poisson's ratio 0.3), and it is prepared by the SLM process of 3D printing. At a load application speed of 0.2 mm / min, the sandwich structure was made to experience the elastic deformation stage, plastic deformation stage until the densification stage, and the load data and displacement data of the process were recorded by sensors and plotted into a force-displacement curve, as Figure 8 shown. The force-displacement curve in the figure shows that the sandwich structure of the chiral mechanical metamaterial with no torsional size effect in this embodiment (CMM sandwich) has a flatter yield platform and a more ideal energy absorption effect compared with the traditional face-centered cubic structure (BCC sandwich) as the core layer; it can be seen from the two indicators of energy absorption and specific energy absorption that the energy absorption performance of the sandwich structure in this embodiment has been improved by 115% and 147% respectively.

[0038] The above specific embodiments can be locally adjusted in different ways by those skilled in the art without departing from the principles and purposes of the present invention. The protection scope of the present invention is subject to the claims and is not limited by the above specific embodiments. All implementation solutions within its scope are subject to the present invention.

Claims

1. A sandwich structure for withstanding loads perpendicular to the panel direction, characterized in that, Comprising: Upper and lower panels and a core layer, wherein: the core layer is made of a chiral mechanical metamaterial without torsional size effect. Specifically: according to the position and rotation direction of the torsional central axis in each main direction, and based on the relative position of the center of each chiral mechanical metamaterial unit cell with respect to the torsional central axis, the torsional unit of each unit cell in this direction is calculated. By traversing cyclically until all the torsional units within the core layer are calculated, the deformation trend of each unit cell in the torsional unit under compression / tension is consistent with the rotation direction in this direction, enabling the core layer of the sandwich structure to undergo plastic deformation of compression / torsion without size effect and achieving energy absorption. The so-called main directions refer to the x-direction, y-direction, and z-direction. The so-called rotation direction refers to left-handed, right-handed, or non-rotation direction. The torsional unit is a rod structure with different deformation displacement trends. The torsional units in the three main directions of the unit cell are geometrically connected to each other and are independent of each other in terms of selection.

2. The sandwich structure for bearing loads perpendicular to the panel direction according to claim 1, characterized in that, The described unit cell includes: six pairs of three twisting units along three principal directions, and the twisting units in each principal direction include: a non-rotating twisting unit, a right-handed twisting unit, a left-handed twisting unit, a twisting unit, a twisting unit, a twisting unit, a twisting unit, a twisting unit, a twisting unit, a twisting unit, and a twisting unit.

3. The sandwich structure for bearing loads perpendicular to the panel direction according to claim 1, characterized in that, The described torsion units are all rod systems composed of an upper square frame, a lower square frame, and four rods connecting the two frames. The joints between the rods are rounded at the transitions. The geometric parameters of the torsion units include: rod diameter , side length of the square frame , and the distance between the upper and lower square frames .

4. The sandwich structure for bearing loads perpendicular to the panel direction according to any one of claims 1-3, characterized in that, The configurations of the chiral mechanical metamaterial include: right-handed structure with N = 1 unit cells in the x-direction, right-handed structure arranged in the z-direction with N = 1, right-handed structure with N = 2, right-handed structure arranged in the z-direction with N = 2, right-handed structure with N = 3, right-handed structure arranged in the z-direction with N = 3, chiral mechanical metamaterial RRR configuration without torsional size effect with N = 1, RRR configuration arranged in the x-direction with N = 1, RRR configuration arranged in the y-direction with N = 1, RRR configuration arranged in the z-direction with N = 1, chiral mechanical metamaterial RRR configuration without torsional size effect with N = 2, RRR configuration arranged in the x-direction with N = 2, RRR configuration arranged in the y-direction with N = 2, RRR configuration arranged in the z-direction with N = 2, chiral mechanical metamaterial RRR configuration without torsional size effect with N = 3, RRR configuration arranged in the x-direction with N = 3, RRR configuration arranged in the y-direction with N = 3, RRR configuration arranged in the z-direction with N = 3, chiral mechanical metamaterial NNR configuration without torsional size effect with N = 1, chiral mechanical metamaterial NNR configuration without torsional size effect with N = 2, chiral mechanical metamaterial NNR configuration without torsional size effect with N = 3, chiral mechanical metamaterial NLR configuration without torsional size effect with N = 1, chiral mechanical metamaterial NLR configuration without torsional size effect with N = 2, chiral mechanical metamaterial NLR configuration without torsional size effect with N = 3, upper panel of chiral mechanical metamaterial sandwich structure without torsional size effect, core material of chiral mechanical metamaterial sandwich structure without torsional size effect, lower panel of chiral mechanical metamaterial sandwich structure without torsional size effect, and chiral mechanical metamaterial NLR configuration without torsional size effect used as core material with N = 5.

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