Multi-mode and programmable non-reciprocal mechanical metamaterial and design method

Abstract

The invention discloses a multi-mode and programmable non-reciprocal mechanical metamaterial and a design method, and the method comprises the steps: firstly, arranging a self-contact notch in a microstructure design domain, dividing a plurality of quadrilateral grids, and setting a density variable for each grid; meanwhile, periodic boundary condition constraints are applied to the design domain, and displacement conditions are set; based on the density variable, determining an interpolation function of the hyperelastic material model parameters and the density variable, designing a target Poisson's ratio and a constraint threshold value of a target function and a constraint function of the model, calculating gradients of the target function and the constraint function about the density variable by adopting an adjoint method, and solving the target Poisson's ratio and the constraint threshold value; outputting an optimized density variable, and finally constructing a required microstructure unit cell shape. The unit cells are connected in an array in a plane to form an orthogonal and uniaxial nonreciprocal periodic metamaterial; mapping the unit cells into a cylinder to obtain a shear nonreciprocal metamaterial; the metamaterial constructed by introducing the self-contact notches has good nonreciprocity, and the structure is programmable.

Description

Technical Field

[0001] The present invention belongs to the technical field related to structural design, and more specifically, relates to a multi-mode and programmable non-reciprocal mechanical metamaterial and a design method thereof. Background Art

[0002] Reciprocity, the ability of a system to maintain symmetry in its response when its inputs and outputs are swapped, is ubiquitous in many physical systems. Breaking this response symmetry can destroy reciprocity, and the resulting diode effect opens up vast potential for controlling material deformation and structural response. Mechanical nonreciprocity, the asymmetric transfer of mechanical quantities between two points in space, is crucial for developing systems capable of channeling, suppressing, and controlling mechanical energy because they offer the potential to channel, suppress, and control mechanical signals and energy in ways that reciprocal systems cannot.

[0003] Existing technologies can achieve nonreciprocal modes in a single direction through the rational design of metamaterials and structures. For example, fishbone metamaterials can exhibit uniaxial nonreciprocal modes; composite materials embedded with nanofillers exhibit shear nonreciprocal modes. However, existing technologies are mostly limited to designing metamaterials with unidirectional nonreciprocity. Practical applications often face multiple working conditions, and unidirectional nonreciprocal metamaterials are easily restricted in use. It is well known that in two-dimensional (2D) space, nine elastic constants can be used to describe material properties. This means that the nonreciprocal behavior of coupling between different loading directions can exhibit multiple modes. Although nonreciprocity has attracted great attention, it is extremely challenging to obtain multiple nonreciprocal modes in a single microstructure. In addition, in metamaterial design methods, many strategies for programmable response have been proposed, including multistability, tunable shape, and programmable stiffness, but programmable nonreciprocity remains to be explored.

[0004] This invention designs metamaterials with multiple nonreciprocal modes by controlling the cutouts within a metamaterial unit cell. This identical microstructural unit can exhibit nonreciprocal modes in orthogonal, uniaxial, and shear directions. The structure can be programmed by varying the number of cutouts, eliminating the need for repeated design and replacement of structures when adjusting isotropic stiffness properties. This further enhances the applicability of multimodal and programmable metamaterials. This approach achieves multidirectional asymmetric stiffness properties not found in natural materials and establishes a framework for describing multimodal nonreciprocal behavior using constitutive tensors, providing a new paradigm for mechanically functional metamaterials. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a multi-mode and programmable non-reciprocal mechanical metamaterial, which introduces self-contact notches in a unit cell so that the designed structure has non-reciprocity under various working conditions.

[0006] To achieve the above objectives, according to one aspect of the present invention, a multi-mode and programmable non-reciprocal mechanical metamaterial is provided. The multi-mode and programmable non-reciprocal mechanical metamaterial is formed by connecting a plurality of unit cells in an array; the unit cells have a lattice structure characterized by a square structure located in the center of the lattice structure and surrounding structures to be cut with C4 rotational symmetry; the sides of the square structure are inclined at an angle to the horizontal axis; the four structures to be cut are provided with cuts at the upper left and lower right corners, forming self-contact gaps; the cuts can be selectively retained or closed by a limiter, thereby achieving programmable control of the non-reciprocal properties of the mechanical metamaterial.

[0007] Furthermore, the unit cell is a linear unit cell structure, the side length of the mesh grid structure feature is 25 mm, the side length of the square structure is 7 mm, the side of the square structure is inclined at an angle of 40° to the horizontal axis, and the line thickness of each geometric shape within the unit cell is 1.5 mm.

[0008] Furthermore, the mechanical metamaterial is made of superelastic silicone material.

[0009] Furthermore, the mechanical metamaterial can be configured into at least one non-reciprocal mode, including an orthogonal and uniaxial non-reciprocal periodic metamaterial formed by connecting the unit cells in an in-plane array, or a shear non-reciprocal metamaterial obtained by rotating the orthogonal and uniaxial non-reciprocal periodic metamaterial 45 degrees around the z-axis and mapping the n×n orthogonal and uniaxial non-reciprocal metamaterial in the xy plane into a cylinder.

[0010] Furthermore, programmed control is achieved by changing the number and state of effective cuts in a unit cell through a limiter, wherein each preset cut position of each unit cell can be configured to be in an open or closed state.

[0011] A design method for a multi-mode and programmable non-reciprocal mechanical metamaterial is provided, comprising the following steps:

[0012] (1) arranging self-contact cuts for the design domain of the microstructure unit cell to be designed, wherein the self-contact cuts are geometric gaps with self-contact nonlinearity applied;

[0013] (2) applying periodic boundary condition constraints to the design domain; at the same time, dividing the design domain into a plurality of quadrilateral grids, each grid having a density variable x;

[0014] (3) Determine the interpolation function of the hyperelastic material model parameters and the density variable based on the density variable x and construct the design model;

[0015] (4) determining the target Poisson's ratio and constraint threshold of the objective function and constraint function of the design model;

[0016] (5) Gradient optimization is used to solve the target Poisson's ratio and the constraint threshold, output the optimized density variable, and construct the shape of the microstructure unit cell.

[0017] Furthermore, the design domain is a square, the layout of the self-contact cutouts in the design domain adopts a rotational symmetry principle of 180 degrees around the center of the square, and the grid size does not exceed 1 / 100 of the side length of the square.

[0018] Furthermore, the periodic boundary condition is set as follows: when the displacement of the upper left corner in the negative y-axis direction is applied, the relative displacement constraint is u 24 -u 22 =u2,u 12 =u 14 -Δu1,u 21 =u 23 and u 13 -u 11 =u1, when the displacement of the lower right corner in the negative direction of the x-axis is applied, the relative displacement constraint is u 24 -u 22 =Δu2,u 12 =u 14 ,u 21 =u 23 -Δu2,u 13 -u 11 =u1, when the upper left corner point is displaced in the positive direction of x-axis, the relative displacement constraint is u 24 =u 22 ,u 14 =u 12 +u1,u 21 =u 23 ,u 13 =u 11 , where u 11 and u 21 are the x and y displacements of the left side of the square, u 12 and u 22 are the x and y displacements of the lower side of the square, u 13 and u 23 are the x and y displacements of the right side of the square, u 14 and u 24 are the x and y displacements of the upper side of the square, and Δu1 and Δu2 are the relative displacements of the left and right sides and the upper and lower sides of the square, respectively.

[0019] Furthermore, unidirectional displacements are specified for the corner points of the square design domain to deform the square design domain. When calculating the constitutive tensors in the uniaxial and orthogonal directions, displacements in the negative y-axis and x-axis directions are applied to the upper left corner and lower right corner of the square, respectively. When calculating the constitutive tensor in the shear direction, a displacement in the x-axis direction is applied to the upper left corner. The grid size does not exceed 1 / 100 of the side length of the square.

[0020] Furthermore, in order to avoid checkerboard patterns and enhance boundary discreteness, the design variables are first filtered using a Helmholtz filter. The interpolation function of the density variable x is A″=A′+x 3 (AA′), where A is the original material parameter of the hyperelastic material model, A′ is one millionth of A, and A″ is the result after interpolation.

[0021] Furthermore, the adjoint method is used to calculate the gradients of the objective function and constraint function with respect to the density variable, and the moving asymptote method (MMA) optimization algorithm is combined to perform the optimization solution.

[0022] Furthermore, the mathematical expression of the design model is:

[0023] minimize (r(x)-r * ) 2

[0024] subject to vol(x)≤vol *

[0025] 0≤x≤1

[0026] The objective function is to minimize the square of the difference between the equivalent Poisson's ratio r(x) and the target non-reciprocal Poisson's ratio r*, and the constraint function is that the volume fraction vol(x) is not greater than the upper limit vol * , the density variable x is constrained to be in the interval [0,1].

[0027] Furthermore, the target Poisson's ratio of the objective function and the constraint function of the design model are determined respectively.

[0028] Furthermore, the target Poisson's ratio satisfies the non-reciprocal Poisson's ratio condition, that is, r 12 ×r 21 <0, more specifically, 0.0016 <r 12 <1.21,-0.45 <r 21 <0 where r 12 is the Poisson's ratio of the microstructure in the x direction, r 21 is the Poisson's ratio of the microstructure in the y direction.

[0029] Furthermore, when the density variable x=1, the corresponding mesh is a solid material, and when the density variable x=0, the corresponding mesh is a hole, thereby determining the shape of the multi-mode non-reciprocal microstructure.

[0030] In general, compared with the prior art, the multi-mode and programmable non-reciprocal mechanical metamaterial provided by the present invention has the following beneficial effects:

[0031] 1. Compared with existing reciprocal structures, the present invention breaks the symmetry of the constitutive tensor by introducing self-contact notches, achieving asymmetric stiffness tensor properties that natural materials do not possess. This material can induce directional response output, expand the application range of current metamaterial systems, and provide a new paradigm for mechanical functional metamaterials.

[0032] 2. Compared with existing non-reciprocal structures with uniaxial modes, the present invention enriches the non-reciprocal response by introducing contact nonlinearity, including uniaxial, orthogonal and shear non-reciprocity, and broadens the potential applications of non-reciprocity in soft robots, mechanical logic circuits and energy harvesters.

[0033] 3. Compared with existing technologies, the structure designed by the present invention is programmable. By introducing external constraints to reconfigure the layout of the cutouts, a reprogrammable strategy can be constructed to control the stiffness, unidirectional displacement transfer, and non-reciprocity of the metamaterial. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 A design flow chart of a multi-mode and programmable non-reciprocal mechanical metamaterial design method provided by the present invention;

[0036] Figure 2 A multi-mode and programmable non-reciprocal microstructure and unit cell structure diagram provided by the present invention, Figure 2 (a) is a single microstructure topology, Figure 2 (b) a unit cell structure with a certain thickness;

[0037] Figure 3 A schematic diagram of a corner point specified unidirectional displacement provided by the present invention, Figure 3 (a) and (b) show the displacements imposed by the orthogonal and uniaxial non-reciprocal modes. Figure 3 (c) The displacement applied in shear non-reciprocal mode;

[0038] Figure 4 The uniaxial and orthogonal non-reciprocal metamaterial obtained by the n×n unit cell array provided by the present invention, Figure 4 (a) is the front view, Figure 4 (b) is a side view;

[0039] Figure 5 This is a schematic diagram of the orthogonal non-reciprocal mode of the n×n unit cell array metamaterial provided by the present invention. Figure 5 (a) is a schematic diagram of the orthogonal non-reciprocal mode. Figure 5 (b) is the displacement change curve of orthogonal pressure loading;

[0040] Figure 6 This is a schematic diagram of the uniaxial non-reciprocal mode of the n×n unit cell array metamaterial provided by the present invention. Figure 6 (a) is a schematic diagram of the uniaxial non-reciprocal mode. Figure 6 (b) is the displacement change curve of uniaxial pressure loading;

[0041] Figure 7 The programmable unit cell structure with different numbers of cuts provided by the present invention, Figure 7 (a) is two incisions, Figure 7 (b) is an incision, Figure 7 (c) No incision;

[0042] Figure 8 Using externally constrained encoding strategies for multimodal and programmable metamaterials, Figure 8 (a) is the programming mode "0 00 0 0", Figure 8 (b) is the programming mode "1 0 0 0 0", Figure 8 (c) is the programming mode "1 1 1 0 0", Figure 8 (d) is the programming mode "1 1 1 1 1";

[0043] Figure 9 is the response of the metamaterial under different coding strategies, Figure 9 (a) is the reaction force under different longitudinal strains, Figure 9 (b) Transverse stress under different longitudinal strains;

[0044] Figure 10 Metamaterials for shear nonreciprocity testing, Figure 10 (a) is the array structure rotated 45 degrees. Figure 10 (b) is the front view of the shear non-reciprocal mode metamaterial cylindrical structure;

[0045] Figure 11 Schematic diagram of shear non-reciprocal mode of periodic array metamaterial. Figure 11(a) is a schematic diagram of the shear non-reciprocal mode. Figure 11 (b) is the angle variation curve of shear moment loading; DETAILED DESCRIPTION

[0046] In order to make the technical solutions and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the present invention.

[0047] See Figure 1-2 The present invention provides a design method for a multi-mode and programmable non-reciprocal mechanical metamaterial. First, a self-contact notch is laid out in the microstructure design domain, dividing the domain into multiple quadrilateral grids and setting a density variable x for each grid. Periodic boundary conditions are then imposed on the design domain, and displacements are specified. Based on the density variable x, an interpolation function between the hyperelastic material model parameters and the density variable is determined, thereby constructing a design model. The target Poisson's ratio and constraint threshold of the design model's objective function and constraint function are calculated using the adjoint method. The target Poisson's ratio and constraint threshold are then solved through gradient optimization, and the optimized density variable is output. Finally, the desired microstructure unit cell shape is constructed. This design method imposes relative displacement constraints on the design domain based on orthotropic anisotropy to achieve periodic boundary conditions. The introduction of self-contact notches in the design domain ensures the feasibility of achieving a non-reciprocal Poisson's ratio.

[0048] Figure 2 To pass Figure 1 Front view of a multi-mode and programmable non-reciprocal mechanical metamaterial unit cell designed by this method. Figure 2 (a) shows the initial microstructure with orthogonal and uniaxial non-reciprocal Poisson's ratio, and its Poisson's ratio is r 21 =-0.4, r 12 =1.2, and it is a linear unit cell structure with a lattice structure. The side length of the square is a = 25 mm. It mainly consists of two parts: the square in the middle and the surrounding structures to be cut with C4 rotational symmetry. The side length of the square is b = 7 mm, and the angle between the side length and the horizontal axis is 40°. Figure 2 (b) is a unit cell structure with a certain thickness of w = 1.5 mm. The upper left corner and the lower right corner are cut along the y-axis direction to produce self-contact gaps, while the upper right corner and the lower left corner are not processed.

[0049] The specific steps are:

[0050] Step 1, see Figure 2 (a) Layout of self-contact cuts for the design domain of the microstructure to be designed; wherein the design domain is a square; the self-contact cuts are geometric gaps with self-contact nonlinearity applied;

[0051] The side length range of the design domain is 1mm≤a≤100mm. In order to destroy the asymmetry of the constitutive tensor, cuts are left at the upper left corner and the lower right corner of the unit cell structure, with self-contact gaps, while the upper right corner and the lower left corner are not processed.

[0052] Step 2: applying periodic boundary condition constraints to the design domain; at the same time, dividing the design domain into a plurality of quadrilateral grids, with a grid size not exceeding 1 / 100 of the side length of a square, and setting a density variable x for each grid;

[0053] Furthermore, a unidirectional displacement is assigned to a corner point of the square design domain, so that the square design domain is deformed. The method of assigning a unidirectional displacement to a corner point is as follows: Figure 3 , when calculating the constitutive tensors in the uniaxial and orthogonal directions, displacements in the negative y-axis direction and the negative x-axis direction are applied to the upper left corner and the lower right corner of the square respectively. When calculating the constitutive tensor in the shear direction, displacement in the x-axis direction is applied to the upper left corner;

[0054] Furthermore, the periodic boundary condition is set as follows: when the displacement of the upper left corner in the negative y-axis direction is applied, the relative displacement constraint is u 24 -u 22 =u2,u 12 =u 14 -Δu1,u 21 =u 23 and u 13 -u 11 =u1. When the displacement of the lower right corner in the negative direction of the x-axis is applied, the relative displacement constraint is u 24 -u 22 =Δu2,u 12 =u 14 ,u 21 =u 23 -Δu2,u 13 -u 11 =u1, when the upper left corner point is displaced in the positive direction of x-axis, the relative displacement constraint is u 24 =u 22 ,u 14 =u 12 +u1,u 21 =u 23 ,u 13 =u 11 , where u 11 and u 21 are the x and y displacements of the left side of the square, u 12 and u 22 are the x and y displacements of the lower side of the square, u 13 and u 23 are the x and y displacements of the right side of the square, u 14 and u24 are the x and y displacements of the upper side of the square, and Δu1 and Δu2 are the relative displacements of the left and right sides and the upper and lower sides of the square, respectively.

[0055] Step 3: Determine the interpolation function of the hyperelastic material model parameters and the density variable based on the density variable x, and construct the design model;

[0056] In order to avoid checkerboard patterns and enhance boundary discreteness, the design variables are first filtered using a Helmholtz filter with the interpolation function A″=A′+x 3 (AA′), where A is the original material parameter of the hyperelastic material model, A′ is one millionth of A, and A″ is the result after interpolation.

[0057] Step 4: Set the volume objective function and Poisson's ratio constraint function;

[0058] The mathematical expression of the design model is:

[0059] minimize (r(x)-r * ) 2

[0060] subject to vol(x)≤vol *

[0061] 0≤x≤1

[0062] The objective function is to minimize the equivalent Poisson's ratio r(x) and the target non-reciprocal Poisson's ratio r * The square of the difference between the two, the constraint function is that the volume fraction vol(x) is not greater than the upper limit vol * , the density variable x is constrained to be in the interval [0,1].

[0063] Step 5: determining the target Poisson's ratio and constraint threshold of the objective function and constraint function of the design model;

[0064] Furthermore, the target Poisson's ratio satisfies the non-reciprocal Poisson's ratio condition, r 12 ×r 21 <0, r 12 =1.2, r 21 =-0.4, where r 12 is the Poisson's ratio of the microstructure in the x direction, r 21 is the Poisson's ratio of the microstructure in the y direction.

[0065] Step 6: Gradient optimization is used to solve the target Poisson's ratio and the constraint threshold, and the optimized density variable is output to construct the shape of the microstructure.

[0066] The adjoint method is used to calculate the gradients of the objective function and constraint function with respect to the density variable, and the moving asymptote method (MMA) optimization algorithm is used to perform the optimization solution.

[0067] Furthermore, when the density variable x=1, the corresponding mesh is a solid material, and when the density variable x=0, the corresponding mesh is a hole, thereby determining the shape of the multi-mode non-reciprocal microstructure.

[0068] Step 7: Periodically array the microstructures in the x and y directions to obtain n×n orthogonal and uniaxial non-reciprocal metamaterials;

[0069] See Figure 4 , Figure 4 is an n×n unit cell array metamaterial for uniaxial and orthogonal mode non-reciprocity testing, which consists of Figure 2 The unit cell structure shown in (b) is obtained by periodic arraying. Figure 4 (a) is the front view of the periodic metamaterial. Figure 4 (b) is a side view of the periodic metamaterial, with a z-direction thickness of d1 = 25 mm.

[0070] See Figure 5 , Figure 5 Schematic diagram of the orthogonal non-reciprocal modes of n×n unit cell array metamaterials. Figure 5 (a) is a schematic diagram of the orthogonal non-reciprocal mode. The same input force F is applied in the orthogonal directions (x and y axes) to obtain the displacement u in the orthogonal directions (y and x axes). right and u top .pass Figure 5 (b) The displacement curve of the loading force F shows that under the same input force F, the metamaterial has significantly different displacement responses, namely F x u right ≠F y u top The introduction of self-contact notches destroys the reciprocity of the structure and makes the structure have obvious orthogonal nonreciprocity indicators. The designed orthogonal nonreciprocal metamaterial shows unidirectional transmission of displacement field and can act as a mechanical diode.

[0071] See Figure 6 , Figure 6 Schematic diagram of the orthogonal non-reciprocal modes of n×n unit cell array metamaterials. Figure 6 (a) is a schematic diagram of the uniaxial non-reciprocal mode. Taking the x-axis as an example, equal and opposite forces F are applied in the x-axis direction to obtain the compression displacement u in the opposite direction of the x-axis. ten and stretch u com .pass Figure 6(b) The displacement versus loading force F curve shows that under the same input force F, the metamaterial has significantly different displacement responses, namely Fu ten ≠-Fu com The introduction of self-contact notches destroys the reciprocity of the structure and gives it a distinct uniaxial nonreciprocity index. The designed uniaxial nonreciprocal metamaterial shrinks longitudinally when stretched or compressed transversely, acting as a mechanical rectifier.

[0072] See Figure 7 , Figure 7 Programmable unit cell structure with different number of cuts. Figure 7 (a) is two incisions, Figure 7 (b) is an incision, Figure 7 (c) There is no cut, and the number of cuts is retained or closed by the limiter. Theoretically, a periodic structure composed of m cut programming cells has 2 m There are three states, each with a different non-reciprocity index, which greatly enriches the functionality of metamaterials.

[0073] See Figure 8 , Figure 8 The coding strategy of using limiters for multi-mode and programmable metamaterials. A typical coding strategy is selected for demonstration, taking a column of cuts as a unit (the same column of cuts can be closed or reserved at the same time), setting a column of cuts closed to "0", setting a column of cuts reserved to "1", Figure 8 (a) Programming mode "0 0 0 0 0", Figure 8 (b) Programming mode "1 0 0 00", Figure 8 (c) Programming mode "1 1 1 0 0", Figure 8 (d) Programming pattern “1 1 1 1 1”.

[0074] See Figure 9 , Figure 9 The responses of metamaterials under different coding strategies. Figure 9 (a) Figure 8 The curves of reaction force changing with longitudinal displacement under the four different coding strategies are listed. Figure 9 (b) Figure 8 The curves of lateral displacement versus longitudinal displacement under the four different encoding strategies are listed. By encoding different binary instruction sets, the metamaterial requires different levels of compression force F to achieve the same input displacement, such as Figure 9 As shown in (a), this demonstrates a reprogrammable displacement-force response. The force-displacement response for each set of binary instructions is reversible until the system is reprogrammed. Similar to the reaction force, the transmission of the displacement field is reprogrammable, as shown in Figure 9(b) is shown. When encoded with an all-zero instruction set, the longitudinal input displacement can be amplified. When all cuts are retained (coding strategy 0 0 0 0 0), the metamaterial has maximum non-reciprocity. It can be seen from this that the present invention can adjust the non-reciprocity by limiting more preset cuts by a limiter, and the non-reciprocity can be reprogrammed through different binary instruction sets. The non-reciprocal mode provides the designed metamaterial with direction-dependent stiffness, unidirectional transmission of the displacement field and a unique shear response, and the reprogrammable properties can adjust these properties, which greatly increases the engineering applicability of the metamaterial structure proposed by the present invention.

[0075] Step eight, rotate the n×n orthogonal and uniaxial non-reciprocal metamaterial 45 degrees around the z-axis, and map the n×n orthogonal and uniaxial non-reciprocal metamaterial in the xy plane into a cylinder to obtain a shear non-reciprocal metamaterial.

[0076] See Figure 10 , Figure 10 (a) Metamaterial used for shear nonreciprocity test, consisting of Figure 4 (a) Rotate the unit cell 45 degrees to obtain, Figure 10 (b) Front view of the shear non-reciprocal mode metamaterial cylinder structure. The structure shown maps the shear behavior in the plane into a cylinder to form a shear non-reciprocal mode metamaterial cylinder.

[0077] Figure 11 Schematic diagram of the shear non-reciprocal mode of periodic array metamaterial. Figure 11 (a) is a schematic diagram of the shear non-reciprocal mode. The shear behavior in the plane is mapped to a cylinder, and then the non-reciprocal shear response is converted into the rotation angle under equal torque. The shear torque T of equal magnitude and opposite direction is applied in the shear direction around the z-axis, and the torsion angle around the z-axis is obtained respectively. Figure 11 (b) The curve of angle changing with torque T shows that under the same torque T input, the metamaterial has significantly different angular responses, namely Tu ten ≠-Tu com The introduction of self-contact notches destroys the reciprocity of the structure and makes it exhibit significant shear nonreciprocity. The different shear moduli under clockwise and counterclockwise rotations enable the metamaterial to act as a rotation limiter for one-way door opening.

[0078] The working principle of the present invention is:

[0079] The present invention breaks the symmetry of the structural constitutive tensor by introducing a self-contact cut in the unit cell, so that the designed structure produces multi-mode non-reciprocal characteristics that natural materials do not have.

[0080] The self-contact notch has constitutive tensor asymmetry in different directions, resulting in significantly different output responses under the same input size in orthogonal, uniaxial and shear reverse directions.

[0081] The number of self-contact cuts can be retained or closed by a limiter. Theoretically, a periodic structure composed of m cut programming cells has 2 m The structure can be programmed by varying the number of cuts, eliminating the need for repeated design and replacement of the structure during use, further enhancing the applicability of multimodal and programmable metamaterials. This approach achieves multimodal asymmetric stiffness properties not found in natural materials, establishing a framework for describing multimodal nonreciprocal behavior using constitutive tensors, providing a new paradigm for mechanically functional metamaterials.

[0082] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-mode and programmable non-reciprocal mechanical metamaterial, characterized in that The mechanical metamaterial is formed by arraying multiple unit cells; the unit cell has a mesh lattice structure characteristic, which consists of a square structure located in the middle of the mesh lattice structure and four surrounding structures to be cut with C4 rotational symmetry; the sides of the square structure are tilted at an angle to the horizontal axis; the four surrounding structures to be cut are provided with cuts at the upper left and lower right corners, forming self-contact gaps at the cuts; the cuts can be selectively retained or closed by a limiter to achieve programmed control of the non-reciprocal properties of the mechanical metamaterial.

2. A multi-mode and programmable non-reciprocal mechanical metamaterial according to claim 1, characterized in that: The unit cell is a linear unit cell structure, the side length of the mesh grid structure feature is 25 mm, the side length of the square structure is 7 mm, the side of the square structure is inclined at an angle of 40° to the horizontal axis, and the basic unit of the structure to be cut on all sides is a fish-shaped grid composed of seven lines, of which the two long sides are the sides of the square structure, and the line thickness of each geometric shape in the unit cell is 1.5 mm.

3. The multi-mode and programmable non-reciprocal mechanical metamaterial according to claim 2, characterized in that: The mechanical metamaterial is made of superelastic silicone material.

4. A multi-mode and programmable non-reciprocal mechanical metamaterial according to any one of claims 1 to 3, characterized in that: The mechanical metamaterial can be configured into at least one non-reciprocal mode, including an orthogonal and uniaxial non-reciprocal periodic metamaterial formed by connecting the unit cells in an in-plane array, or a shear non-reciprocal metamaterial obtained by rotating the orthogonal and uniaxial non-reciprocal periodic metamaterial 45 degrees around the z-axis and mapping the n×n orthogonal and uniaxial non-reciprocal metamaterial in the xy plane into a cylinder.

5. The multi-mode and programmable non-reciprocal mechanical metamaterial according to claim 4, characterized in that: The programmed control is achieved by changing the number and state of the effective cutouts in the unit cell by the limiter, wherein each preset cutout position of each unit cell can be configured to be in an open or closed state.

6. A method for designing a multi-mode and programmable non-reciprocal mechanical metamaterial according to any one of claims 1 to 5, characterized in that: The following steps are involved: S1: Layout self-contact cuts for the design domain of the microstructure unit cell to be designed, wherein the self-contact cuts are geometric gaps with self-contact nonlinearity applied; S2: applying periodic boundary condition constraints to the design domain, and at the same time, dividing the design domain into a plurality of quadrilateral grids, where the density variable of each grid is x; S3: Determine the interpolation function of the hyperelastic material model parameters and the density variable based on the density variable x, and construct the design model; S4: Determine the target Poisson's ratio and constraint threshold of the objective function and constraint function of the design model; S5: Gradient optimization solves the target Poisson's ratio and constraint threshold, outputs the optimized density variable, and constructs the shape of the microstructure unit cell.

7. The design method of multi-mode and programmable non-reciprocal mechanical metamaterial according to claim 6, characterized in that: The design domain is a square, and the layout of the self-contact cutouts in the design domain adopts a rotational symmetry principle of 180 degrees around the center of the square. The grid size does not exceed 1 / 100 of the side length of the square.

8. The design method of multi-mode and programmable non-reciprocal mechanical metamaterial according to claim 6, characterized in that: The periodic boundary condition is set as follows: when the displacement of the upper left corner point in the negative y-axis direction is applied, the relative displacement constraint is u 24 -u 22 =u2,u 12 =u 14 -Δu1,u 21 =u 23 and u 13 -u 11 =u1, when the displacement of the lower right corner in the negative direction of the x-axis is applied, the relative displacement constraint is u 24 -u 22 =Δu2,u 12 =u 14 ,u 21 =u 23 -Δu2,u 13 -u 11 =u1, when the upper left corner point is displaced in the positive direction of x-axis, the relative displacement constraint is u 24 =u 22 ,u 14 =u 12 +u1,u 21 =u 23 ,u 13 =u 11 , where u 11 and u 21 are the x and y displacements of the left side of the square, u 12 and u 22 are the x and y displacements of the lower side of the square, u 13 and u 23 are the x and y displacements of the right side of the square, u 14 and u 24 are the x and y displacements of the upper side of the square, and Δu1 and Δu2 are the relative displacements of the left and right sides and the upper and lower sides of the square, respectively.

9. The design method of multi-mode and programmable non-reciprocal mechanical metamaterial according to claim 6, characterized in that: The interpolation function is A″=A′+x 3 (AA′), where A is the original material parameter of the hyperelastic material model, A′ is one millionth of A, and A″ is the result after interpolation.

10. The design method of multi-mode and programmable non-reciprocal mechanical metamaterial according to claim 6, characterized in that: The mathematical expression of the design model is: The objective function is to minimize the square of the difference between the equivalent Poisson's ratio r(x) and the target non-reciprocal Poisson's ratio r*, and the constraint function is that the volume fraction vol(x) is not greater than the upper limit vol * , the density variable x is constrained to be in the interval [0,1], and the target Poisson's ratio satisfies the non-reciprocal Poisson's ratio condition, that is, r 12 ×r 21 <0, where r 12 is the Poisson's ratio of the microstructure in the x direction, r 21 is the Poisson's ratio of the microstructure in the y direction.

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