A lattice-like metamaterial that achieves both negative thermal expansion and negative Poisson's ratio

Abstract

The present invention belongs to the field of mechanical metamaterials, and specifically relates to a lattice metamaterial that can achieve dual negative properties of negative thermal expansion and negative Poisson's ratio. The present invention automatically achieves thermal contraction and cold expansion of the overall geometric dimensions of the unit cell, that is, an equivalent negative thermal expansion coefficient, through the non-uniform stretching / contraction deformation of rods made of different materials when the ambient temperature changes. The present invention not only has a negative thermal expansion coefficient, but also has the mechanical properties of a special material with a negative Poisson's ratio of tensile expansion. The present invention has the geometric characteristics of a lattice, and thus has the mechanical properties of a light weight, high specific stiffness, and excellent strength. The actual material negative thermal expansion coefficient values ​​that can be obtained in the two main directions of the material of the present invention are ‑71.9ppm / ℃ and ‑11.4ppm / ℃ respectively; the actual material Poisson's ratio values ​​that can be obtained are ‑0.18 and ‑1.6. The present invention does not have a size effect, that is, the geometric dimensions of the metamaterial can still ensure the designed negative thermal expansion coefficient and negative Poisson's characteristics after being enlarged or reduced in the same proportion.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical metamaterials, and in particular relates to a lattice metamaterial that can achieve the dual negative properties of negative thermal expansion and negative Poisson's ratio. Background Art

[0002] The coefficient of thermal expansion is an important thermophysical parameter used to characterize the change in the length of a solid substance along a certain direction when the unit temperature changes. Generally, the coefficient of thermal expansion of natural solid materials is positive, so when the temperature rises (falls), the material size will increase (decrease) due to thermal expansion and contraction. In a temperature fluctuating environment, the changes in the geometric dimensions of the material induced by thermal expansion and contraction affect the performance of the engineering structure and damage the design function and accuracy of high-end industrial equipment and precision instruments. In order to solve engineering problems related to thermal expansion, it is urgent to develop specific thermal expansion materials, including negative thermal expansion materials. The purpose of manipulating the thermal expansion behavior of the structure can be achieved by artificially customizing the thermal expansion properties of the material.

[0003] Under uniaxial loading, Poisson's ratio is defined as the ratio of the strain in the material perpendicular to the load direction to the strain in the load direction. For most solid materials, including metals, polymers, and ceramics, the Poisson's ratio ranges from 0.25 to 0.35. In contrast, negative Poisson's ratio materials, due to their different Poisson's ratio values ​​from those of ordinary solid materials, possess advanced material properties, including enhanced fracture toughness and compressive strength, extremely high shear modulus, and high energy absorption.

[0004] Currently, research on single-function mechanical metamaterials that achieve both negative Poisson's ratio and negative thermal expansion is widespread, but patent applications for multifunctional metamaterials that combine these two unconventional material properties are rare. Multifunctional materials that possess both negative thermal expansion and negative Poisson's ratio can, when the operating temperature rises, compensate for the harmful thermal expansion generated by other materials within the structure through anomalous thermal contraction, thereby reducing the structural thermal strain and stress levels. Furthermore, the negative Poisson's ratio enhances the material's mechanical properties, thereby improving the structure's resistance to impact damage. Furthermore, lattice materials are widely used in structural weight reduction designs due to their high specific stiffness, strength, and low density. Dual-negative metamaterials with lattice geometries have great potential for application in a variety of fields, including aerospace, precision instruments, transportation, and biomedicine.

[0005] According to relevant literature, both thermal expansion and Poisson's ratio properties are closely related to the microstructure of periodic materials. Achieving negative thermal expansion requires the introduction of a dual-material design during the microstructure design. Since the microstructure design principles for achieving two negative material properties are compatible, it is possible to achieve both equivalent and negative material properties simultaneously through a rational dual-component material layout design, and to fabricate the new lattice material using traditional machining techniques. Summary of the Invention

[0006] This invention provides a lattice-based mechanical metamaterial with the dual negative properties of negative thermal expansion and negative Poisson's ratio. This metamaterial is achieved by arranging rods of different materials within a planar design domain to form the unique microscopic topology of the metamaterial's unit cell. To impart the lattice material with these dual negative properties, the layout of the rods within the unit cell and the selection of the materials used for each rod are carefully designed. Furthermore, to ensure the metamaterial exhibits mechanical orthotropic properties, the unit cell structure is designed to exhibit quarter-quadrant geometric symmetry.

[0007] The technical means adopted in the present invention are as follows:

[0008] A lattice-based metamaterial that achieves both negative thermal expansion and a negative Poisson's ratio is constructed from multiple unit cells. These unit cells are centrosymmetric, so a quarter-unit cell structure is introduced. The quarter-unit cell structure is symmetrical along two orthogonal directions, resulting in a complete dual-material lattice unit cell configuration.

[0009] The quarter unit cell structure is composed of 27 metal rods, and the metal rods include rods made of low thermal expansion materials and rods made of high thermal expansion materials.

[0010] The quarter-cell structure has a side length of L = X mm. Nodes are placed every L0 = X / 6 mm in both the horizontal and vertical directions, resulting in a total of 49 nodes distributed equidistantly in two orthogonal directions, arranged in a 7×7 pattern. To determine the length and position of the members within the cell using the assigned nodes, all nodes are uniformly numbered. The node numbering sequence begins with the node at the lower left corner of the quarter-cell (numbered 1), and increases vertically upward until the last node (numbered 7). After increasing one node number horizontally, the node numbering continues vertically downward until the last node (numbered 14). This numbering scheme continues to obtain all node numbers from 1 to 49.

[0011] Based on the 49 nodes and their numbers, the positions and lengths of the low thermal expansion material rod 1 and the high thermal expansion material rod 2 are determined. The following nodes are obtained by connecting the high thermal expansion material rod 2: node 2 is connected to node 9, node 5 is connected to node 17, node 17 is connected to node 25, node 15 is connected to node 29, node 29 is connected to node 31, node 25 is connected to node 31, node 37 is connected to node 39, node 33 is connected to node 39, node 33 is connected to node 41, node 39 is connected to node 46, node 41 is connected to node 48, node 43 is connected to node 45, and node 47 is connected to node 49.

[0012] The following nodes are obtained by connecting the low thermal expansion material rod 1: node 1 and node 9 are connected, node 3 and node 9 are connected, node 3 and node 5 are connected, node 1 and node 15 are connected, node 9 and node 23 are connected, node 17 and node 21 are connected, node 15 and node 23 are connected, node 23 and node 25 are connected, node 23 and node 29 are connected, node 23 and node 31 are connected, node 31 and node 37 are connected, node 37 and node 45 are connected, and node 33 and node 47 are connected.

[0013] The in-plane geometric dimensions of the square unit cell of the double-negative lattice metamaterial are 200mm×200mm and the thickness is 5mm.

[0014] The cross-section of each metal rod is rectangular, with a height of 5 mm and a width of 1 mm.

[0015] Among the 27 metal rods, 13 are made of high thermal expansion material and 14 are made of low thermal expansion material.

[0016] The high thermal expansion material rod (2) is aluminum alloy Al 7075-T6, whose theoretical thermal expansion coefficient value is 22.5 ppm / °C; the low thermal expansion material rod (1) is Invar, whose theoretical thermal expansion coefficient value is 1.0 ppm / °C.

[0017] When preparing a unit cell structure, the connection between rods of the same material can be achieved by welding or integrated molding; the connection between heterogeneous rods requires cutting a groove at the connection point using wire cutting technology, and then assembling the rods with an interference fit.

[0018] When the ambient temperature of a bimaterial unit cell rises, the disparate thermal expansion coefficients of the heterogeneous rods cause uncoordinated axial thermal expansion and deformation, triggering a thermal stretching control mechanism. This mechanism causes the rods within the unit cell to fold inward, filling the voids within the cell. This process causes the unit cell to contract inward, compensating for the thermal expansion of the rods themselves. Consequently, the material's equivalent thermal expansion coefficient, represented by the overall in-plane dimensions of the unit cell, is calculated to be negative.

[0019] When the ambient temperature drops, the thermal stretching mechanism is triggered, causing the unit cell to expand outward, thereby compensating for the contraction of the rod material itself when it cools down. At this point, the unit cell will exhibit the anomalous thermophysical property of thermal contraction and expansion when the ambient temperature changes.

[0020] When a lattice unit cell is subjected to a horizontal tensile load alone, it exhibits anomalous expansion in the vertical direction. In this case, the unit cell exhibits a material mechanical property with a negative Poisson's ratio.

[0021] The present invention has the following advantages:

[0022] The present invention automatically realizes the thermal contraction and cold expansion of the overall geometric dimensions of the unit cell, i.e., an equivalent negative thermal expansion coefficient, through the non-uniform stretching / contracting deformation of rods made of different materials when the ambient temperature changes.

[0023] The invention has a negative thermal expansion coefficient and also has the mechanical properties of a special material with a negative Poisson's ratio of tensile expansion.

[0024] The present invention has the geometric characteristics of a lattice, and thus has the material mechanical properties of light weight, high specific stiffness and excellent strength.

[0025] The actual negative thermal expansion coefficient values ​​of the material that can be obtained in the two main directions of the material are -71.9 ppm / °C and -11.4 ppm / °C respectively; the actual Poisson's ratio values ​​of the material that can be obtained are -0.18 and -1.6.

[0026] The present invention has no size effect, that is, the designed negative thermal expansion coefficient and negative Poisson's characteristics can still be guaranteed after the geometric size of the metamaterial is enlarged or reduced in the same proportion.

[0027] The rods within the unit cell of the present invention can be cut from homogeneous metal sheets using wire cutting or laser cutting techniques. Heterogeneous rods can be connected by cutting slots at the joints to facilitate assembly between rods of different materials. Furthermore, the designed lattice metamaterial can also be printed using advanced dual-material additive manufacturing techniques.

[0028] Based on the above reasons, the present invention can be widely promoted in fields such as metamaterial design. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the structure of the double-negative property lattice metamaterial and its square unit cell of negative thermal expansion and negative Poisson's ratio in a specific embodiment of the present invention.

[0030] Figure 2 Schematic diagram of node sets and member cross sections used to determine the layout of unit cell members in a specific embodiment of the present invention.

[0031] Figure 3 The two types of rods made of different materials in 1 / 4 unit cell are specifically numbered in the specific embodiment of the present invention.

[0032] Figure 4 This is a thermal deformation diagram of the double-negative property lattice metamaterial of negative thermal expansion and negative Poisson's ratio along two main directions of the material under the action of temperature load in a specific embodiment of the present invention.

[0033] Figure 5 1 is a strain diagram of the lattice metamaterial with double negative properties of negative thermal expansion and negative Poisson's ratio in a specific embodiment of the present invention when a unit positive strain is loaded on the X-axis, and a strain diagram along the X-axis when a unit positive strain is loaded on the Y-axis.

[0034] In the figure: 1 low thermal expansion material rod; 2 high thermal expansion material rod. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0036] Figure 1 Shown is a lattice metamaterial that can achieve the dual negative properties of negative thermal expansion and negative Poisson's ratio, demonstrated by an 8×4 array. Its unit cell structure is composed of low thermal expansion material rods 1 and high thermal expansion material rods 2.

[0037] like Figure 1 As shown, the material of the dotted line rods in the unit cell structure is Invar steel, and the material of the solid line rods is aluminum alloy Al 7075-T6.

[0038] Figure 1 The lattice unit cell structure shown is composed of 162 metal rods. The length and position of each rod are determined by Figure 2 The set of nodes in is determined.

[0039] Figure 2 The node set shown here determines the length and position of the members within a quarter-cell. The quarter-cell has a side length of L = 100 mm. Nodes are placed every L0 = 16.67 mm horizontally and vertically, resulting in 49 nodes within the quarter-cell.

[0040] Figure 3 The solid high thermal expansion rods within the 1 / 4 unit cell are numbered. Among them, high thermal expansion rod 1 is connected by nodes 2 and 9, rod 2 is connected by nodes 5 and 17, rod 3 is connected by nodes 17 and 25, rod 4 is connected by nodes 15 and 29, rod 5 is connected by nodes 29 and 31, rod 6 is connected by nodes 25 and 31, rod 7 is connected by nodes 37 and 39, rod 8 is connected by nodes 33 and 39, rod 9 is connected by nodes 33 and 41, rod 10 is connected by nodes 39 and 46, rod 11 is connected by nodes 41 and 48, rod 12 is connected by nodes 43 and 45, and rod 13 is connected by nodes 47 and 49.

[0041] Figure 3The dashed low thermal expansion members within the 1 / 4 unit cell are numbered. Among them, low thermal expansion member 1 is connected by node 1 and node 9, member 2 is connected by node 3 and node 9, member 3 is connected by node 3 and node 5, member 4 is connected by node 1 and node 15, member 5 is connected by node 9 and node 23, member 6 is connected by node 17 and node 21, member 7 is connected by node 15 and node 23, member 8 is connected by node 23 and node 25, member 9 is connected by node 23 and node 29, member 10 is connected by node 23 and node 31, member 11 is connected by node 31 and node 37, member 12 is connected by node 37 and node 45, member 13 is connected by node 33 and node 47, and member 14 is connected by node 33 and node 47.

[0042] Figure 4 Shown are the thermal deformation diagrams of the negative thermal expansion and negative Poisson's ratio double negative lattice metamaterial unit cell under the action of temperature load T=100℃ along the X-axis direction (left) and the Y-axis direction (right). The thermal deformation diagram is obtained by establishing a finite element model of the unit cell structure based on the beam element BEAM188 in the commercial finite element software ANSYS. After applying the ambient temperature load, the displacement degrees of freedom of the corresponding nodes of the two sets of opposite sides of the unit cell are coupled to facilitate the calculation of the equivalent thermal expansion coefficient of the unit cell. The calculation method of the thermal expansion coefficient α is α=ε T / T. Where ε T is the thermal strain of the unit cell, and its value can be obtained by measuring the relative thermal displacement u of the corresponding nodes on the opposite side of the unit cell. T Calculated with the total length of the unit cell 2L, that is, ε T =u T / 2L. Finite element analysis revealed a thermal strain of -7.19 along the X-axis for the unit cell, corresponding to an equivalent thermal expansion coefficient of -71.9 ppm / °C. This demonstrates the realization of negative thermal expansion along the X-axis for the unit cell.

[0043] Similarly, the thermal strain value of the unit cell along the Y-axis is obtained to be -1.14, which corresponds to an equivalent thermal expansion coefficient of -11.4ppm / °C. This proves the realization of the negative thermal expansion property of the unit cell along the Y-axis.

[0044] Figure 5 The figure shows the deformation diagram of the unit cell along the Y axis (left) and the deformation diagram of the unit cell along the X axis (right) obtained after applying a displacement load in the X axis direction of the double negative lattice metamaterial with negative thermal expansion and negative Poisson's ratio. The deformation diagram is obtained by establishing a finite element model of the unit cell structure based on the beam element BEAM188 in the commercial finite element software ANSYS. When the equivalent effect is changed to ε X = 0.1, and then perform the Y-axis degree of freedom coupling operation on the nodes at the boundary of the unit cell along the Y-axis to calculate the unit cell Poisson's ratio. The calculation method of the unit cell Poisson's ratio is v XY= -ε Y / ε X Among them, ε Y The value can be obtained by measuring the relative displacement u of the nodes at the boundary of the unit cell along the Y axis Y Calculated with the total length of the unit cell 2L, that is, ε Y =u Y / 2L. The finite element analysis shows that the strain value of the unit cell in the Y-axis direction is -0.0186, and the corresponding Poisson's ratio is -0.186. This proves that the Poisson's ratio of the unit cell v XY is a negative value.

[0045] Similarly, the equivalent effect is obtained when the Y = 0.1 in the Y-axis direction, the strain value of the unit cell along the X-axis is measured to be -0.164, and the corresponding Poisson's ratio is -1.64. This proves that the Poisson's ratio of the unit cell v YX Both are negative values.

[0046] 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 lattice metamaterial that can achieve the dual negative properties of negative thermal expansion and negative Poisson's ratio, characterized in that: It is composed of a combination of multiple unit cell structures. The unit cell structure is a centrosymmetric structure. Therefore, the construction of a quarter unit cell structure is introduced. After the quarter unit cell structure is symmetrical along two orthogonal directions, the complete configuration of the dual-material lattice unit cell structure is obtained. The quarter-unit cell structure is composed of 27 metal rods, and the metal rods include two types of low thermal expansion material rods (1) and high thermal expansion material rods (2); The side length of a quarter-cell structure is L = X mm. A node is arranged every L0 = X / 6 mm in both the horizontal and vertical directions, i.e., the quarter-cell structure has 49 nodes distributed equidistantly in two orthogonal directions at 7 × 7 intervals. To determine the length and position of the rods within the cell using the arranged nodes, all nodes are uniformly numbered. The node numbering sequence is as follows: the node at the lower left corner of the quarter-cell is the starting node (numbered 1), and the node numbers increase vertically upward until the last node (numbered 7). After increasing the node number horizontally, the node numbers increase vertically upward until the last node (numbered 14). All node numbers from 1 to 49 are obtained using the above numbering method. Based on 49 nodes and their numbers, the positions and lengths of the low thermal expansion material rod (1) and the high thermal expansion material rod (2) are determined; wherein the high thermal expansion material rod (2) is obtained by connecting the following nodes: node 2 is connected to node 9, node 5 is connected to node 17, node 17 is connected to node 25, node 15 is connected to node 29, node 29 is connected to node 31, node 25 is connected to node 31, node 37 is connected to node 39, node 33 is connected to node 39, node 33 is connected to node 41, node 39 is connected to node 46, node 41 is connected to node 48, node 43 is connected to node 45, and node 47 is connected to node 49; The low thermal expansion material rod (1) is obtained by connecting the following nodes: node 1 is connected to node 9, node 3 is connected to node 9, node 3 is connected to node 5, node 1 is connected to node 15, node 9 is connected to node 23, node 17 is connected to node 21, node 15 is connected to node 23, node 23 is connected to node 25, node 23 is connected to node 29, node 23 is connected to node 31, node 31 is connected to node 37, node 37 is connected to node 45, and node 33 is connected to node 47.

2. The lattice metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio double negative properties as claimed in claim 1, characterized in that: The cross-section of the metal rods is rectangular, with a height of 5 mm and a width of 1 mm.

3. A lattice metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio double negative properties as claimed in claim 1 or 2, characterized in that: The high thermal expansion material rod (2) is aluminum alloy Al 7075-T6, whose theoretical thermal expansion coefficient is 22.5 ppm / °C; the low thermal expansion material rod (1) is Invar, whose theoretical thermal expansion coefficient is 1.0 ppm / °C.

4. A lattice metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio double negative properties as claimed in claim 1 or 2, characterized in that: When the metal rods are used to prepare the unit cell structure, the connection between the rods of the same material is achieved by welding or integrated molding; The connection of heterogeneous rods requires cutting out slots at the connection points using wire cutting technology, and then assembling the rods with an interference fit.

5. The lattice metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio double negative properties as claimed in claim 3, characterized in that: When the metal rods are used to prepare the unit cell structure, the connection between the rods of the same material is achieved by welding or integrated molding; The connection of heterogeneous rods requires cutting out slots at the connection points using wire cutting technology, and then assembling the rods with an interference fit.

6. A lattice-based metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio double negative properties as claimed in claim 1, 2 or 5, characterized in that: The geometric dimensions of the square unit cell surface of the unit cell structure are 200 mm×200 mm, and the thickness is 5 mm.

7. The lattice metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio double negative properties as claimed in claim 3, characterized in that: The geometric dimensions of the square unit cell surface of the unit cell structure are 200 mm×200 mm, and the thickness is 5 mm.

8. The lattice metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio double negative properties as claimed in claim 4, characterized in that: The geometric dimensions of the square unit cell surface of the unit cell structure are 200 mm×200 mm, and the thickness is 5 mm.

9. The lattice metamaterial capable of achieving both negative thermal expansion and negative Poisson's ratio according to claim 1, 2, 5, 7 or 8, characterized in that: When subjected to a horizontal tensile load alone, the lattice unit cell structure exhibits anomalous expansion behavior in the vertical load direction; at this time, the unit cell will exhibit material mechanical properties with a negative Poisson's ratio.

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