CN113772616A - Multi-level micro-nano mechanical structure for enhancing damage resistance of functional surface - Google Patents

Multi-level micro-nano mechanical structure for enhancing damage resistance of functional surface Download PDF

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CN113772616A
CN113772616A CN202110965746.6A CN202110965746A CN113772616A CN 113772616 A CN113772616 A CN 113772616A CN 202110965746 A CN202110965746 A CN 202110965746A CN 113772616 A CN113772616 A CN 113772616A
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mechanical
functional layer
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CN113772616B (en
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牛东
刘红忠
张明星
彭海
李大超
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Xian Jiaotong University
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    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B3/00Devices comprising flexible or deformable elements, e.g. comprising elastic tongues or membranes
    • B81B3/0018Structures acting upon the moving or flexible element for transforming energy into mechanical movement or vice versa, i.e. actuators, sensors, generators
    • B81B3/0027Structures for transforming mechanical energy, e.g. potential energy of a spring into translation, sound into translation
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B3/00Devices comprising flexible or deformable elements, e.g. comprising elastic tongues or membranes
    • B81B3/0062Devices moving in two or more dimensions, i.e. having special features which allow movement in more than one dimension
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B3/00Devices comprising flexible or deformable elements, e.g. comprising elastic tongues or membranes
    • B81B3/0064Constitution or structural means for improving or controlling the physical properties of a device
    • B81B3/0067Mechanical properties
    • B81B3/0072For controlling internal stress or strain in moving or flexible elements, e.g. stress compensating layers
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B5/00Devices comprising elements which are movable in relation to each other, e.g. comprising slidable or rotatable elements
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B82NANOTECHNOLOGY
    • B82YSPECIFIC USES OR APPLICATIONS OF NANOSTRUCTURES; MEASUREMENT OR ANALYSIS OF NANOSTRUCTURES; MANUFACTURE OR TREATMENT OF NANOSTRUCTURES
    • B82Y40/00Manufacture or treatment of nanostructures
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B2203/00Basic microelectromechanical structures
    • B81B2203/01Suspended structures, i.e. structures allowing a movement
    • B81B2203/019Suspended structures, i.e. structures allowing a movement characterized by their profile
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B2203/00Basic microelectromechanical structures
    • B81B2203/06Devices comprising elements which are movable in relation to each other, e.g. slidable or rotatable
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B2207/00Microstructural systems or auxiliary parts thereof
    • B81B2207/05Arrays
    • B81B2207/053Arrays of movable structures
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B81MICROSTRUCTURAL TECHNOLOGY
    • B81BMICROSTRUCTURAL DEVICES OR SYSTEMS, e.g. MICROMECHANICAL DEVICES
    • B81B2207/00Microstructural systems or auxiliary parts thereof
    • B81B2207/07Interconnects

Abstract

A multi-level micro-nano mechanical structure for enhancing the damage resistance of a functional surface comprises a micro-nano composite structure functional layer, an interconnection network structure functional layer and a mechanical artificial structure functional layer which are connected; the micro-nano composite structure functional layer is a micro-column array structure which plays a surface function, the interconnection network structure functional layer is a hard phase and soft phase interconnection structure, hard phases are connected by soft phase materials to form an unstable parallelogram, and the unstable parallelogram spontaneously rotates or reconstructs under the action of plane stress at the tail end of a micro-column, so that the apparent numerical value of the stress and the strain at the tail end of the micro-column is reduced; the mechanical artificial structure functional layer is an array structure composed of artificial lattices with reconfigurable mechanical properties, and through time-space domain reconstruction of the artificial lattices, a stress transmission path and strain energy density are optimized, and stress concentration of a functional surface is reduced; the invention introduces a dynamic structure, improves the damage tolerance of the surface functional layer, improves the service cycle of the functional surface and ensures the performance of the functional surface.

Description

Multi-level micro-nano mechanical structure for enhancing damage resistance of functional surface
Technical Field
The invention belongs to the technical field of micro-nano structure functional surfaces, and particularly relates to a multi-level micro-nano mechanical structure for enhancing the damage resistance of a functional surface.
Background
The micro-nano scale structure is constructed on the surface of the material, so that the surface function of the material is improved, the interface state of the material is regulated, and a functional surface which meets different requirements is formed, for example, the material has the characteristics of ice resistance, super hydrophobicity, light trapping and the like, and the micro-nano scale structure has wide application prospects in the fields of aerospace, automobiles, microelectronics, new energy sources and the like.
However, in the service process, under the action of external loads, such as particle abrasion, dropping impact, fluid shearing and the like, the mechanical properties and structural characteristics of the structure are limited, and the functional surface can show a local over-high stress or strain state, so that local over-high pressure and stress concentration are caused, and mechanical failures such as collapse, fracture and the like of the structure are caused. Taking an aircraft skin surface functional layer capable of realizing ice prevention/removal as an example, when an aircraft runs at a high speed, a skin surface micro-nano structure bears higher impact load and concentrated stress under high-speed impact of dust, gravel, rain, snow and the like, and a local structure can cause surface mechanical damage such as structural fracture and the like.
At present, to the damage-tolerant problem of functional surface, domestic and foreign main research focuses on reinforcing and optimizing the static attribute of material and structure, mainly include through promoting the mechanical attribute promotion and the structure collaborative optimization of micro-nano structure material, along with the improvement of damage-tolerant requirement, the requirement of reinforcing technique to material and structure based on static state only can be more and more strict, the research and development degree of difficulty also can be bigger and bigger, it still involves few people to improve the damage-tolerant still of functional surface through dynamic change attribute, through introducing the dynamic attribute of material and structure, can further expand the space of functional surface damage-tolerant design.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a multi-level micro-nano mechanical structure for enhancing the damage resistance of a functional surface, which improves the stress transmission, distribution and homogenization effects of the functional surface under the action of external load by introducing a dynamic structure and utilizing the time variation of the geometric characteristics and the mechanical properties of the structure, improves the damage resistance tolerance of a surface functional layer, improves the service cycle of the functional surface and ensures the performance of the functional surface.
In order to achieve the purpose, the invention adopts the technical scheme that:
a multi-level micro-nano mechanical structure for enhancing the damage resistance of a functional surface comprises a micro-nano composite structure functional layer 1, an interconnection network structure functional layer 2 and a mechanical artificial structure functional layer 3 which are connected together;
the functional layer 1 of the micro-nano composite structure is a micro-column array structure which plays a role in surface, and is used for realizing a required surface function and realizing material surface modification;
the interconnected network structure functional layer 2 is an interconnected structure of a hard phase 6 and a soft phase 7 and is used for connecting the micro-nano composite structure functional layer 1 and the mechanical artificial structure functional layer 3, the hard phases 6 are connected by the soft phase 7 to form an unstable parallelogram, and the unstable parallelogram spontaneously rotates or reconstructs under the action of plane stress at the tail end of the microcolumn 4, so that the load bearing area is increased, and the apparent numerical value of the stress and the strain at the tail end of the microcolumn 4 is reduced;
the mechanical artificial structure functional layer 3 is an array structure composed of artificial lattices with reconfigurable mechanical properties, and through time-space domain reconstruction of the artificial lattices, a stress transmission path and strain energy density are optimized, and stress concentration of a functional surface is reduced.
The artificial lattice with reconfigurable mechanical properties can change stress/strain curves and strain energy density, and the mechanical artificial structure functional layer 3 realizes the improvement of the mechanical properties of local regions through the reconfiguration of the mechanical properties of local artificial lattices, reduces local stress concentration and improves the damage resistance.
When external local load acts on the micro-nano composite structure functional layer 1, the borne micro-column 4 can transmit the terminal plane stress downwards to the interconnected network structure functional layer 2, and the lower end bearing area is increased and the apparent stress is reduced through the relative rotation effect of the hard phase 6 and the soft phase 7 structure of the interconnected network structure functional layer 2; then, in the process of continuously transferring the stress downwards, the mechanical artificial structure functional layer 3 improves or changes the mechanical property of a local area by reconstructing the property of the artificial crystal lattice, and adjusts the path and the spatial distribution effect of the stress transfer, so that the damage resistance of the area is improved.
The structure form of the micro-column 4 of the micro-nano composite structure functional layer 1 comprises a cylinder, a prism and a cone.
Functional nano particles 5 are unevenly distributed in the micro-column 4, the nano particles 5 comprise zero-dimensional quantum dots, one-dimensional nano wires, two-dimensional nano sheets and the like, and the mechanical properties of all areas of the micro-column 4 are uneven due to different distribution modes, so that the micro-column 4 is changed in different forms under the action of an external load, the form change comprises bending, rotation and torsion, and the fracture resistance of the micro-column 4 array is improved.
The micro-column 4 is in submicron or micron size.
The planar shapes of the hard phase 6 and the soft phase 7 in the functional layer 2 of the interconnected network structure comprise a rectangle, a square, an ellipse and a triangle.
The sizes of the hard phase 6 and the soft phase 7 in the functional layer 2 of the interconnected network structure are in submicron or micron level.
The artificial lattice with the reconfigurable mechanical property is an artificial lattice with double/multistable mechanical characteristics, and the artificial lattice with the double/multistable mechanical characteristics can be subjected to mechanical state transformation under the action of a load, so that the change of the elastic modulus and the strain energy density is realized.
The artificial lattice with bi/multistable mechanical characteristics comprises a frame and a beam structure, wherein the frame comprises a body center structure, a hexahedron, a hexagonal prism and a tetrahedron, the beam structure comprises a cosine beam, an oblique beam and a double beam, and the distribution forms of the beam structure comprise a triangle, a cross and a sphere-like surface.
The change of the mechanical property of the artificial crystal lattice with the bi/multistable mechanical characteristics comes from an external load or an external physical field, the mechanical property of the artificial crystal lattice promotes the stable transformation of the crystal lattice through the external load, or an acting force is applied through the external physical field to actively drive the crystal lattice to be transformed, and the external physical field comprises a magnetic field and an electric field.
The artificial lattice array with bi/multistable mechanical characteristics is a uniform array of lattices with the same mechanical property or a non-uniform array of a plurality of lattices.
The effective gains of the present invention are: under the action of an external load, the micro-column array acting with the external load drives the hard phase and the soft phase in the functional layer of the interconnection network structure to rotate through the plane stress at the tail end, so that the bearing area is increased, and the magnitude of the stress transmitted from the surface is reduced; then, when the surface stress is transmitted to the mechanical artificial structure functional layer through the interconnection network structure functional layer, the reconstruction of the artificial lattice mechanical property can be driven to occur under the action of the load or the external physical field, the distribution range of the stress is expanded, and the stress is reduced.
According to the invention, the stress distribution, transmission and homogenization effects are improved through the dynamic change of the structure, the local damage and instability of the surface of the traditional micro-nano composite structure easily caused by stress concentration are promoted, a new design and manufacturing thought is provided for the design of the functional surface of the micro-nano structure, the damage tolerance of the functional surface is favorably improved, and the micro-nano composite structure is suitable for the research and development of the damage-resistant functional surface of an anti-icing/electronic stealth skin of an aircraft, the self-cleaning surface of a solar cell panel and the drag reduction structure of an underwater vehicle.
Drawings
Fig. 1 is a schematic structural diagram of embodiment 1 of the present invention.
Fig. 2 is a schematic view of a mechanical artificial structure functional layer in embodiment 1 of the present invention.
Fig. 3 is a schematic diagram of a morphological change of a functional layer of a micro-nano composite structure in embodiment 1 of the present invention.
Fig. 4 is a schematic diagram of the rotation of the hard phase and the soft phase of the functional layers of the interconnection network structure in embodiment 1 of the present invention.
FIG. 5 is a schematic view of a first artificial lattice in example 1 of the present invention; wherein, the diagram (a) is the diagram before the first artificial lattice is not changed, and the diagram (b) is the diagram after the first artificial lattice is changed.
Fig. 6 is a schematic structural diagram of embodiment 2 of the present invention.
Fig. 7 is a schematic view of a mechanical artificial structure functional layer in embodiment 2 of the present invention.
FIG. 8 is a schematic view of a second artificial lattice in example 2 of the present invention; wherein, the diagram (a) is the diagram before the second artificial lattice is not changed, and the diagram (b) is the diagram after the second artificial lattice is changed.
Fig. 9 is a schematic diagram illustrating a change of the active artificial lattice under the driving of an external field in embodiment 3 of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and examples.
Embodiment 1, referring to fig. 1, a multi-level micro-nano mechanical structure for enhancing the damage resistance of a functional surface comprises a micro-nano composite structure functional layer 1, an interconnection network structure functional layer 2 and a mechanical artificial structure functional layer 3 which are sequentially connected together;
referring to fig. 2, the micro-nano composite structure functional layer 1 is a micro-column array structure which exerts a surface function; in order to realize a certain surface function, a specific micro-column 4 array needs to be designed on the surface, the micro-column 4 array is a micro-column uniform array, and the diameter of the micro-column is 0.5-50 μm;
referring to fig. 3, the asymmetric portions of the nanoparticles 5 are distributed on the upper and lower sides of the microcolumn 4 by the nanoparticle bulk phase distribution technique, so that the bottom concentration is high, and under the action of an external load, the microcolumn 4 can be subjected to bending deformation and form change, so as to change the internal stress state, thereby avoiding the occurrence of fracture due to overlarge stress of the single microcolumn 4, wherein the form of the nanoparticles 5 includes zero dimension, one dimension, and two dimensions, such as: magnetic nano iron oxide particles, magnetic iron sulfide nanowires, magnetic graphene and the like.
Referring to fig. 4, the interconnected network structure functional layer 2 is an interconnected structure of a hard phase 6 and a soft phase 7, and is used for connecting the micro-nano composite structure functional layer 1 and the mechanical artificial structure functional layer 3, the hard phases 6 are connected to form an unstable parallelogram, and the unstable parallelogram rotates under the action of plane stress at the tail end of the microcolumn 4, so that the loaded area is increased, and the tail end stress of the microcolumn 4 is reduced.
Considering the matching relationship between the microcolumns 4 and the interconnection network structure functional layer 2, the characteristic size of the hard phase 6 of the interconnection network structure functional layer 2 is about 500 μm, in the embodiment, the planar shape of the hard phase 6 is rectangular, and the shape of the soft phase 7 is parallelogram; the microcolumns 4 are terminated to a hard phase 6 interconnecting the functional layers 2 of the network structure.
Referring to fig. 1 and 5, the mechanical artificial structure functional layer 3 is an array structure composed of a first artificial lattice 8 with a reconfigurable mechanical property, the first artificial lattice 8 is composed of a body center structure frame and a cross cosine beam, the first artificial lattice 8 can be structurally transformed under the action of external force, when a load exceeds a threshold value of a steady-state structure, the first artificial lattice 8 is transformed, at the moment, the cosine beam supports against the lower end to support, so that the elastic modulus of the first artificial lattice 8 is increased, the strain energy density is increased, and the mechanical property of the bearing unit is improved.
The mechanical artificial structure functional layer 3 is composed of uniform first artificial lattices 8, and under the action of local high stress load of the interconnected network structure functional layer 2, when stress exceeds a threshold value, the structure of the first artificial lattices 8 is subjected to stable state transformation, and local mechanical properties of the first artificial lattices 8 are changed, so that bearing capacity is more dispersed to non-bearing units, and the structural damage resistance is further improved.
Embodiment 2, referring to fig. 6, a multi-level micro-nano mechanical structure for enhancing the damage resistance of a functional surface includes a micro-nano composite structure functional layer 1, an interconnection network structure functional layer 2, and a mechanical artificial structure functional layer 3, which are sequentially connected together;
referring to fig. 7, the micro-nano composite structure functional layer 1 is a micro-column array structure which exerts a surface function; in order to realize a certain surface function, a specific micro-column 4 array is required to be designed on the surface, the micro-column array is a micro-cylinder uniform array, and the diameter of the micro-cylinder is 0.5-100 mu m;
magnetic nano particles 5 are asymmetrically distributed on the upper side and the lower side of the micro-column 4 through a nano particle bulk phase distribution technology, so that the concentration of the bottom is high, the micro-column 4 can be bent and deformed under the action of an external load, the shape is changed, the internal stress state is changed, and the phenomenon that the single micro-column 4 is broken due to overlarge stress is avoided.
The interconnection network structure functional layer 2 is an interconnection structure of a hard phase 6 and a soft phase 7, is used for connecting the micro-nano composite structure functional layer 1 and the mechanical artificial structure functional layer 3, can rotate under the action of plane stress at the tail end of the microcolumn 4, so that the loaded area is increased, and the stress at the tail end of the cylinder 4 is reduced, wherein the hard phase 6 and the soft phase 7 are formed by structural distribution of nano particle bodies in uniform materials, and the structural rigidity of the plane is caused, so that the rigidity of part of the area is high, and the rigidity of part of the area is low, and the interconnection network structure of the hard phase 6 and the soft phase 7 is formed.
Considering the matching relation between the microcolumns 4 and the interconnection network structure functional layer 2, the characteristic size of a hard phase 6 of the interconnection network structure functional layer 2 is about 500 mu m, the planar shape of the hard phase 6 is rectangular, and the shape of a soft phase 7 is parallelogram; the tail end of the microcolumn 4 is connected to the hard phase 6 of the interconnection network structure functional layer 2;
referring to fig. 7 and 8, the mechanical artificial structure functional layer 3 is an array structure composed of second artificial lattices 9 with reconfigurable mechanical properties; the second artificial lattice 9 is composed of a cubic frame and a crossed cosine beam, and can be structurally transformed under the action of external force, when the load exceeds a threshold value of a stable structure, the structure of the second artificial lattice 9 is transformed, the two second artificial lattices 9 are abutted together, so that the elastic modulus of the second artificial lattice 9 is increased, the strain energy density is increased, and the mechanical property of the bearing unit is improved.
The mechanical artificial structure functional layer 3 is composed of uniform second artificial lattices 9, when stress exceeds a threshold value under the action of local high stress load of the interconnection network structure functional layer 2, the structures of the second artificial lattices 9 are subjected to stable state transformation, strain is released and the second artificial lattices 9 abut against the supporting columns of the cubic frame, and the local mechanical properties of the structures of the second artificial lattices 9 are improved, so that bearing capacity is more dispersed to low strain energy units, stress at high stress positions is reduced, and the damage resistance of the structures is further improved.
Embodiment 3, referring to fig. 9, this embodiment is an improvement on embodiment 2, and the mechanical artificial structure functional layer 3 is composed of an active artificial lattice 10, and the material of the active artificial lattice 10 includes a Shape Memory Polymer (SMP) and a responsive hydrogel, and after an external field is applied, the structure of the active artificial lattice 10 can be changed, so that the mechanical property of the active artificial lattice 10 is changed, and further, the mechanical artificial structure functional layer 3 is reconstructed.

Claims (10)

1. A multi-level micro-nano mechanical structure for enhancing the damage resistance of a functional surface is characterized in that: the micro-nano composite structure comprises a micro-nano composite structure functional layer (1), an interconnection network structure functional layer (2) and a mechanical artificial structure functional layer (3) which are connected together;
the micro-nano composite structure functional layer (1) is a micro-column array structure which plays a role in surface, and is used for realizing a required surface function and realizing material surface modification;
the interconnected network structure functional layer (2) is an interconnected structure of a hard phase (6) and a soft phase (7) and is used for connecting the micro-nano composite structure functional layer (1) and the mechanical artificial structure functional layer (3), the hard phases (6) are connected by the soft phase (7) to form an unstable parallelogram, and the unstable parallelogram spontaneously rotates or reconstructs under the action of plane stress at the tail end of the microcolumn (4), so that the load bearing area is increased, and the apparent numerical value of the stress and the strain at the tail end of the microcolumn (4) is reduced;
the mechanical artificial structure functional layer (3) is an array structure formed by artificial lattices with reconfigurable mechanical properties, and through time-space domain reconstruction of the artificial lattices, a stress transmission path and strain energy density are optimized, and stress concentration of a functional surface is reduced.
2. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 1, characterized in that: the structure form of the micro-column (4) of the micro-nano composite structure functional layer (1) comprises a cylinder, a prism and a cone.
3. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 1, characterized in that: functional nano particles (5) are unevenly distributed in the micro-column (4), the nano particles (5) comprise zero-dimensional quantum dots, one-dimensional nano wires and two-dimensional nano sheets, and different distribution modes lead to uneven mechanical properties of all areas of the micro-column (4), so that the micro-column (4) is changed in different forms under the action of an external load, the form changes include bending, rotation and torsion, and the fracture resistance of the micro-column (4) array is improved.
4. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 1, characterized in that: the size of the micro-column (4) is in submicron or micron scale.
5. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 1, characterized in that: the planar shapes of the hard phase (6) and the soft phase (7) in the interconnected network structure functional layer (2) comprise a rectangle, a square, an ellipse and a triangle.
6. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 1, characterized in that: the sizes of the hard phase (6) and the soft phase (7) in the functional layer (2) of the interconnection network structure are in submicron or micron level.
7. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 1, characterized in that: the artificial lattice with reconfigurable mechanical properties is an artificial lattice with bi/multistable mechanical characteristics, and the artificial lattice with bi/multistable mechanical characteristics can be subjected to mechanical state transformation under the action of a load, so that the change of the elastic modulus and the strain energy density is realized.
8. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 7, wherein: the artificial lattice with bi/multistable mechanical characteristics comprises a frame and a beam structure, wherein the frame comprises a body center structure, a hexahedron, a hexagonal prism and a tetrahedron, the beam structure comprises a cosine beam, an oblique beam and a double beam, and the distribution forms of the beam structure comprise a triangle, a cross and a sphere-like surface.
9. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 7, wherein: the change of the mechanical property of the artificial crystal lattice with the bi/multistable mechanical characteristics comes from an external load or an external physical field, the mechanical property of the artificial crystal lattice promotes the stable transformation of the crystal lattice through the external load, or an acting force is applied through the external physical field to actively drive the crystal lattice to be transformed, and the external physical field comprises a magnetic field and an electric field.
10. The multi-level micro-nano mechanical structure for enhancing the damage resistance of the functional surface according to claim 7, wherein: the artificial lattice array with bi/multistable mechanical characteristics is a uniform array of lattices with the same mechanical property or a non-uniform array of a plurality of lattices.
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