A programmable mechanical metamaterial structure generation method and system based on reaction-diffusion morphogenesis mechanism

Abstract

This invention provides a programmable mechanical metamaterial structure generation method and system based on a reaction-diffusion morphogenesis mechanism. By establishing a reaction-diffusion kinetic model, the structural morphology self-organizes under the coupling effect of local reaction and spatial diffusion, thereby generating structural morphologies with complex topological features and aperiodic spatial distribution characteristics. By setting spatial parameter fields such as diffusion coefficient, supply rate, and disappearance rate within the design domain, and introducing a direction control field to adjust the diffusion direction, the scale characteristics, connectivity, and anisotropy characteristics of the generated structure can be regionalized and continuously controlled. Through threshold transformation, boundary extraction, and geometric reconstruction of the morphology generation results, the generated structure can be directly converted into a two-dimensional or three-dimensional geometric model. This invention expands the design space of mechanical metamaterial structures and realizes an effective connection between structure generation and engineering design and manufacturing.

Description

Technical Field

[0001] This invention belongs to the field of structure generation design and computational mechanics technology, and in particular relates to a programmable mechanical metamaterial structure generation method and system based on reaction-diffusion morphogenesis mechanism. Background Technology

[0002] With the development of engineering structural materials, mechanical metamaterials, and additive manufacturing technologies, engineering structures with complex topologies have demonstrated significant application value in material design, structural optimization, and functional integration. For example, in the design of mechanical metamaterials, by rationally designing the geometric topology of structural units, properties such as negative Poisson's ratio, high specific strength, high energy absorption capacity, and multifunctional coupling can be achieved. Therefore, how to efficiently generate manufacturable geometric configurations with complex topologies has become an important research problem in the field of structural materials and metamaterials design.

[0003] Currently, the design methods for mechanical metamaterial structures mainly include periodic design methods based on regular unit structures, structural design methods based on topology optimization, and parametric modeling methods based on geometric construction. Among them, methods based on regular unit structures typically design periodic cells and array them to form macroscopic structures, such as honeycomb structures, truss structures, and various lattice structures. These methods have advantages such as simple design and ease of modeling, but because their structural units usually have strong periodicity and regularity, the morphological diversity and topological complexity of the generated structures are limited, making it difficult to achieve structural forms with complex spatial distribution characteristics.

[0004] Topology optimization methods optimize material distribution within a given design domain to obtain structural forms that meet specific performance indicators. While this method can generate mechanical structures to a certain extent, its computational process typically relies on large-scale finite element analysis, resulting in high computational costs. Furthermore, the optimization results often depend on initial conditions and optimization parameters, easily leading to fine-scale structures or irregular boundaries, requiring further geometric reconstruction before they can be used in engineering manufacturing. In addition, topology optimization methods are usually tailored to specific working conditions, lacking a universal mechanism for generating structural forms.

[0005] In recent years, with the development of computational modeling techniques, structure generation methods based on natural morphogenesis mechanisms have gradually attracted attention. Morphogenesis is a ubiquitous self-organizing process in nature, forming mechanical structures with self-organizing characteristics through local interactions and diffusion coupling. Among them, the reaction-diffusion model is one of the classic theoretical models describing the morphogenesis process. This model, through the coupling of local reaction dynamics and spatial diffusion processes, can spontaneously evolve from an initial homogeneous state into various spatial structural morphologies such as spots, stripes, and networks. This type of model has been extensively studied in the fields of biological morphogenesis, chemical reaction systems, and pattern formation.

[0006] Because reaction-diffusion models can generate structures with rich topological features in continuous space, they have potential applications in the design of mechanical metamaterial structures. However, existing research based on reaction-diffusion models mainly focuses on morphological evolution mechanisms or pattern generation. The generated results are usually in the form of continuous field variables or images, making it difficult to directly convert them into geometric models required for engineering structural design. Furthermore, existing methods often lack systematic control over the structure generation region, parameter space, and morphological anisotropy during the structure generation process, resulting in limited controllability and engineering applicability of the generated structures. Simultaneously, the lack of a unified conversion process between morphological simulation results and engineering-usable computer-aided design (CAD) models makes it difficult to directly apply the generated structures to engineering practices such as finite element analysis or additive manufacturing. Summary of the Invention

[0007] The purpose of this invention is to provide a programmable mechanical metamaterial structure generation method and system based on a reaction-diffusion morphogenesis mechanism, which can generate structural morphologies with complex topological features and aperiodic spatial distribution characteristics, thus expanding the design space of mechanical metamaterial structures; enabling regional and continuous control of the scale characteristics, connectivity, and anisotropy characteristics of the generated structure; and enabling the generated structure to be directly converted into a two-dimensional or three-dimensional geometric model, thereby achieving an effective connection between structure generation and engineering design and manufacturing.

[0008] To achieve the above objectives, this invention provides a method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism, comprising the following steps: Establish the design domain for structural generation based on the external boundary and internal constraints of the target structure; Define the reaction-diffusion control parameter field within the design domain and construct the directional control vector field; Based on the reaction-diffusion control parameter field and the directional control vector field, a reaction-diffusion kinetic equation based on the Gray-Scott model is constructed. Setting initial conditions for the concentration field within the design domain ; Boundary conditions are applied to the reaction-diffusion control equations, and numerical discretization is performed to obtain a stable spatial structure model. After a stable spatial structure pattern is formed, the suppressor concentration field is extracted, and a threshold function is set to convert the continuous field into a binary structure field. The binary structure field is interpolated, resampled, and its boundaries are smoothed. Then, contour extraction and two-dimensional transformation are performed to obtain a two-dimensional geometric model. The two-dimensional geometric model is converted into a three-dimensional triangular mesh model to obtain a mechanical metamaterial structure.

[0009] Preferably, a reaction-diffusion control parameter field, including a first diffusion coefficient field, is defined within the design domain. Second diffusion coefficient field Material supply rate field and the matter extinction rate field .

[0010] Preferably, a direction control vector field is constructed: ; In the formula, and They represent the vector field at... direction and The directional component.

[0011] Preferably, the reaction-diffusion kinetic equation based on the Gray–Scott model is as follows: in, and These represent the activator concentration field and the suppressor concentration field, respectively. For the material supply rate, The rate of matter extinction. For time variables, For gradient operators; When a directional control vector field exists, the diffusion operator is expressed in an anisotropic diffusion form: in, Represents the concentration field variable. Let the diffusion tensor be determined by the direction vector field. It is an anisotropic diffusion operator.

[0012] Preferably, the reaction-diffusion control equation applies boundary conditions including Dirichlet boundary conditions or periodic boundary conditions, which, according to the spatial constraint matrix, restrict the regions where structures are prohibited from forming, so that the concentration field in the corresponding regions remains zero.

[0013] Preferably, numerical discretization is performed to form a stable spatial structure pattern, including: Spatial discretization employs the finite difference method, while time propagation utilizes the explicit time integration method. ; ; in, and Let them represent the right-hand terms of the reaction-diffusion equation, respectively. For time step, Let be the activator concentration field at time t. Let be the suppressor concentration field at time t; Through continuous iterative calculations, a stable spatial structure pattern gradually evolves from the initial state.

[0014] Preferably, the suppressor concentration field is extracted after a stable spatial structure pattern is formed. As a structural description function, and through a threshold function ; The continuous field is converted into a binary structured field, where Represents a solid structure region. Indicates the void area. Preferably, the binary structure field is subjected to interpolation resampling and boundary smoothing, specifically using a Gaussian filtering method for smoothing: ; in, For Gaussian kernel function, Preferably, the reaction-diffusion kinetic model is the Gray-Scott model, or other reaction-diffusion models capable of generating spatial self-organizing structures; The reaction-diffusion control parameter field is either a constant distribution or a spatially varying function distribution.

[0015] Preferably, the direction control vector field is a globally uniform direction field or a spatially varying vector field.

[0016] A programmable mechanical metamaterial structure generation system based on a reaction-diffusion morphogenesis mechanism includes: The design domain construction module is used to establish the design domain for structural generation based on the external boundary and internal constraints of the target structure. The parameter field definition module is used to define the reaction-diffusion control parameter field within the design domain and to construct the direction control vector field. The kinetic equation construction module is used to construct reaction-diffusion kinetic equations based on the Gray-Scott model according to the reaction-diffusion control parameter field and the direction control vector field. The initial condition setting module is used to set the initial conditions of the concentration field within the design domain; The numerical solution module is used to apply boundary conditions to the reaction-diffusion kinetic equation and perform numerical discretization to form a stable spatial structure mode. The binarization conversion module is used to extract the suppressor concentration field after a stable spatial structure pattern is formed, and to set a threshold function to convert the continuous field into a binary structure field. The two-dimensional geometric model generation module is used to perform interpolation resampling and boundary smoothing on the binary structure field, followed by contour extraction and two-dimensional transformation to obtain a two-dimensional geometric model. The three-dimensional mesh model generation module is used to convert the two-dimensional geometric model into a three-dimensional triangular mesh model to obtain a mechanical metamaterial structure.

[0017] Therefore, the present invention employs the above-mentioned method and system for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism, and the technical effects are as follows: This invention enables the automatic generation of structural morphologies with complex topological features. Traditional structural design methods typically rely on regular periodic units or topology optimization processes, which limits the complexity and diversity of structural morphologies. This invention utilizes a reaction-diffusion morphogenesis mechanism, through the coupling of local reactions and spatial diffusion, to allow the system to spontaneously evolve from its initial state into spatial structural patterns with characteristic scales. This achieves the automatic generation of complex topological structures, significantly improving the efficiency of mechanical metamaterial structural design.

[0018] This invention enables controllable adjustment of structural morphology. By setting control parameters such as diffusion coefficient, supply rate, and extinction rate of spatial distribution within the design domain, and by introducing a directional control mechanism to adjust the directionality of the diffusion process, the dimensional characteristics, connectivity, and spatial distribution of the generated structure can be systematically controlled through parameter adjustment, thereby improving the flexibility and controllability of structural design.

[0019] This invention enables the direct generation of geometric structural models usable in engineering. By converting the reaction-diffusion generated structural field into a geometric boundary representation and further constructing a two-dimensional or three-dimensional structural model, the generated structure can be directly used for engineering applications such as computer-aided design, numerical analysis, and additive manufacturing. This forms an integrated process from structure generation to engineering modeling, improving the efficiency of structural design and application. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the basic process of the reaction-diffusion speciation model; Figure 2 This is a schematic diagram and example of the process for generating structures and outputting CAD models based on the reaction-diffusion morphogenesis mechanism. Figure 2 (a) is a schematic diagram of the structure generation method: Figure 2 (b) is an example of adaptive structure generation; Figure 2 (c) is an example of heterogeneous structure generation; Figure 3 A schematic diagram of typical Turing forms in nature and their corresponding reaction-diffusion generation structures; Figure 4 To generate parameters through conceptual morphology on a square plane, resulting in a rich variety of Turing structures; Figure 5 It is a controllable deformable functional heterostructure generated based on a reaction-diffusion morphogenesis mechanism; Figure 5 (a) By setting spatially distributed morphogenetic parameters during the reaction-diffusion evolution process, structural regions with different morphological characteristics are generated in the same structure, and a local magnified schematic diagram is shown. Figure 5 (b) is a schematic diagram comparing the experimental results and numerical simulation results of the sample prepared based on the generated structure under external load. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0023] Example 1 A method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism includes the following steps: S1. Establish the design domain for structure generation. Based on the external boundary and internal constraints of the target structure, construct the design domain within the two-dimensional computational region and define a spatial constraint matrix to describe the regions where structure generation is allowed and prohibited. Regions where structure generation is allowed are assigned a value of 1, and regions where structure generation is prohibited are assigned a value of 0. This spatial constraint matrix spatially restricts the subsequent morphological process.

[0024] S2. Define the reaction-diffusion control parameter field within the design domain, including the first diffusion coefficient field. Second diffusion coefficient field Material supply rate field and the matter extinction rate field .

[0025] The parameter field can be spatially uniformly distributed or spatially varying functional distribution, in order to control the structural scale, topological morphology and connectivity in different regions.

[0026] The reaction-diffusion control parameter field can be a constant distribution or a spatially varying functional distribution. Preferably, different diffusion coefficient, supply rate, or extinction rate parameter distributions can be set within the design domain to achieve regulation of structural morphology and scale characteristics in different regions.

[0027] S3. Construct a direction control vector field within the design domain as needed. ; In the formula, and They represent the vector field at... direction and The directional component.

[0028] Used to regulate the directionality of the diffusion process, enabling the structure to develop anisotropic morphological characteristics during evolution. The direction control vector field can be a globally uniform direction field or a spatially varying vector field, to regulate the directionality of the diffusion process, thereby forming a structural morphology with anisotropic characteristics.

[0029] S4, such as Figure 1 As shown, two continuous field variables are defined within the design domain. and , represent the activator concentration field and the suppressor concentration field, respectively, and a reaction-diffusion kinetic equation based on the Gray–Scott model is established: in, and These represent the activator concentration field and the suppressor concentration field, respectively. For the material supply rate, The rate of matter extinction. For time variables, For gradient operators; When a directional control vector field exists, the diffusion operator is expressed in an anisotropic diffusion form: in, Represents the concentration field variable. Let the diffusion tensor be determined by the direction vector field. It is an anisotropic diffusion operator.

[0030] The Gray-Scott model is preferred for reaction-diffusion kinetics, but other reaction-diffusion models that can generate spatial self-organizing structures, such as the Gierer-Meinhardt model, the Schnakenberg model, or other reaction-diffusion systems with activator-inhibitor mechanisms, can also be used.

[0031] S5. Set initial conditions for the concentration field within the design domain. ; The initial conditions can be uniform or non-uniform.

[0032] S6. Apply boundary conditions to the reaction-diffusion governing equations. These boundary conditions can be Dirichlet or periodic. Simultaneously, based on the spatial constraint matrix, impose restrictions on regions where structures are prohibited from forming, ensuring the concentration field within those regions remains zero.

[0033] S7. Solve the reaction-diffusion control equations numerically using discretization. Spatial discretization employs the finite difference method, while time progression uses an explicit time integration method. ; ; in, and Let them represent the right-hand terms of the reaction-diffusion equation, respectively. For time step, Let be the activator concentration field at time t. Let be the suppressor concentration field at time t; Through continuous iterative calculations, the system gradually evolves from its initial state into a stable spatial structure pattern.

[0034] S8. When the system evolves to a preset time or reaches a stable state, extract the suppressor concentration field. As a structural description function, and through a threshold function ; The continuous field is converted into a binary structured field, where Represents a solid structure region. Indicates the void area. For the threshold, As a structure description function.

[0035] S9. Interpolate and resample the binary structure field and smooth the boundaries to reduce jagged edges caused by the discrete mesh and improve geometric continuity. Gaussian filtering is preferred for smoothing. ; in, For Gaussian kernel function, S10. Extract the boundary contour of the smoothed structural field and convert the structural geometric boundary into a two-dimensional vectorized geometric representation, thereby generating a two-dimensional geometric model that can be used for computer-aided design.

[0036] S11. Depending on the application requirements, the two-dimensional structure can be stretched or copied along the thickness direction to construct a three-dimensional structural model, and a three-dimensional triangular mesh model can be generated by the isosurface extraction method.

[0037] S12. Export the generated two-dimensional or three-dimensional structural model as an engineering design file and use it for computer-aided design, finite element analysis or additive manufacturing, thereby realizing the design and manufacturing of complex structural materials or mechanical metamaterial structures.

[0038] Figure 2 This is a schematic diagram and example of the process for generating structures and outputting CAD models based on the reaction-diffusion morphogenesis mechanism. Figure 2 (a) By inputting morphological control parameters, design domain geometry and anisotropic information, the reaction-diffusion solver is used to perform evolution calculations to obtain the spatial distribution of the structure and output it as a CAD model that can be used for additive manufacturing. Figure 2 (b) To generate a structure through a reaction-diffusion evolution process under given design domain geometric constraints and diffusion anisotropy conditions, and to obtain the corresponding solid structure through additive manufacturing; Figure 2 (c) By setting a non-uniform spatial parameter distribution, different structural forms are generated in different regions, and a continuous transition interface is formed at the boundary of the regions.

[0039] Figure 3 This diagram illustrates typical Turing morphologies in nature and their corresponding reaction-diffusion generation structures. The top row shows typical Turing-characteristic structures in nature, including labyrinthine, coral-like, and porous structures; the bottom row shows the parameters generated by the reaction-diffusion model in different morphologies. Examples of corresponding structural forms generated under the given conditions.

[0040] Figure 4 To generate parameters through conceptual morphology on a square plane, a rich variety of Turing structures can be obtained.

[0041] Figure 5 It is a controllable deformable functional heterostructure generated based on a reaction-diffusion morphogenesis mechanism. Figure 5 (a) By setting spatially distributed morphogenetic parameters during the reaction-diffusion evolution process, structural regions with different morphological characteristics are generated in the same structure, including soft structure regions, transitional intermediate structure regions, and hard structure regions; a magnified view shows the continuous transition interface formed between different structural regions; Figure 5 (b) is a schematic diagram comparing the experimental results and numerical simulation results of the sample prepared based on the generated structure under external load, where the right side shows the corresponding stress distribution results. The overall structure achieves controllable deformation under lateral pressure.

[0042] Therefore, the present invention employs a programmable mechanical metamaterial structure generation method and system based on a reaction-diffusion morphogenesis mechanism, which can generate structural morphologies with complex topological features and aperiodic spatial distribution characteristics, thus expanding the design space of mechanical metamaterial structures; enabling regional and continuous control of the scale characteristics, connectivity, and anisotropy characteristics of the generated structures; and enabling the generated structures to be directly converted into two-dimensional or three-dimensional geometric models, thereby achieving effective integration between structure generation and engineering design and manufacturing.

[0043] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism, characterized in that, Includes the following steps: Establish the design domain for structural generation based on the external boundary and internal constraints of the target structure; Define the reaction-diffusion control parameter field within the design domain and construct the directional control vector field; Based on the reaction-diffusion control parameter field and the directional control vector field, a reaction-diffusion kinetic equation based on the Gray-Scott model is constructed. Setting initial conditions for the concentration field within the design domain ; Boundary conditions are applied to the reaction-diffusion control equations, and numerical discretization is performed to obtain a stable spatial structure model. After a stable spatial structure pattern is formed, the suppressor concentration field is extracted, and a threshold function is set to convert the continuous field into a binary structure field. The binary structure field is interpolated, resampled, and its boundaries are smoothed. Then, contour extraction and two-dimensional transformation are performed to obtain a two-dimensional geometric model. The two-dimensional geometric model is converted into a three-dimensional triangular mesh model to obtain a mechanical metamaterial structure.

2. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, Define the reaction-diffusion control parameter field within the design domain, including the first diffusion coefficient field. Second diffusion coefficient field Material supply rate field and the matter extinction rate field .

3. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, Constructing the direction control vector field: ； In the formula, and They represent the vector field at... direction and The directional component.

4. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, The reaction-diffusion kinetic equations based on the Gray–Scott model are as follows: in, and These represent the activator concentration field and the suppressor concentration field, respectively. For the material supply rate, The rate of matter extinction. For time variables, For gradient operators; When a directional control vector field exists, the diffusion operator is expressed in an anisotropic diffusion form: in, Represents the concentration field variable. Let the diffusion tensor be determined by the direction vector field. It is an anisotropic diffusion operator.

5. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, The reaction-diffusion control equation applies boundary conditions, including Dirichlet boundary conditions or periodic boundary conditions, which restrict the formation of structures in the region based on the spatial constraint matrix, so that the concentration field in the corresponding region remains zero.

6. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, Numerical discretization is performed to form a stable spatial structure pattern, including: Spatial discretization employs the finite difference method, while time propagation utilizes the explicit time integration method. ； ； in, and Let them represent the right-hand terms of the reaction-diffusion equation, respectively. For time step, Let be the activator concentration field at time t. Let be the suppressor concentration field at time t; Through continuous iterative calculations, a stable spatial structure pattern gradually evolves from the initial state.

7. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, After a stable spatial structure pattern is formed, the suppressor concentration field is extracted. As a structural description function, and through a threshold function ； The continuous field is converted into a binary structured field, where Represents a solid structure region. Indicates the void area. For the threshold, As a structure description function.

8. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, The reaction-diffusion kinetics model can be replaced by other reaction-diffusion models that can generate spatial self-organizing structures, or other reaction-diffusion models with activator-inhibitor mechanisms. The reaction-diffusion control parameter field is either a constant distribution or a spatially varying function distribution.

9. The method for generating programmable mechanical metamaterial structures based on a reaction-diffusion morphogenesis mechanism according to claim 1, characterized in that, The direction control vector field is either a globally uniform direction field or a spatially varying vector field.

10. A programmable mechanical metamaterial structure generation system based on a reaction-diffusion morphogenesis mechanism, characterized in that, To perform the method of claim 1, comprising: The design domain construction module is used to establish the design domain for structural generation based on the external boundary and internal constraints of the target structure. The parameter field definition module is used to define the reaction-diffusion control parameter field within the design domain and to construct the direction control vector field. The kinetic equation construction module is used to construct reaction-diffusion kinetic equations based on the Gray-Scott model according to the reaction-diffusion control parameter field and the direction control vector field. The initial condition setting module is used to set the initial conditions of the concentration field within the design domain; The numerical solution module is used to apply boundary conditions to the reaction-diffusion kinetic equation and perform numerical discretization to form a stable spatial structure mode. The binarization conversion module is used to extract the suppressor concentration field after a stable spatial structure pattern is formed, and to set a threshold function to convert the continuous field into a binary structure field. The two-dimensional geometric model generation module is used to perform interpolation resampling and boundary smoothing on the binary structure field, followed by contour extraction and two-dimensional transformation to obtain a two-dimensional geometric model. The three-dimensional mesh model generation module is used to convert the two-dimensional geometric model into a three-dimensional triangular mesh model to obtain a mechanical metamaterial structure.

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