Shell-based mechanical metamaterial design strategy based on level set function weighted combination

Abstract

The invention provides a shell-based mechanical metamaterial design strategy based on level set function weighted combination. The framework is inspired by a three-period minimal curved surface, and a shell-based mechanical metamaterial database is constructed by adopting a level set function weighted combination strategy. The effective elastic performance of the metamaterial is evaluated through the homogenization theory of voxel modeling. A back propagation neural network model is developed, and the model can realize reverse mapping between geometric parameters and material attributes of a shell base unit. In addition, the reliability of the homogenization theory is verified by adopting a quasi-static compression test, and the effective elastic characteristic and the compression response of the shell-based structure are evaluated. Research results show that the shell-based mechanical metamaterial not only shows isotropic elasticity and high rigidity exceeding the upper limit of the Hashin-Shtrikman theory, but also has significantly improved yield strength and energy absorption ability under compression. According to the design, a series of light-weight and high-rigidity-strength structures are finally formed, and 3D printing forming is conducted through the PolyJet technology.

Description

Technical field:

[0001] The present invention relates to the field of protective structure design and reverse design, and in particular to a shell-based mechanical metamaterial design strategy based on weighted combination of level set functions. Background technology:

[0002] With the rapid advancement of science and technology and the deepening of globalization, the research and development of major equipment in key areas such as national defense, aerospace, and vehicle and ship manufacturing has risen to a national strategy. These equipment need to adapt to high-speed operation, heavy loads, long-range endurance, and extreme environments, forcing performance requirements to continue to increase. In this context, lightweight, high performance, and energy efficiency have become the core orientations of industrial design and manufacturing. Traditional impact energy-absorbing structures mostly rely on material damping to dissipate energy, but this method has shortcomings in energy absorption efficiency and mechanical property regulation.

[0003] Curved surface - a special mathematical model, is widely used in the field of structural lightweight and impact resistance enhancement due to its unique geometric and mechanical properties. However, the current structural design mainly relies on experience and intuition, lacks theoretical support, and limits its development in terms of lightweight, stiffness and yield strength. In addition, the traditional homogeneous curved surface lattice structure is prone to form inclined shear bands under load, resulting in performance degradation, especially in complex or extreme environments, this limitation is more obvious.

[0004] The development and progress of 3D printing technology has made it possible to process and prepare arbitrarily complex structural models, providing a convenient way to realize the processing of porous structures with specific mesoscopic configurations. By combining different 3D printing technology principles, porous structures of different types of matrix materials and solid skeletons of different molding processes can be processed and prepared to meet the needs of specific scenarios. Summary of the invention:

[0005] The purpose of the present invention is to overcome the problems existing in existing protective structures and to provide a shell-based mechanical metamaterial design strategy based on weighted combination of level set functions.

[0006] The present invention can be implemented by the following technical solutions:

[0007] (1) Based on three-periodic minimal surfaces (TPMS), shell-based mechanical metamaterials are constructed using the weighted combination strategy of level set functions.

[0008] (2) Evaluate the effective elastic properties of mechanical metamaterials through homogenization theory based on voxel modeling.

[0009] (3) Develop a back-propagation neural network model to achieve the inverse mapping between the geometric parameters of the shell-based unit and the material properties.

[0010] (4) Design a series of shell-based mechanical metamaterials, compare and select the optimal structure, and use PolyJet technology for 3D printing.

[0011] (5) Quasi-static compression tests are used to verify the reliability of the homogenization theory and to evaluate the effective elastic properties and compression response of the proposed shell-based structure.

[0012] The beneficial effects of the present invention are:

[0013] The provided design framework is applicable to various types of protective structure products, such as the side protection structure design of ships and the structural safety design to resist extreme environments in the aerospace field.

[0014] The provided design framework develops a parameterized unit candidate library for shell-based structures, expands the design space and performance range of curved microstructures, and uses a back-propagation neural network model to significantly improve the efficiency of the design process, reduce trial-and-error costs, and make mechanical metamaterial design more efficient and economical.

[0015] The resulting series of shell-based mechanical metamaterials have the following advantages: compared with traditional structures, they achieve highly lightweight design; their deformation mode is beneficial to improving energy absorption efficiency while maintaining good structural stiffness and strength.

[0016] The resulting series of shell-based mechanical metamaterials have the following characteristics: the self-supporting structure of shell-based metamaterials reduces the need for temporary support materials during additive manufacturing, improves material utilization efficiency and simplifies the production process; the design of its internal flow channels ensures that there will be no residual material during the manufacturing process, thereby optimizing the internal quality and overall performance of the material; the unique curved surface features effectively reduce stress concentration and enhance the durability and reliability of the material when under load, and the favorable buckling deformation characteristics enhance the energy absorption capacity in the plastic stage, enabling the material to better protect the structure itself and its functions when subjected to impact or load. Description of the drawings:

[0017] In order to further clarify the process of the present invention and the features of each embodiment, a more specific description of each embodiment of the present invention will be presented with reference to the accompanying drawings. It should be understood that these drawings are only typical embodiments of the present invention and are not to be considered as limiting the scope thereof.

[0018] Figure 1 This is a shell-based mechanics metamaterial unit library constructed using a level set function weighted combination strategy according to an embodiment of the present invention.

[0019] Figure 2 This is a shell-based mechanical super-material model constructed based on voxels according to an embodiment of the present invention.

[0020] Figure 3is the Young's modulus E / E of the shell-based mechanical metamaterial unit library of the embodiment of the present invention. 0 Comparison of data points and the Hashin-Shtrikman theoretical upper limit.

[0021] Figure 4 This is a shell-based lattice structure manufactured by PolyJet additive manufacturing according to an embodiment of the present invention.

[0022] Figure 5 Schematic diagram of a universal testing machine according to an embodiment of the present invention.

[0023] Figure 6 It is the compression response of the shell-based lattice structure of the embodiment of the present invention. Specific implementation method:

[0024] In order to make the purpose and technical solution of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings. A shell-based mechanical metamaterial design strategy based on weighted combination of level set functions includes the following steps:

[0025] Step 1: Based on the three-periodic minimal surface, the shell-based mechanical metamaterial is constructed using the weighted combination strategy of the level set function;

[0026] Step 2: Evaluate the effective elastic properties of the metamaterials through the homogenization theory based on voxel modeling;

[0027] Step 3: Develop a back-propagation neural network model to achieve the inverse mapping between the geometric parameters of the shell-based unit and the material properties;

[0028] Step 4: Design and form a series of shell-based mechanical metamaterials, compare and select the optimal structure, and use PolyJet technology for 3D printing;

[0029] Step five, a quasi-static compression test is used to verify the reliability of the homogenization theory and evaluate the effective elastic properties and compression response of the proposed shell-based structure.

[0030] like Figure 1In the structural design stage, a tunable shell-based microstructure with periodicity, mirror symmetry and smooth surface is constructed based on the design strategy of weighted combination of level set functions. This periodicity allows the microstructure to be arbitrarily arranged to form a macroscopic lattice structure. The mirror symmetry helps to achieve uniform distribution of internal stress of the structure, while the smooth surface avoids stress concentration under external loads. Inspired by TPMS, the control equation f(x, y, z) is constructed using the parity characteristics of four trigonometric functions and the linear combination of functions. This equation defines the primitive surface. The primitive surface is offset by the same distance t along the two normal directions, and the space between the two offset surfaces is solidified to obtain the shell-based structure, as shown in Equation (2). The typical TPMS structure - Primitive can be given by a specific expression (3). The parameter a in the design 1 ,a 2 ,a 3 ,a 4 The weight coefficient as a function determines the specific impact on the overall surface structure.

[0031] f(x,y,z)=a 1 f 1 +a 2 f 2 +a 3 f 3 +a 4 f 4 (1)

[0032] TPMS lattice:φ solid (x,y,z)=(f(x,y,z)+t)(f(x,y,z)-t) (2)

[0033] f 1 =cos x+cos y+cos z (3)

[0034] f 2 =cos 2 x+cos 2 y+cos 2 z (4)

[0035] f 3 =cos xcosy+cos ycosz+cos zcosx (5)

[0036] f 4 =sin 2 x+sin 2 y+sin 2 z (6)

[0037] The initial shell-based surface geometry model was voxelized. This process was implemented in the MATLAB software environment, such as Figure 2 . By converting continuous geometric structures into discrete voxel arrays, the spatial distribution of microstructures can be accurately simulated and analyzed; secondly, graph theory is used to construct a connection relationship graph between voxels, and the connected component algorithm of the graph is applied to systematically identify and mark disconnected areas, accurately screening out manufacturable curved microstructures, thereby ensuring the consistency and functionality of material manufacturing and application.

[0038] Based on parameterized shell-based mechanical metamaterials and homogenization theory, a novel structure with configuration parameters (a 1 ,a 2 ,a 3 ,a 4 , t) and material properties (Young's modulus (E), Poisson's ratio (v), shear modulus (G), volume fraction (vol)).

[0039] Back Propagation Neural Network (BPNN) effectively maps material properties to the geometric parameters of shell-based mechanical metamaterials. A BPNN data set mainly consists of a training set, a validation set, and a test set. Specifically, the BPNN model includes an input layer, an output layer, and a hidden layer. 1 ,a 2 ,a 3 ,a 4 , t) as the input layer, and the material properties (Young's modulus (E), Poisson's ratio (v), shear modulus (G), volume fraction (vol)) as the target output. Based on the gradient descent error, BPNN adjusts the weights and biases of each layer starting from the output layer and returns to the input layer in turn. Once the output error is reduced to the preset acceptable value, the training process converges. The loss function used in the training process is the mean absolute error (MAE), which is expressed by formula (7), where is the predicted value, y is the true value, and n is the sample size of the test data set. BPNN is used to learn and verify a certain amount of data, and finally a prediction model is obtained.

[0040]

[0041] The candidate library of microstructure units contains high stiffness structures whose Young's modulus E / E0 is close to the upper limit of Hashin-Shtrikman theory, such as Figure 3 shown.

[0042] Figure 4 It shows a 5×5×5 shell-based lattice structure obtained from a microstructure array in the unit library, which is 3D printed using PolyJet technology, and the printing substrate is an improved resin material PC+.

[0043] Conduct quasi-static compression tests. Figure 5 Schematic diagram of the universal testing machine used.

[0044] Figure 6 The compressive response of the structure is shown. Thanks to the improved shell-based mechanical metamaterial, its load-displacement curve presents a stable plastic platform segment, which is beneficial to improving the energy absorption efficiency. In addition, corresponding to the layer-by-layer compressive deformation of the structure, no shear bands that are detrimental to the structural integrity are observed.

[0045] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A shell-based mechanical metamaterial design strategy based on weighted combination of level set functions, characterized in that: The following steps are involved: Step 1: Based on the three-periodic minimal surface, the shell-based mechanical metamaterial is constructed using the weighted combination strategy of the level set function; Step 2: Evaluate the effective elastic properties of the metamaterials through the homogenization theory based on voxel modeling; Step 3: Develop a back-propagation neural network model to achieve the inverse mapping between the geometric parameters of the shell-based unit and the material properties; Step 4: Design and form a series of shell-based mechanical metamaterials, compare and select the optimal structure, and use PolyJet technology for 3D printing; Step five, a quasi-static compression test is used to verify the reliability of the homogenization theory and evaluate the effective elastic properties and compression response of the proposed shell-based structure.

2. According to claim 1, a shell-based mechanical metamaterial design strategy based on weighted combination of level set functions is characterized in that: The lattice structure of the formed shell-based mechanical metamaterial is composed of a single-cell shell-based lattice array, including a self-supporting structure and an internal flow channel, and a lattice network model with different topological characteristics is established using MATLAB software.

3. The shell-based mechanical metamaterial design strategy based on weighted combination of level set functions according to claim 1, characterized in that: The microstructure that constitutes the shell-based mechanical metamaterial is a thin shell surface unit.

4. The shell-based mechanical metamaterial design strategy based on weighted combination of level set functions according to claim 1, characterized in that: During the 3D printing process, the size of each microstructure is controlled within 1 cm × 1 cm; the size of the overall structure is set to 5 cm × 5 cm, and a temporary support structure is set to ensure that the resin substrate can correctly form the expected shell-based lattice structure.

5. The shell-based mechanical metamaterial design strategy based on weighted combination of level set functions according to claim 1, characterized in that: Step 1 specifically includes: (1) Construct the governing equations to define the original surface; (2) offset the original surface by the same distance t along two normal directions; (3) The space between the two offset surfaces is solidified to obtain a shell-based structure.

6. The shell-based mechanical metamaterial design strategy based on weighted combination of level set functions according to claim 5, characterized in that: The control equation f(x,y,z) is: f(x,y,z)=a1f1+a2f2+a3f3+a4f4 f1=cos x+cos y+cos z f2=cos 2 x+cos 2 y+cos 2 z f3=cos xcosy+cos ycosz+cos zcosx f4=without 2 x+sin 2 and+without 2 z Among them, parameters a1, a2, a3, a4 are used as weight coefficients of the function; x, y, z are coordinates.

7. The shell-based mechanical metamaterial design strategy based on weighted combination of level set functions according to claim 6, characterized in that: Step 2 includes: (1) The surface geometric model of the shell-based structure is voxelized using MATLAB software; (2) Simulate and analyze the spatial distribution of microstructures by converting continuous geometric structures into discrete voxel arrays; (3) Use graph theory to construct a connection relationship diagram between voxels, apply the connected component algorithm of the graph to identify and mark disconnected areas, and screen out manufacturable surface microstructures, thereby ensuring the consistency and functionality of material manufacturing and application.

8. The shell-based mechanical metamaterial design strategy based on weighted combination of level set functions according to claim 7, characterized in that: Step three includes: (1) Based on parameterized shell-based mechanical metamaterials and homogenization theory, a data set containing the correspondence between configuration parameters and material properties is constructed, where the configuration parameters include a1, a2, a3, a4, t, and the material properties include Young's modulus, Poisson's ratio, shear modulus, and volume fraction; (2) A back-propagation neural network is used to map the material properties to the geometric parameters of the shell-based mechanical metamaterial.

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