A shell-based metamaterial design strategy based on weighted combination of level set functions

Abstract

The present application proposes a shell-based metamaterial design strategy based on level set function weighted combination. The framework is inspired by three-periodic minimal surfaces, and adopts a level set function weighted combination strategy to construct a shell-based metamaterial database. The effective elastic properties of the metamaterial are evaluated by the homogenization theory of voxel modeling. A backpropagation neural network model is developed, which can realize the reverse mapping between the geometric parameters and material properties of the shell-based unit. In addition, the present application verifies the reliability of the homogenization theory by using quasi-static compression tests, and evaluates the effective elastic properties and compression response of the proposed shell-based structure. The research results show that the shell-based metamaterial not only shows isotropic elasticity and high stiffness beyond the upper limit of Hashin-Shtrikman theory, but also has significant improvement in yield strength and energy absorption capacity under compression. The design finally forms a series of lightweight, high-stiffness structures, and is 3D printed by PolyJet technology.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of protective structure design and reverse design, and particularly relates to a shell-based mechanical metamaterial design strategy based on weighted combination of level set functions. BACKGROUND

[0002] With the rapid progress of technology and the deepening of globalization, the research and development of major equipment in key fields such as national defense, aerospace and shipbuilding has risen to a national strategy. These equipment need to adapt to high-speed operation, heavy load, long-range endurance and extreme environment, forcing the performance requirements to continue to improve. In this context, lightweight, high performance and energy efficiency have become the core orientation of industrial design and manufacturing. Traditional impact energy absorption structures rely on material damping to dissipate energy, but this approach has limitations in energy absorption efficiency and mechanical property regulation.

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

[0004] The development of 3D printing technology makes it possible to process and manufacture any complex structure model, providing a convenient way to realize the processing of porous structures with specific microstructure. Combined with different 3D printing technology principles, different types of base materials and different solid skeleton forming processes, porous structures can be processed and manufactured to meet specific scene requirements. SUMMARY

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

[0006] The present application can be realized by the following technical solutions:

[0007] (1) Based on three-period minimal surface (TPMS), a shell-based mechanical metamaterial is constructed using a weighted combination strategy of level set functions.

[0008] (2) The effective elastic properties of the mechanical metamaterial are evaluated based on the homogenization theory of voxel modeling.

[0009] (3) A backpropagation neural network model is developed to realize the reverse mapping between the geometric parameters and material properties of the shell-based unit.

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

[0011] (5) The reliability of the homogenization theory is verified by quasi-static compression test, and the effective elastic properties and compression response of the shell-based structure are evaluated.

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

[0013] The design framework provided is suitable for various protective structures, such as the design of protective structures for the side of a ship, and the safety design of structures resisting extreme environments in the field of aerospace.

[0014] The design framework provided develops a parameterized unit candidate library for shell-based structures, expands the design space and performance range of curved surface microstructures, significantly improves the efficiency of the design process using a backpropagation neural network model, reduces trial and error costs, and makes the design of mechanical metamaterials more efficient and economical.

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

[0016] The series of shell-based mechanical metamaterials formed have the following characteristics: the self-supporting structure of the shell-based metamaterial reduces the need for temporary support materials during additive manufacturing, improving material utilization efficiency and simplifying the production process; the design of internal flow channels ensures that there is no residual material during the manufacturing process, thereby optimizing the internal mass and overall performance of the material; the unique curved surface feature effectively reduces stress concentration, enhances the durability and reliability of the material under load, and the beneficial buckling deformation feature improves energy absorption capacity in the plastic stage, making the material better protect the structure itself and its functions when subjected to impact or load. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to further illustrate the process and features of the embodiments of the present application, more specific descriptions of the embodiments of the present application will be presented with reference to the accompanying drawings. It should be considered that these drawings only depict typical embodiments of the present application, and therefore should not be considered as limiting the scope thereof.

[0018] Figure 1 The shell-based mechanical metamaterial unit library constructed by the level set function weighting combination strategy for the embodiments of the present application.

[0019] Figure 2 The shell-based mechanical metamaterial model constructed based on voxels for the embodiments of the present application.

[0020] Figure 3A comparison chart of Young's modulus E / E0 data points of the shell-based mechanical metamaterial unit library of the embodiment of the present application and Hashin-Shtrikman theoretical upper limit.

[0021] Figure 4 A shell-based lattice structure manufactured by PolyJet additive manufacturing of the embodiment of the present application.

[0022] Figure 5 A schematic diagram of the universal testing machine of the embodiment of the present application.

[0023] Figure 6 The compression response of the shell-based lattice structure of the embodiment of the present application. DETAILED DESCRIPTION

[0024] In order to make the purpose and technical scheme of the present application clearer and more understandable, the present application will be further described in detail below in combination with the drawings. A shell-based mechanical metamaterial design strategy based on weighted combination of level set functions, comprising the following steps:

[0025] Step one, based on three-period minimal surface, using weighted combination strategy of level set function, constructing shell-based mechanical metamaterial;

[0026] Step two, evaluating the effective elastic properties of the metamaterial through homogenization theory based on voxel modeling;

[0027] Step three, developing a backpropagation neural network model to realize the reverse mapping between the geometric parameters and material properties of the shell-based unit;

[0028] Step four, designing a series of shell-based mechanical metamaterials, comparing and selecting the optimal structure to be 3D printed by PolyJet technology;

[0029] Step five, verifying the reliability of the homogenization theory by quasi-static compression test, evaluating the effective elastic properties and compression response of the proposed shell-based structure.

[0030] As Figure 1In the structural design stage, the design strategy based on the weighted combination of level set functions is used to construct the tunable shell-based microstructure with periodicity, mirror symmetry and smooth surface. This periodicity allows the microstructure to be arranged arbitrarily to form a macroscopic lattice structure, the mirror symmetry helps to achieve uniform distribution of internal stress of the structure, and the smooth surface avoids stress concentration under external load. Inspired by TPMS, the control equation f(x, y, z) is constructed by using the odd-even characteristics of four trigonometric functions and the linear combination of functions, which defines the original surface. By offsetting the original surface along two normal directions by the same distance t, the final shell-based structure is obtained by solidifying the space between the two offset surfaces, as shown in equation (2). The typical TPMS structure-Primitive can be given by a specific expression (3). The parameters a1, a2, a3, a4 in the design are the weight coefficients of the functions, which determine the specific influence on the overall surface structure.

[0031] f(x, y, z) = a1f1 + a2f2 + a3f3 + a4f4 (1)

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

[0033] f1 = cos x + cos y + cos z (3)

[0034] f2 = cos 2 x + cos 2 y + cos 2 z (4)

[0035] f3 = cos x cos y + cos y cos z + cos z cos x (5)

[0036] f4 = sin 2 x + sin 2 y + sin 2 z (6)

[0037] The initial shell-based surface geometry model is voxelized. This process is implemented in the MATLAB software environment, as shown in Figure 2 . By converting the continuous geometric structure into a discrete voxel array, the spatial distribution of the microstructure is accurately simulated and analyzed; secondly, the connection relationship graph between voxels is constructed using graph theory, and the connected component algorithm of the graph is used to systematically identify and mark the disconnected regions, accurately select the manufacturable surface microstructure, and ensure the consistency and functionality of material manufacturing and application.

[0038] Based on the parametric shell-based metamaterials and homogenization theory, a dataset containing the correspondence between the geometric parameters (a1, a2, a3, a4, t) and material properties (Young's modulus (E), Poisson's ratio (v), shear modulus (G), volume fraction (vol)) is constructed.

[0039] A back propagation neural network (BPNN) effectively maps the material properties to the geometric parameters of the shell-based metamaterials. A BPNN dataset 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, with the geometric parameters (a1, a2, a3, a4, 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, the 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 a preset acceptable value, the training process converges. The loss function used in the training process is the mean absolute error (MAE), represented by equation (7), where, is the predicted value, y is the true value, and n is the sample size of the test dataset. Using the BPNN to learn and validate a certain amount of data, the final prediction model is obtained.

[0040]

[0041] The candidate library of microstructure units contains high-stiffness structures with Young's modulus E / E0 close to the Hashin-Shtrikman theoretical upper bound, such as Figure 3

[0042] Figure 4 A 5x5x5 shell-based lattice structure obtained from an array of microstructure units in the unit library is shown, which is 3D printed by the PolyJet technology, with the improved resin material PC+ as the printing substrate.

[0043] Quasi-static compression tests are carried out, Figure 5 A schematic diagram of the universal testing machine used is shown.

[0044] Figure 6 The compression response of the structure is shown, benefiting from the improved shell-based metamaterials, the load-displacement curve presents a stable plastic plateau section, which is conducive to improving the energy absorption efficiency. In addition, corresponding to the layer-by-layer compression deformation of the structure, no shear band that is detrimental to the integrity of the structure is observed.

[0045] ​The above merely describes the preferred embodiments of the present application, and it should be pointed out that those skilled in the art can make several improvements and refinements without departing from the principles of the present application, and these improvements and refinements should also be considered as the protection scope of the present application.

Claims

1. A design strategy for shell-based mechanical metamaterials based on a weighted combination of level set functions, characterized in that, Includes the following steps: Step 1: Based on the three-period minimum surface, a shell-based mechanical metamaterial is constructed using a weighted combination strategy of level set functions; Step 2: Evaluate the effective elastic properties of metamaterials using homogenization theory based on voxel modeling; Step 3: Develop a backpropagation neural network model to achieve the inverse mapping between the geometric parameters and material properties of the shell-based unit; Step four: Design and form a series of shell-based mechanical metamaterials, compare and select the optimal structure, and then 3D print it using PolyJet technology; Step 5: Verify the reliability of the homogenization theory using quasi-static compression tests, and evaluate the effective elastic properties and compressive response of the proposed shell-based structure. Step one specifically includes: (1) Construct the following governing equation f(x,y,z) to define the original surface: f(x,y,z)=a1f1+a2f2+a3f3+a4f4 f1 = cos x + cos y + cos z f2=cos 2 x+cos 2 and+cos 2 z f3=cos xcosy+cos ycosz+cos zcosx f4=sin 2 x+sin 2 and without 2 z Where parameters a1, a2, a3, a4 serve as the weighting coefficients of the function; x, y, z are the coordinates; (2) Offset the original surface by the same distance t along the two normals respectively; (3) Solidify the space between the two offset surfaces to obtain the shell-based structure; Step two includes: (1) The surface geometric model of the shell-based structure was voxelized using MATLAB software; (2) By converting continuous geometry into discrete voxel arrays, the spatial distribution of microstructures is simulated and analyzed; (3) Use graph theory to construct a connection graph between voxels, apply the connected component algorithm of the graph to identify and mark disconnected regions, and screen out the fabricatable surface microstructures to ensure the consistency and functionality of material manufacturing and application. Step three includes: (1) Based on parameterized shell-based metamaterials and homogenization theory, a dataset containing the correspondence between configuration parameters and material properties is constructed. The configuration parameters include a1, a2, a3, a4, and t, and the material properties include Young's modulus, Poisson's ratio, shear modulus, and volume fraction. (2) The material properties are mapped onto the geometric parameters of the shell-based mechanical metamaterial using a backpropagation neural network.

2. The shell-based mechanical metamaterial design strategy based on weighted combination of level set functions according to claim 1, characterized in that, The resulting shell-based mechanical metamaterial has a lattice structure composed of a single-cell shell-based lattice array, which includes a self-supporting structure and internal flow channels. Furthermore, lattice network models with different topological characteristics were established using MATLAB software.

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

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 1cm×1cm; the size of the overall structure is set to 5cm×5cm, and a temporary support structure is set to ensure that the resin substrate can correctly form the expected shell-based lattice structure.

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