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Abstract This article presents a novel approach for generating metamaterial designs by leveraging texture information learned from stochastic microstructure samples with exceptional mechanical properties. This eXplainable Artificial Intelligence (XAI)-based approach reduces the reliance on brainstorming and trial-and-error in inspiration-driven design practices. The key research question is whether the texture information extracted from stochastic microstructure samples can be used to design metamaterials with periodic structural patterns that surpass the original stochastic microstructures in mechanical properties. The proposed approach employs a pretrained supervised neural network and applies the Activation Maximization Texture Synthesis (AMTS) method to extract representative textures from high-performance stochastic microstructure samples. These textures serve as building blocks for creating novel periodic metamaterial designs. Using three benchmark cases of stochastic microstructure-inspired periodic metamaterial design, we compare the proposed approach with an earlier XAI design approach based on Gradient-weighted Regression Activation Mapping (Grad-RAM). Unlike the proposed approach, Grad-RAM extracts local microstructure patches directly from the original sample images rather than synthesizing representative textures to generate novel periodic metamaterial designs. Both XAI-based design approaches are evaluated based on the mechanical properties of the resulting designs. The relative merits of both approaches in terms of design performance and the need for human intervention are discussed. 

Abstract This paper presents a novel approach for generating metamaterial designs by leveraging texture information learned from stochastic microstructure samples with exceptional mechanical properties. This eXplainable Artificial Intelligence (XAI)-based approach reduces the reliance of brainstorming and trial-and-error in inspiration-driven design practices. The key research question is whether the texture information extracted from stochastic microstructure samples can be used to design metamaterials with periodic structural patterns that surpass the original stochastic microstructures in mechanical properties. The proposed approach employs a pretrained supervised neural network and applies the Activation Maximization Texture Synthesis (AMTS) method to extract representative textures from high-performance stochastic microstructure samples. These textures serve as building blocks for creating novel periodic metamaterial designs. Using three benchmark cases of stochastic microstructure-inspired periodic metamaterial design, we compare the proposed approach with an earlier XAI design approach based on Gradient-weighted Regression Activation Mapping (Grad-RAM). Unlike the proposed approach, Grad-RAM extracts local microstructure patches directly from the original sample images rather than synthesizing representative textures to generate novel periodic metamaterial designs. Both XAI-based design approaches are evaluated based on the mechanical properties of the resulting designs. The relative merits of both approaches in terms of design performance and the need for human intervention are discussed. 

Abstract Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. This complete connectivity is crucial for manufacturability and structure-fluid interaction applications (e.g., fluid-filled lattices). In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units with the constraint of complete connectivity. First, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Second, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design framework is evaluated by comparing the performances of the obtained designs with those of known designs in the metamaterial database. Merits and shortcomings of the proposed framework are also discussed. 

Abstract Increasing the thickness of the electrodes is considered the primary strategy to elevate battery energy density. However, as the thickness increases, rate performance, cycling performance, and mechanical stability are affected due to the sluggish ion transfer kinetics and compromised structural integrity. Inspired by the natural hierarchical porous structure of trees, electrodes with bioinspired architecture are fabricated to address these challenges. Specifically, electrodes with aligned columns consist of tree‐inspired vertical channels, and hierarchical pores are constructed by screen printing and ice‐templating, imparting enhanced electrochemical and mechanical performance. Employing an aqueous‐based binder, the LiNi_0.8Mn_0.1Co_0.1O₂cathode achieves a high areal energy density of 15.1 mWh cm⁻²at a rate of 1C at mass loading of 26.0 mg cm⁻², benefitting from the multiscale pores that elevated charge transfer kinetics in the thick electrode. The electrodes demonstrate capacity retention of 90% at the 100th cycle at a high current density of 5.2 mA cm⁻². To understand the mechanisms that promote electrode performance, simplified electro‐chemo‐mechanical models are developed, the drying process and the charge‐discharge process are simulated. The simulation results suggested that the improved performance of the designed electrode benefits from the lower ohmic overpotential and less strain gradient and stress concentration due to the hierarchical porous architecture. 

Abstract Porous metamaterial units filled with fluid have been used in engineering systems due to their ability to achieve desired properties (e.g., effective thermal conductvity). Designing 3D porous metamaterial units while ensuring complete connectivity of both solid and pore phases presents a significant challenge. In this study, we propose a generative graph neural network-based framework for designing the porous metamaterial units infilled with liquid. Firstly, we propose a graph-based metamaterial unit generation approach to generate porous metamaterial samples with complete connectivity in both solid and pore phases. Secondly, we establish and evaluate three distinct variational graph autoencoder (VGAE)-based generative models to assess their effectiveness in generating an accurate latent space representation of metamaterial structures. By choosing the model with the highest reconstruction accuracy, the property-driven design search is conducted to obtain novel metamaterial unit designs with the targeted properties. A case study on designing liquid-filled metamaterials for thermal conductivity properties is carried out. The effectiveness of the proposed graph neural network-based design approach is evaluated by comparing the performances of the obtained designs with those of existing designs in the training database. Merits and shortcomings of the proposed framework are also discussed. 

Abstract In this paper, we propose and compare two novel deep generative model-based approaches for the design representation, reconstruction, and generation of porous metamaterials characterized by complex and fully connected solid and pore networks. A highly diverse porous metamaterial database is curated, with each sample represented by solid and pore phase graphs and a voxel image. All metamaterial samples adhere to the requirement of complete connectivity in both pore and solid phases. The first approach employs a Dual Decoder Variational Graph Autoencoder to generate both solid phase and pore phase graphs. The second approach employs a Variational Graph Autoencoder for reconstructing/generating the nodes in the solid phase and pore phase graphs and a Transformer-based Large Language Model (LLM) for reconstructing/generating the connections, i.e., the edges among the nodes. A comparative study was conducted, and we found that both approaches achieved high accuracy in reconstructing node features, while the LLM exhibited superior performance in reconstructing edge features. Reconstruction accuracy is also validated by voxel-to-voxel comparison between the reconstructions and the original images in the test set. Additionally, discussions on the advantages and limitations of using LLMs in metamaterial design generation, along with the rationale behind their utilization, are provided. 

Abstract In this paper, we propose and compare two novel deep generative model-based approaches for the design representation, reconstruction, and generation of porous metamaterials characterized by complex and fully connected solid and pore networks. A highly diverse porous metamaterial database is curated, with each sample represented by solid and pore phase graphs and a voxel image. All metamaterial samples adhere to the requirement of complete connectivity in both pore and solid phases. The first approach employs a Dual Decoder Variational Graph Autoencoder to generate both solid phase and pore phase graphs. The second approach employs a Variational Graph Autoencoder for reconstructing/generating the nodes in the solid phase and pore phase graphs and a Transformer-based Large Language Model (LLM) for reconstructing/generating the connections, i.e., the edges among the nodes. A comparative study is conducted, and we found that both approaches achieved high accuracy in reconstructing node features, while the LLM exhibited superior performance in reconstructing edge features. Reconstruction accuracy is also validated by voxel-to-voxel comparison between the reconstructions and the original images in the test set. Additionally, discussions on the advantages and limitations of using LLMs in metamaterial design generation, along with the rationale behind their utilization, are provided. 

Abstract Bridging the gaps among various categories of stochastic microstructures remains a challenge in the design representation of microstructural materials. Each microstructure category requires certain unique mathematical and statistical methods to define the design space (design representation). The design representation methods are usually incompatible between two different categories of stochastic microstructures. The common practice of pre-selecting the microstructure category and the associated design representation method before conducting rigorous computational design limits the design freedom and reduces the possibility of obtaining innovative microstructure designs. To overcome this issue, this paper proposes and compares two methods, the deep generative modeling-based method and the curvature functional-based method, to understand their pros and cons in designing mixed-category stochastic microstructures for desired properties. For the deep generative modeling-based method, the Variational Autoencoder is employed to generate an unstructured latent space as the design space. For the curvature functional-based method, the microstructure geometry is represented by curvature functionals, of which the functional parameters are employed as the microstructure design variables. Regressors of the microstructure design variables-property relationship are trained for microstructure design optimization. A comparative study is conducted to understand the relative merits of these two methods in terms of computational cost, continuous transition, design scalability, design diversity, dimensionality of the design space, interpretability of the statistical equivalency, and design performance. 

This work presents a systematic study of the relationship between structural stochasticity and the crush energy absorption capability of lattice structures, with controlled stiffness and weight. We develop a Voronoi tessellation-based approach to generate multiple series of lattice structures with either equal weight or equal stiffness, smoothly transitioning from periodic to stochastic configurations for crush energy absorption analysis. The generated lattice series fall into two categories, originating from periodic honeycomb and diamond lattice structures. A new stochasticity metric is proposed for quantifying the structural stochasticity and is compared with the state-of-the-art stochasticity metrics to ensure a consistent measurement. The crush energy absorption properties are obtained using explicit finite element analysis and we observe similar stochasticity-property trends in simulations using both elastic-plastic and hyperelastic materials. We report a new observation that an intermediate level of stochasticity between periodic and high randomness leads to the best crush energy absorption performance. Our analysis reveals that this optimal performance arises from enhanced activation of deformation hinges, promoting efficient energy absorption.