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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. 

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. 

Reconstructing 3D granular microstructures within volumes of arbitrary geometries from limited 2D image data is crucial for predicting the material properties, as well as performances of structural components accounting for material microstructural effects. We present a novel generative learning framework that enables exascale reconstruction of granular microstructures within complex 3D geometric volumes. Building upon existing transfer learning techniques using pre-trained convolutional neural networks (CNN), we introduce several key innovations to overcome the difficulties inherent in arbitrary geometries. Our framework incorporates periodic boundary conditions using circular padding techniques, ensuring continuity and representativeness of the reconstructed microstructures. We also introduce a novel seamless transition reconstruction (STR) method that creates statistically equivalent transition zones to integrate multiple pre-existing 3D microstructure volumes. Based on STR, we propose a cost-effective strategy for reconstructing microstructures within complex geometric volumes, minimizing computational waste. Validation through numerical experiments using kinetic Monte Carlo simulations demonstrates accurate reproduction of grain statistics, including grain size distributions and morphology. A case study involving the reconstruction of a 4-blade propeller microstructure illustrates the method’s capability to efficiently handle complex geometries. The proposed framework significantly reduces computational demands while maintaining high reconstruction quality, paving the way for scalable microstructure reconstruction in materials design and analysis. 

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. 

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 restricts the design freedom and hinders the discovery of innovative microstructure designs. To overcome this issue, this paper proposes and compares two novel 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. 

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.