Harnessing Structural Stochasticity in Designing Architectured Materials: Deep Generative Design and Curvature Functional-Based Design

Bridging the gaps among various categories of microstructures, which include the periodic microstructures and various types of stochastic microstructure, remains a challenge in architectured material design. Traditionally, different microstructure categories require significantly different mathematical methods to define the design space. The purpose of this work is to establish a computational framework that provides a unified design space that embodies various categories of structural patterns for the design automation of mixed-category microstructures. The structural patterns include various stochastic patterns such as random particles, random fibers, random cells, spinodal structures, random amorphous structures, etc., as well as periodic structural patterns collected from metamaterial research works.<br/>First, we established a property-aware Variational Autoencoder-based deep generative design framework that embodies both stochastic and periodic 2D microstructure patterns. The proposed framework is demonstrated on two sets of design case studies: (i) searching a periodic metamaterial pattern with desired properties with a stochastic pattern as the starting point, and (ii) searching a stochastic microstructure with desired properties with a periodic pattern as the starting point.<br/>Second, we present an in-depth investigation on designing 3D mixed-category stochastic microstructures for desired properties. We establish and compare two methods, a data-driven method based on deep generative models and a mathematical method based on curvature functionals. The metrics of comparison include design performance, computational cost, scalability, interpretability of the statistical equivalency, and convenience of generating functional graded structure designs. This work is concluded with a summary of the pros and cons of each method.