Optimization and Supervised Machine Learning Methods for Inverse Design of Cellular Mechanical Metamaterials

Cellular mechanical metamaterials (CMMs) are a special class of materials that consist of microstructural architectures of macroscopic hierarchical frameworks that can have extraordinary properties. These properties largely depend on the topology and arrangement of the unit cells constituting the microstructure. The material hierarchy facilitates the synthesis and design of CMMs on the micro-scale to achieve enhanced properties (i.e., improved strength, toughness, low density) on the component (macro)-scale. However, designing on-demand cellular metamaterials usually requires solving a challenging inverse problem to explore the complex structure-property relations. The first part of this study (Ch. 3) proposes an experience-free and systematic design methodology for microstructures of CMMs using an advanced stochastic searching algorithm called micro-genetic algorithm (μGA). Locally, this algorithm minimizes the computational expense of the genetic algorithm (GA) with a small population size and a conditionally reduced parameter space. Globally, the algorithm employs a new search strategy to avoid local convergence induced by the small population size and the complexity of the parameter space. What's more, inspired by natural evolution in the GA, this study applies the inverse design method with the standard GA (sGA) as a sampling algorithm for intuitively mapping material-property spaces of CMMs, which requires the selection of objective properties and stochastic search of property points within the property space. The mapping methodology utilizing the sGA is proposed in the second part of the study (Ch. 4). This methodology involves a robust strategy that is shown to identify more comprehensive property spaces than traditional mapping approaches. The resulting property space allows designers to acknowledge the limitations of material performance, and select an appropriate class of CMMs based on the difficulty of the realization and fabrication of their microstructures. During the fabrication process, manufacturing defects cause uncertainty in the microstructures, and thus the structural properties. The third part of the study (Ch. 5) investigates the effects of the uncertainty stemming from manufacturing defects on the material property space. To accelerate the uncertainty quantification (UQ) via the Monte Carlo method, this study utilizes a machine learning technique to bypass the expensive simulations to compute properties. In addition to reducing the computational expense of the simulations, the deep learning method has been proven to be practical to accomplish non-intuitive design tasks. Due to the numerous combinations of properties and complex underlying geometries of metamaterials, it is numerically intractable to obtain optimal material designs that satisfy multiple user-defined performance criteria at the same time. Nevertheless, a deep learning method called conditional generative adversarial networks (CGANs) is capable of solving this many-to-many inverse problem. The fourth part of the study (Ch. 6) proposes a new inverse design framework using CGANs to overcome this challenge. Given combinations of target properties, the framework can generate a group of geometric patterns providing these target properties. Therefore, the proposed strategy provides alternative solutions to satisfy on-demand requirements while increasing the freedom in the fabrication process. Besides, with the advances in additive manufacturing (AM), the design space of an engineering material can be further enlarged by multi-scale topology optimization. As the interplay between microstructure and macrostructure drives the overall mechanical performance of engineering materials, it is necessary to develop a multi-scale design framework to optimize structural features in these two scales simultaneously. The final part of the study (Ch. 7) presents a concurrent multi-scale topology optimization method of CMMs. Structures in micro and macro scales are optimized concurrently by utilizing sequential quadratic programming (SQP) with the Solid Isotropic Material with Penalization (SIMP) method and a numerical homogenization approach.