Computational modeling and design of mechanical metamaterials: A machine learning approach

Abstract

Mechanical metamaterials are a special class of materials, whose mechanical properties are primarily determined by their geometry and topology. Due to their unique properties and wide applications, mechanical metamaterials have gained increasing attention in recent years. To name a few, mechanical metamaterials have been used in designing soft robotics, equipment with local tunable functionalities, etc. For better exploitation of their huge potential, the ability to design mechanical metamaterials with particular desired properties is of key importance. Traditional design methods rely heavily on experimental characterization and are often driven by heuristic rules, which are time consuming and economically inefficient. This dissertation aims to establish a computational design framework that enables rational, efficient, and robust designs for mechanical metamaterials. The challenge is addressed by applying classical numerical methods and leveraging modern machine learning tools. The research results can be grouped with three major outcomes. First, we propose a multi-scale computational homogenization scheme based on a neural network surrogate energy model to simulate cellular mechanical metamaterials under large deformation. Compared with direct numerical simulation, the proposed scheme reduces the computational cost up to two orders of magnitude. The second part focuses on inverse design problems.Within the framework of topology and shape optimization, we successfully design cellular mechanical metamaterials with several pre-defined goals: achieving negative Poisson's ratio, precise control of instabilities, and arbitrary tuning of band gaps for phononic structures. Besides classical shape optimization methods, we also propose design approaches inspired by generative models in machine learning. Composite mechanical metamaterials with controllable overall elastic moduli are designed, fabricated with additive manufacturing, and experimentally validated. The final part of this dissertation makes a mathematical abstraction of the design/inverse problems and focuses on general partial differential equation (PDE) constrained optimization problems. We propose amortized finite element analysis (AmorFEA), in which a neural network is trained to produce accurate PDE solutions in an unsupervised fashion, while preserving many of the advantages of the traditional finite element method (FEM).