Computational Homogenization of Thin-Shell Microstructures

Abstract

Microstructures, ubiquitous in everyday materials such as cloth, foams, and honeycombs, influence the physical properties and behaviors of materials at a macroscopic level. Advances in fabrication technologies have facilitated the design of engineered microscale structures, unlocking a new spectrum of materials with unprecedented properties. These developments challenge traditional modeling and simulation approaches due to increased geometric and kinematic complexities. This thesis addresses these challenges through advanced homogenization strategies that bridge the gap between microscale phenomena and macroscale behaviors. The first part of the thesis introduces a novel continuum scale model that utilizes high-order interpolants. This model enhances the simulation of complex materials by accurately capturing the nonlinear and anisotropic behaviors intrinsic to microstructured materials. The development of this model is supported by a comprehensive pipeline, which includes the generation of detailed training data and an optimized fitting process to ensure the robustness and accuracy of the simulations. In the second part, we focus specifically on the homogenization of microstructured sheets, adapting our earlier methods to suit the particular challenges of surface simulations. This adaptation addresses the limitations of traditional volumetric methods in dealing with thin materials, enhancing the practicality of our computational models for real-world applications. The contributions of this thesis aim to enhance the theoretical understanding and practical application of material homogenization. By providing these new methods and insights, this thesis hopes to support further research and development in fields where the customizability of material properties is increasingly crucial.