PhD Final Defense – Rahul Dev Kundu

Computational Design of Metamaterials and Metastructures for Extreme and Programmable Behavior by Topology Optimization

Advisor: Prof. Xiaojia Shelly Zhang

Abstract

Computational design of metamaterials and metastructures is a rich and ever-growing research field, as it offers an enlarged design space, better process automation, and faster discovery of unprecedented functionalities as compared to traditional trial-and-error or intuition-based design approaches. Topology optimization is one such computational design approach that enables informed spatial material allocation to achieve desired performance goals with reduced material usage. While it has been popularly used in compliance minimization problems for single-material systems, recent developments in multiple directions, such as multimaterial systems, stress- or mechanism-based design goals, and unusual microstructure design with negative Poisson's ratios, have broadened the design scope and applications. This dissertation further extends the capabilities of topology optimization for unconventional design goals to realize different extreme and programmable responses in structures and metamaterials.

The research is built upon linear and nonlinear elasticity theory, finite element methods, gradient-based topology optimization, and experimental investigations. The research focuses on realizing unconventional and programmable properties, such as extreme strength and stiffness in linear elastic small strain regime, and highly nonlinear and rate-dependent behavior in finite strain regime. The research improves structural strength by intelligent use of different anisotropic and isotropic material phases, and realizes a wide range of extremal stiffness by a parameterized periodic microstructure that maintains smooth transitions in geometry and extremal properties. Beyond linear elastic regime, the research realizes complex programmable nonlinear behavior in soft metamaterials by inverse design of individual components and their interactions. Furthermore, it enables design of smart soft structures that behave intelligently according to different actuation-rates. The optimized designs feature complex geometries and effective distributions of the constituent material phases that reveal key insights about the interrelations between structural geometry and deformation that enable different extreme and programmable behavior. Some of the optimized designs are physically realized to assess the strengths and limitations of the presented design methods via experimental investigations.

This dissertation established a diverse set of optimization frameworks, presented problem-specific optimization formulations, generated suitable optimized metastructures and metamaterials, and conducted experimental verification by physically realizing many of the optimized designs to expand the state-of-the-art topology optimization capabilities in both the linear and nonlinear regimes of solid mechanics. In the process, it identified the physical mechanisms that contribute to extreme stiffness and strength, and that realize highly nonlinear and rate-dependent behavior in different structures and metamaterials. The research findings are envisioned to fundamentally advance the computational design capabilities for metamaterials and metastructures for extreme and programmable responses, potentially benefiting various engineering disciplines.