Systematic inverse design and physical realization of nonlinear elastic and thermoelastic responses for metamaterials
Advisor: Professor Xiaojia Shelly Zhang
Abstract
The development of metamaterials with precisely programmable behaviors can benefit a broad range of engineering applications. The functions of many applications require soft materials that undergo large and highly nonlinear deformations. Most of the established nonlinear mechanical metamaterials are obtained via forward design accompanied by heuristic trial-and-error and restricted to regular patterns from small design spaces, impeding the reach of more complex and useful nonlinear behaviors for diverse needs. These inherent restrictions can be potentially overcome by integrating the inverse design strategy with a powerful computational morphogenesis method known as topology optimization on the condition that a comprehensive set of technical challenges ranging from mechanics theory and numerical computation to fabrication and validation are fully resolved.
By addressing these challenges, this thesis establishes a new paradigm for systematic, automated, and objective-oriented creations of structures and metamaterials with arbitrarily programmable nonlinear mechanical and thermomechanical responses under large deformations. The research is built upon the theory of finite elasticity and thermoelasticity, nonlinear finite element method, topology optimization, advanced fabrication, and experimental investigations. The research focuses on the inverse design and physical realization of nonlinear force-displacement relations, nonlinear three-dimensional deformation modes, temperature-adaptive and -switchable nonlinear behaviors, and thermally actuated spontaneous mechanical responses. The optimally synthesized metamaterials feature complex geometries and distributions of potentially multiple constituents and precisely achieve a wide variety of highly nonlinear elastic and thermoelastic behaviors, facilitating new and exotic functionalities and applications. With innovations in the advanced fabrication of soft materials, several families of optimized structures and metamaterials are accurately manufactured and tested, and their unique programmed responses are physically realized.
The thesis has yielded a comprehensive family of optimization formulations for the inverse design of wide-ranging nonlinear elastic and thermoelastic responses, obtained a broad collection of optimized structures and metamaterials with categorized sets of behaviors, revealed diverse sophisticated underlying physical mechanisms, established a complete topology optimization framework for programming anisotropic and temperature-active soft materials, and significantly broadened the application of topology optimization in nonlinear solid mechanics. We envision our translatable findings will fundamentally advance the inverse design capacity of metamaterials with complex nonlinear behavior for various disciplines.
