PhD Final Defense – Chao Wang

Topology Optimization of Mechanical and Magnetic Architected Structures with Controllable Static and Dynamic Responses

Advisor: Professor Shelly Zhang

Abstract

Architected structures can achieve unprecedented mechanical properties through tailored geometry, material distribution, and internal microstructures. When integrated with stimuli-responsive smart materials, they become adaptive systems with tunable responses under varying operational conditions. However, designing such multifunctional systems remains challenging due to complex mechanics, multi-physics interactions, and dynamic effects. Moreover, translating numerical designs into manufacturable structures and practical applications presents additional challenges. This thesis develops multi-physics and multi-material topology optimization approaches for designing mechanical and magnetic architected structures with programmable static and dynamic responses, while investigating their manufacturing strategies and engineering applications.

The first part of the thesis focuses on magnetically responsive soft materials, which can achieve reversible deformation under magnetic actuation. An integrated pipeline is developed that combines modeling, design, manufacturing, and applications. A computational framework is first introduced and experimentally validated for predicting the nonlinear elastic response of magnetorheological elastomers with different matrix compositions, particle volume fractions, geometries, and deformation modes. Building on this modeling foundation, topology optimization frameworks are developed for hard-magnetic soft materials to realize prescribed three-dimensional large deformation while accounting for manufacturing requirements. To bridge computational design and physical realization, fabrication strategies based on mold casting and direct ink writing are established. In particular, a toolpath generation method is developed to translate optimized continuous magnetization fields into printable paths for direct ink writing. The optimized magnetic soft materials are further applied to wireless robotic implants for controlled tissue deformation, demonstrating their potential for biomedical mechanotherapy applications.

The second part of the thesis extends topology optimization for dynamic response control. A frequency-domain topology optimization method is developed for multi-material composite structures subjected to stationary stochastic excitation. By integrating random vibration analysis, response power spectral density evaluation, and multi-material design, the framework enables direct control of displacement-, velocity-, and acceleration-based response measures over prescribed frequency ranges. This formulation supports broadband vibration mitigation, dynamic amplification, signal filtering, and the balance between dynamic performance and structural load-bearing requirements. The framework is further extended to periodic mechanical metamaterials for dynamic shape programming and enhanced energy dissipation. Finally, magnetically tunable wave-control metamaterials are designed by coupling magnetic shape morphing with incremental dynamic analysis, enabling external magnetic fields to reconfigure deformation states and wave propagation characteristics.

Overall, this thesis establishes a unified computational design paradigm for mechanical and magnetic architected structures across static and dynamic regimes. By integrating topology optimization, nonlinear mechanics, magneto-mechanical coupling, stochastic dynamics, advanced manufacturing, and experimental validation, the developed frameworks enable the design of multifunctional systems for applications in soft robotics, biomedical devices, resilient structures, energy dissipation, and adaptive wave control.