Mechanical and Civil Engineering Seminar: PhD Thesis Defense

Abstract:

The rapid pace of development of new responsive and structural materials along with significant advances in synthesis techniques, which may incorporate multiple materials in complex architectures, provides an opportunity to design functional devices and structures of unprecedented performance. These include implantable medical devices, soft-robotic actuators, wearable haptic devices, mechanical protection, and energy storage or conversion devices. However, the full realization of the potential of these emerging techniques requires a robust, reliable, and systematic design approach. This thesis explores these ideas through optimal design methods. By investigating pressing engineering problems which exploit these advances in materials and manufacturing, we develop optimal design methods to realize next-generation structures. Our exploration into modeling, computation, and mathematical regularization for optimal design is conducted through considering model design problems of responsive actuators and impact resistant structures. While these serve to ground the fundamental study, they are also relevant, pressing engineering problems.

The first application we consider is the design of responsive structures. Recent developments in material synthesis and 3D printing of anisotropic materials, such as liquid crystal elastomers (LCE), have facilitated the realization of structures with arbitrary morphology and tailored material orientation. These methods may also produce integrated structures of passive and active material. This creates a trade-off between stiffness and actuation flexibility when designing such structures. Thus, we turn to optimal design. This is complicated by anisotropic behavior and finite deformations, manufacturing constraints, and choice of objective function. Like many optimal design problems, the naive formulations are ill-posed, giving rise to mesh dependence, lack of convergence, and other numerical deficiencies. So, starting with a simple setting using linear kinematics and working all the way to finite deformation, we develop a systematic mathematical theory that motivates, and then rigorously proves, an alternate well-posed formulation. We examine suitable objective functions before studying a series of examples in both small and finite deformation. However, the manufacturing process constrains the design. This is a result of extrusion-based 3D printing methods aligning nematic directors along the print path. We extended the formulation with these considerations to produce print-aware designs while also recovering the fabrication pathway. We demonstrate the formulation by designing and producing physical realizations of these actuators.

Next, we explore optimal design of impact resistant structures. The complex physics and numerous failure modes of structural impact create challenges when designing for impact resistance. Here, we apply gradient-based topology optimization to the design of such structures. We start by constructing a variational model of an elastic-plastic material enriched with gradient phase-field damage, and present a novel method to accurately and efficiently compute its transient dynamic evolution. Sensitivities over this trajectory are computed through the adjoint method, and we develop a numerical method to solve the resulting adjoint dynamical system. We demonstrate this formulation by studying the optimal design of 2D solid-void structures undergoing blast loading. Then, we explore the trade-offs between strength and toughness in the design of a bimaterial spall-resistant structure undergoing dynamic impact.

We conclude by summarizing the presented work and discussing the contributions towards the overarching goal of optimal design for emerging materials technologies. From our study, key issues have arose which must be addressed to further progress the field. We examine these and lay a pathway for future studies which will allow optimal design to tackle complicated, pressing engineering problems.