Effective continuum models for the buckling of non-periodic architected sheets that display quasi-mechanism behaviors

In this work, we construct an effective continuum model for architected sheets that are composed of bulky tiles connected by slender elastic joints. Due to their mesostructure, these sheets feature quasi-mechanisms -- low-energy local kinematic modes that are strongly favored over other deformations. In sheets with non-uniform mesostructure, kinematic incompatibilities arise between neighboring regions, causing out-of-plane buckling. The effective continuum model is based on a geometric analysis of the sheets' unit cells and their energetically favorable modes of deformation. Its major feature is the construction of a strain energy that penalizes deviations from these preferred modes of deformation. The effect of non-periodicity is entirely described through the use of spatially varying geometric parameters in the model. Our simulations capture the out-of-plane buckling that occurs in non-periodic specimens and show good agreement with experiments. While we only consider one class of quasi-mechanisms, our modeling approach could be applied to a diverse set of shape-morphing systems that are of interest to the mechanics community

Electromagnetic Wave Theory and Applications

Contains table of contents for Section 3, reports on nine research projects and a list of publications.National Aeronautics and Space Administration Contract 958461U.S. Navy - Office of Naval Research Grant N00014-92-J-1616University of California/Jet Propulsion Laboratory Contract 960408U.S. Army - Corps of Engineers/Cold Regions Research and Engineering Laboratory Contract DACA89-95-K-0014Mitsubishi CorporationU.S. Navy - Office of Naval Research Agreement N00014-92-J-4098Federal Aviation AdministrationDEMACOJoint Services Electronics Program Grant DAAHO4-95-1-003

Optimal Design of Soft Responsive Actuators and Impact Resistant Structures

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 this 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. We begin by reviewing classical optimal design methods, the mathematical difficulties they raise, and the practical approaches of overcoming these difficulties. We introduce the canonical problem of compliance minimization of a linear elastic structure. After illustrating the intricacies of this seemingly simple problem, we detail contemporary methods used to address the underlying mathematical issues. We then turn to extending these classical methods for emerging materials and technologies. We must incorporate optimal design with rich physical models, develop computational approaches for efficient numerics, and study mathematical regularization to obtain well-posed optimization problems. Additionally, care must be taken when selecting an application-tailored objective function which captures the desired behavior. Finally, we must also take into account manufacturing constraints in scenarios where the fabrication pathway affects the structural layout. We address these issues by exploring model optimal design problems. 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 as extrusion-based 3D printing aligns 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 creates 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 time 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 spall-resistant structure composed of two materials of differing properties undergoing dynamic impact. We conclude by summarizing the presented work and discuss the contribution 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.</p