Cellular materials are ubiquitous in our world being found in natural and engineered systems as structural materials, sound and energy absorbers, heat insulators and more. Stochastic foams made of polymers, metals and even ceramics find wide use due to their novel properties when compared to monolithic materials. Properties of these so called hybrid materials, those that combine materials or materials and space, are derived from the localization of thermomechanical stresses and strains on the mesoscale as a function of cell topology. The effects of localization can only be generalized in stochastic materials arising from their inherent potential complexity, possessing variations in local chemistry, microstructural inhomogeneity and topological variations. Ordered cellular materials on the other hand, such as lattices and honeycombs, make for much easier study, often requiring analysis of only a single unit-cell. Theoretical bounds predict that hybrid materials have the potential to push design envelopes offering lighter stiffer and stronger materials. Hybrid materials can achieve very low and even negative coefficients of thermal expansion (CTE) while retaining a relatively high stiffness - properties completely unmatched by monolithic materials. In the first chapter of this thesis a two-dimensional lattice is detailed that possess near maximum stiffness, relative to the tightest theoretical bound, and low, zero and even appreciably negative thermal expansion. Its CTE and stiffness are given in closed form as a function of geometric parameters and the material properties. This result is confirmed with finite elements (FE) and experiment. In the second chapter the compressive stiffness of three-dimensional ordered foams, both closed and open cell, are predicted with FE and the results placed in property space in terms of stiffness and density. A novel structure is identified that effectively achieves theoretical bounds for Young's, shear and bulk modulus simultaneously, over a wide range of relative densities, greatly expanding the property space of available materials with a pragmatic manufacturable structure. A variety of other novel and previously studied ordered foam topologies are also presented that are largely representative of the spectrum of performance of such materials, shedding insight into the behavior of all cellular materials.

Materials found in nature exhibit remarkable properties allowing natural living systems to survive. An outstanding example of this is the byssus of marine mussels. Mussels utilize byssal threads in the byssus to anchor themselves onto a variety of surfaces and endure the harsh intertidal environment. Byssal threads display a composite microstructure as well as intricate macro-scale architectures. This dissertation presents four studies that address questions regarding byssal thread geometry, physical parameters affecting adhesion, and the relationship between the thread microstructure and mechanical properties. Mussels utilize a mushroom-shaped geometry for their byssal threads: the threads consist of a distal thread (stalk) terminating in a plaque (mushroom-tip). Previous studies on adhesion associated with the mushroom-shaped geometry have focused on the effects of geometrical parameters such as tip thickness and the ratio of the stalk to tip radius. Mussels deposit byssal threads radially, which are loaded at various angles during wave motion. This introduces a more complex geometry than previously studied in regard to adhesion and detachment. Due to these differences, we focused on the effects of casting angle and loading angle on adhesive strength utilizing synthetic mimics. We find that the optimal configuration for adhesive strength is when the loading angle and casting angle are equivalent. Evidence suggests that suction may play a role in the adhesive strength of mushroom shaped structures. Using byssal threads as inspiration, we utilized synthetic mimics to study the effects of suction at the macroscopic scale. To determine the critical stress necessary for defect propagation and detachment a fracture mechanics-based model is introduced, and compared with experimental results. The findings indicate that there is a greater increase in adhesive strength due to suction at the macro-scale, which is length-scale dependent. Lastly, we assess the relationship between the thread microstructure and mechanical properties. Different protein domains in the collagenous core were targeted with chemical treatments and stress relaxation measurements were conducted to determine which energy dissipative mechanisms are present during the relaxation process. This complements previous studies which largely focused on elastic properties, by concentrating on the viscoelastic properties of the threads. Results show that the silk-like domains are largely responsible for energy dissipation via protein unfolding and/or rearrangement during the relaxation process. Under cyclic loading, distal threads exhibit a stress-strain behavior reminiscent of shapememory and superelastic effects observed in some metal alloys. Previous studies have revealed that distal threads undergo phase transitions in their microstructure as they are loaded. A hyperelastic Neo-Hookean-based model is introduced that incorporates the mechanical properties from two distinct phases in the microstructure to address the contributions from the collagen core. In addition, a Mullins-based model is used to fit the composite cyclic data and provide insight into the mechanical response of the composite thread.