Nanomechanics of Hierarchical Cellular Solids

Materials Science and Engineering, a young and vibrant discipline with its inception in the 1950s, has expanded into three directions: metals, polymers, and ceramics (and their mixtures, composites). Beyond the traditional scope, biological materials have drawn much attention since 1990s due to their optimal structures, which rise from hundreds of million years of evolution. Generally, biological materials are complex composites and possess varieties of hierarchical structures, multifunctionality, self-organization and self-assembly. From the point of view of mechanics, mechanical properties of natural (or biological) materials are outstanding, although their constituent materials are weak. This is because the necessary mechanical support is in great need due to their surrounding environment. Therefore, their efficiency provides us with useful indications as to how to synthesize new materials inspired by natural ones, and thus drives scientists and engineers to reveal the mechanisms behind the observed phenomena of interest. In this regard, the tendency in the design of novel materials apparently holds a promising future in new Material Science. To date, it is widely accepted that the research on biological materials is a multidisciplinary field including chemistry, physics, and biology etc. Although some progress has been already made, there is still a long way to go to mass fabricate bio-inspired materials. In this thesis, employing a “bottom-up” approach, we have devised three hierarchical models (2-D hierarchical woven, 2-D hierarchical honeycomb and 3-D hierarchical foam) inspired by structures found in natural materials and investigated their mechanical properties. The common characteristic of these structures is their being quasi-self-similar. Regarding the derivation of their mechanical properties, we consider the (n-1)th level structure to be a continuous medium and from it we calculate the mechanical properties of the nth level structure. In the first chapter, we introduce the motivation for this work. By reviewing the literature on both well-studied and less familiar natural materials, we summarize their structural characteristics and biomechanical mechanisms. Chapter 2 deals with our first model—1-D or 2-D hierarchical woven tissue, and the elastic anisotropy of the structure is derived, based on the well-known stiffness averaging method by volumes. In order to verify the theory, an experiment on leaves, which are modeled as one-dimensional hierarchical woven structures, is performed. Also, a comparison between theoretical predictions and experimental data on tendons from the literature is made. The considered structure could be used as a scaffold, which can provide the mechanical support and optimize tissue regeneration at each hierarchical level. Chapters 3-5 discuss our second model—2-D hierarchical honeycomb. Incorporating the surface effect, the in-plane linear-elastic properties, elastic buckling properties, fracture strength and toughness are derived. Chapter 3 examines the linear elastic properties and the stiffness efficiency thanks to the minimum-weight analysis, and the parametric analysis shows that the structure can be optimized. Chapter 4 discusses elastic buckling by employing the Euler buckling formula; besides local buckling, progressive buckling is also investigated. The progressive failure behavior is found to be similar to that of balsa wood. Strength efficiency is also illustrated. Employing “Quantized Fracture Mechanics” (Pugno, 2002; Pugno and Ruoff, 2004), Chapter 5 modifies the classical strength formulas of the conventional honeycomb and investigates the defective hierarchical honeycomb; the fracture toughness of the perfect and defective hierarchical honeycomb are both derived. In general, hierarchical honeycombs can be used as energy-absorbing materials and bioscaffolds for directional tissue regeneration. Chapter 6 models our third hierarchical structure—3-D hierarchical foam. The Young’s modulus and plastic strength are derived based on structural analysis. When the characteristic size of the lowest level is very small (less than 10nm), surface effects play an important role in determining the mechanical properties of the structure. The hierarchical foam could be used as nano-porous gold. Chapter 7 provides conclusions and an outlook for future work.