Elasticity is often viewed as a “classical” subject that was largely closed as an area of research by the end of the 19th century. It is rarely taught in the undergraduate physics curriculum. It, however, remains essential for the vast materials industry, and developments of new materials, measurement techniques, and theory have brought it back as a dynamic research topic. These lectures will first review the fundamental concepts of elasticity theory, with a greater emphasis on nonlinearities than can be found in most physics text books, and the bulk and surface excitation spectrum it predicts. It will then discuss the elasticity of at least a subset of the specific materials: nematic elastomers, graphene, and smectic-A liquid crystals, and filamentous networks. Finally, it will consider the exotic elasticity of topological or near-topological mechanical networks.
Lecture III: Elasticity of Topological Mechanical Networks
A. Introduction to topological mechanics
B. Guest-Hutchinson modes and their consequences.
C. Surface excitations
D. Real materials and the breaking of topological constraints