Applications of Algebraic Topology in Elasticity
In this book chapter we discuss some applications of algebraic topology in elasticity. This includes the necessary and sufficient compatibility equations of nonlinear elasticity for non-simply-connected bodies when the ambient space is Euclidean. Algebraic topology is the natural tool to understand the topological obstructions to compatibility for both the deformation gradient F and the right Cauchy-Green strain C. We will investigate the relevance of homology, cohomology, and homotopy groups in elasticity.