A Hilbert complex for nonlinear elasticity and its applications

In this talk, I will introduce a Hilbert complex for nonlinear elasticity which is isomorphic to the de Rham complex for vector-valued differential forms. This isomorphism allows one to employ standard properties of the de Rham complex to study nonlinear elasticity. For example, one can study voids and inclusions in microstructures using the Hodge decomposition. Another example is associated to the discretization of the de Rham complex using the Finite Element Exterior Calculus (FEEC). I will also discuss the application of FEEC for developing mixed finite element methods for nonlinear elasticity.