Dual Formulations of the Elasticity Problem for a Homogeneous Elastic Body with Fractures

We extend previous results on the dual formulations for an elastic body without fractures to a model of a homogeneous elastic body with fractures. In particular, in the framework of Legendre-Fenchel duality, we were able to provide three equivalent formulations for the problem where the displacement, the stress, and the strain are the unknowns respectively. We also provide a characterization of the image of the convex cone of admissible displacements under the linearized strain tensor.