A finite element method for the simulation of strong and weak discontinuities in solid mechanics

In this paper we introduce and analyze a finite element method for elasticity problems with interfaces. The method allows for discontinuities, internal to the elements, in the approximation across the interface. We propose a general approach that can handle both perfectly and imperfectly bonded interfaces without modifications of the code. For the case of linear elasticity, we show that optimal order of convergence holds without restrictions on the location of the interface relative to the mesh. We present numerical examples for the linear case as well as for ductile contact and crack propagation model problems