An elastoplastic-damage model for quasi brittle materials in the framework of the strong discontinuity approach

In the paper, an anisotropic elastoplastic-damage model is formulated in the context of the strong discontinuity approach (SDA) (Simo, Oliver, and Armero 1993) for Finite Element (FE) analysis of mode-I fracture in quasi brittle materials. The constitutive relations of the elastoplastic-damage material degenerate to traction-displacement relations at the line of discontinuity. As a consequence, no special internal length parameter needs to be introduced. The equations are integrated exactly without any numerical parameter. The parameter defining the amplitude of the displacement jump within the finite element is condensed out at the material level without employing the standard static condensation technique. This approach results in a form of the linearized constitutive equations formally identical to continuum models. Therefore the standard return mapping algorithm is used to solve the nonlinear equations. Algorithmic issues and details of the implementation are discussed with emphasis on unloading and reloading conditions. The applicability of the SDA finite element model as well as its numerical performance is investigated by means of a representative example.