Discontinuous failure analysis for mode-I and mode-II localization problems

In this paper failure is assumed to be a discrete phenomenon. A modelling in which a crack or a shear band is incorporated in the shape functions of the finite element formulation is used. A discontinuous function of the displacement gradients acts as an additional localized mode with a length scale parameter that is independent of the element size. A predefinition of the failure zone is not necessary and the crack or shear band can be described with a relatively small number of finite elements. The model is elaborated for simple mode-I and mode-II problems. A comparison with standard continuum models for failure has been made. (C) 1998 Elsevier Science Ltd. All rights reserved.