Finite elements with embedded displacement discontinuity: a generalized variable formulation

This paper is intended to bring a contribution towards a satisfactory simulation of those fracture phenomena which result in the appearance and development of discrete cracks. To this purpose, a general mixed nite element formulation is proposed, based on the concept of generalized variables in Pragerʹs sense. The dis- placement eld inside an element is modelled by the sum of two contributions: a regular (continuous) part which is governed by standard shape functions, and a possibly discontinuous one which is introduced soon after a suitable criterion is satis ed. The formulation is rst specialized to a one-dimensional case, then a triangular element for two-dimensional problems is described in detail. Analytical and numerical examples are presented in order to clarify the formulation and to point out the essential role of inter-element conformity.