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 finite element formulation is proposed, based on the concept of generalized variables in Prager's sense. The displacement field 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 satisfied. The formulation is first 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.
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Bolzon et al. (2000) studied this question.
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