A continuum finite elements (FE) formulation involving discontinuity of the displacement field to simulate fracture mechanics problems for brittle or quasi-brittle solids is proposed. A homogeneous discontinuity is assumed in a cracked finite element, and a new simple stress-based implementation of the displacement discontinuity is introduced by an appropriate stress field correction to simulate, as usually done in an elastic–plastic classical FE formulation, the mechanical effects of the crack, i.e. the proposed formulation does not introduce any discontinuous displacement field by mean of special or modified shape functions. Both linear elastic and elastic–plastic behaviour of the non-cracked material can be considered. 2D fracture problems are solved by the proposed procedure, to predict the load–displacement behaviour as well as the crack patterns in brittle structures. The new proposed simple FE formulation for discontinuous problems is computationally economic, and maintains the internal continuity of the numerical model with well-known numerical benefits.
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