Keywords: interfaces, strong discontinuities, embedded discontinuities, damaging behaviour.

The analysis of elements with displacement discontinuities, due either to crack formation or to the presence of interfaces that can debond during the process, usually requires very detailed geometric models, that can follow the propagation of the discontinuity. This is done introducing zero thickness interface elements, that, however, enlarge significantly the number of degrees of freedom. Furthermore, in the commonly used interface elements, it is difficult to model dissipative interfaces avoiding a fictitious elastic opening. As an alternative models based on embedded interfaces have been proposed , that do not appear as interelements discontinuities, and that can follow any path within the elements of the mesh. These models include the extended finite element method (XFEM) and the strong discontinuity approach (SDA) methods. In this paper the development of a SDA based intra-element interface model is examined. It is shown that the kinematic assumptions are the same as in the XFEM, and that special enrichment functions are needed in order to comply with the essential boundary conditions. Then a variational principle is formulated, from which all the relevant equations of the model are obtained. The principle also yields the discretised form of the contiuity conditions for the stresses acting on the interface. Using a recently proposed algorithmic framework, based on the formal analogy between the enriched continuum and the theory of classical plasticity, that avoids static condensation at the element level, the model can be effectively implemented within the context of a classical finite element code.

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