Finite Elements with non-Homogeneous Embedded Discontinuities

In the paper, a model for the physical phenomenon of fracture in a continuummedium is presented. The proposed formulation falls in the context of the Strong DiscontinuitiesApproach (SDA) implemented by means of Elements with Embedded Discontinuities(EED). In the contribution, an improved enhanced displacement field is proposed, such that thedisplacement jumps are not constant within each finite element. In this way, by means of anappropriate choice of the interface degrees of freedom, the crack path and the displacementjumps can be modeled as continuous functions across the element boundaries. First the generalthermodynamically consistent weak formulation is presented. It derives from a mixed generalizedmulti-fields Hu-Washizu functional based on the enriched kinematics. The continuum andthe interface are ruled by different constitutive equations, defined by distinct free energy anddissipation functionals. Then, in the spirit of the EED approach, the non linear evolution problemin the continuum and at the interface is solved by means of a local algorithm, at the FiniteElement level, that yields simultaneously the amplitude of the jump increment, the stress valueat the Gauss points of the element and the traction on the interface surface.The performance of different enriched finite elements using different degrees of interpolationfor either the regular and the enhanced fields, and thus considering constant and non constant jumps, are compared through some 2D applications.