Hybrid Equilibrium Finite Element Formulation for Cohesive Crack Propagation

Abstract

Equilibrium elements have been developed in hybrid formulation with independent equilibrated stress fields on each element. Traction equilibrium condition, at sides between adjacent elements and at sides of free boundary, is enforced by use of independent displacement laws at each side, assumed as Lagrangian parameters. The displacement degrees of freedom belongs to the element side, where an extrinsic interface can be embedded. The embedded interface is defined by the same stress fields of the hybrid equilibrium element and it does not require any additional degrees of freedom. The extrinsic interface is developed in the consistent thermodynamic framework of damage mechanics with internal variable and produces a bilinear response in a traction separation diagram. The proposed extrinsic interface can be modelled on every single element side or can be modelled only on a set of predefined element sides.