Cohesive-frictional interface in an equilibrium based finite element formulation

The Hybrid Equilibrium Element (HEE) formulation, with quadratic stress field is defined in the class of statically admissible solutions, which implicitly satisfy the homogeneous equilibrium equations. The inter-element equilibrium condition and the boundary equilibrium condition are exactly imposed by considering a quadratic displacement fields at the element sides, as an interfacial Lagrangian variable, in a classical hybrid formulation. The displacement degrees of freedom are independently defined for each element side, where a cohesive-frictional 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 cohesive-frictional interface is defined in extrinsic form, as a rigid-damage cohesive zone model (CZM), developed in the consistent thermodynamic framework of damage mechanics with internal variable and produces a bilinear response in a traction separation diagram.