Hybrid finite element approach to quasi-brittle fracture

The modelling of quasi-brittle fracture processes by a hybrid finite element formulation is introduced. Both the nodal displacements defined in the whole domain of the problem and the equivalent nodal forces defined on the fracture interfaces, where all nonlinearities are supposed to be concentrated, are introduced first as independent variables. The displacements are then eliminated by static condensation, and only the degrees of freedom which represent the dual generalized (in Prager's sense) variables (tractions and opening displacements) defined on the interfaces are retained. These generalized variables are related to each other through a softening cohesive law, enforced in a suitable weighted averaged sense. The comparison with the standard finite element methods based on displacements only, with other mixed finite element formulations, as well as with the symmetrical version of the boundary element method is also pointed out, mainly for the discussion on the stability and bifurcation of quasi-brittle fracture processes.