A small deformations effective stress model of gradient plasticity phase-field fracture

A variational formulation of small strain ductile fracture, based on a phase-field modeling crack propagation, is proposed. The an effective stress description gradient plasticity, combined with AT1 model. Starting from established statements finite-step elastoplasticity for generalized standard materials, mixed statement consistently derived, incorporating in rigorous way update both the elastoplastic and dissipations. complex interaction between brittle dissipation mechanisms modeled by assuming plasticity driven propagation non-variational function equivalent plastic then introduced to modulate developed strains. Particular care has been devoted consistent Newton–Raphson scheme case Mises global return mapping relative tangent matrix, supplemented line-search scheme, solution problem fixed phase field. resulting algorithm proved be very robust computationally effective. Application several benchmark tests show robustness accuracy proposed