A ductile phase-field fracture formulation with regularized fracture toughness through a gradient-extended micromorphic approach

In this work, a phase-field formulation is proposed to describe ductile fracture in fiber-reinforced concrete materials. By incorporating an elastoplastic bulk material formulation into the promising Representative Crack Element (RCE) framework, physically meaningful kinematic behaviors at the crack surface could be observed when facing crack opening, closing and shear loading scenarios. A nonlocal Drucker–Prager-type plasticity formulation is realized through the gradient-extended micromorphic approach, leading to mesh-insensitive plasticity in the Finite Element framework. Further, the critical fracture energy release rate is coupled to plasticity through the micromorphic variable, yielding the final ductile phase-field fracture formulation. Several representative examples are presented to further illustrate the characteristics of the proposed formulation.