Dynamic Phase-Field Fracture in Viscoelastic Materials using a First-Order Formulation

Abstract

In this contribution we present analytical results on a model for dynamic fracture in viscoelastic materials at small strains that have been obtained in full depth in [1]. In the model, the sharp crack interface is regularized with a phase-field approximation, and for the phase-field variable a viscous evolution with a quadratic dissipation potential is employed. A non-smooth penalization prevents material healing. The viscoelastic momentum balance is formulated as a first order system and coupled in a nonlinear way to the non-smooth evolution equation of the phase field. We give a full discretization in time and space using a discontinuous Galerkin method for the first-order system. We discuss the existence of discrete solutions and, with the step size in space and time tending to zero, their convergence to a suitable notion of weak solution of the system. Eventually, we provide a numerical benchmark and compare it with simulation results found in [2].