Efficient and reliable phase‐field simulation of brittle fracture using a nonsmooth multigrid solution scheme

Abstract

In the last decades the phase‐field approach to fracture [1–3] has gained wide popularity due to advantages such as straight‐forward modeling of complex crack patterns and crack branching while allowing standard finite‐element discretizations. Time‐discrete phase‐field models of brittle fracture are typically formulated in terms of biconvex minimization problems for which a standard monolithic Newton‐Raphson scheme usually fails to converge. Solutions can be found by using operator‐splitting methods [2] or predictor‐corrector schemes [4]. Such methods come at the cost of high computational efforts. Furthermore, models incorporating the thermodynamically consistent local irreversibility of the damage phase‐field contain nonsmooth terms [2]. To improve the stability and to reduce the computational costs originating from the biconvexity and the nonsmoothness of the energy functional, we employ a nonsmooth multigrid method that can solve such problems roughly in the time of one equivalent linear problem [5] and which has been shown to be globally convergent [5]. We will demonstrate the computational speed of the proposed solution scheme by means of a classical benchmark problem of brittle fracture.