A polyconvex phase‐field approach to fracture with application to finite‐deformation contact problems

Variationally consistent phase‐field methods allow for an efficient investigation of complex three‐dimensional fracture problems (see [1, 2]). However, formulations for large deformation problems often exhibit a lack of numerical stability for different loading scenarios. In the underlying contribution a novel formulation for finite strain polyconvex elasticity is adapted to phase‐field fracture problems. In particular we introduce a new anisotropic split based on the principal invariants of the right Cauchy‐Green strain tensor for a proper treatment of fracture within the polyconvex framework (see [4]). This polyconvex phase‐field fracture formulation can be implemented in a straightforward manner and improves the numerical stability. Furthermore, a fourth order crack density functional is considered to improve accuracy and convergence. To account for the C1 requirement the system is embedded in a sophisticated isogeometric framework with the ability of local refinement. Eventually, a variationally consistent Mortar contact algorithm is applied (see [3]) to handle contact boundaries. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)