Phase‐field approach to fracture for finite‐deformation contact problems

The present contribution deals with a variationally consistent Mortar contact algorithm applied to a phase‐field fracture approach for finite deformations, see [4]. A phase‐field approach to fracture allows for the numerical simulation of complex fracture patterns for three dimensional problems, extended recently to finite deformations (see [2] for more details). In a nutshell, the phase‐field approach relies on a regularization of the sharp (fracture‐) interface. In order to improve the accuracy, a fourth‐order Cahn‐Hilliard phase‐field equation is considered, requiring global C 1 continuity (see [1]), which will be dealt with using an isogeometrical analysis (IGA) framework. Additionally, a newly developed hierarchical refinement scheme is applied to resolve for local physical phenomena e.g. the contact zone (see [3] for more details). The Mortar method is a modern and very accurate numerical method to implement contact boundaries. This approach can be extended in a straightforward manner to transient phase‐field fracture problems. The performance of the proposed methods will be examined in a representative numerical example. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)