Isogeometric phase-field modeling of brittle and ductile fracture in shell structures

Abstract

Phase-field modeling of brittle and ductile fracture is a modern promising approach that enables a unified description of complicated failure processes (including crack initiation, propagation, branching, merging), as well as its efficient numerical treatment [1-4]. In the present work, we apply this approach to model fracture in shell structures, considering both thin and thick shells. For thin shells, we use an isogeometric Kirchhoff-Love shell formulation [5-6], which exploits the high continuity of the isogeometric shape functions in order to avoid rotational degrees of freedom, i.e., the shell geometry is modeled as a surface and its deformation is fully described by the displacements of this surface. For thick shells, we use an isogeometric assumed natural strain (ANS) solid shell formulation [7], i.e., a 3D solid formulation enhanced with the ANS method in order to alleviate geometrical locking effects. According to the discretization of the structural formulations, an isogeometric basis is also used for the phase-field. While the phase-field fracture formulation for solid shells is basically the same as for standard solids, some reformulation is necessary for thin shells, accounting for the interaction of stresses devoted to membrane and bending deformation. We test both formulations on several numerical examples and perform comparisons of the results obtained by the two methods to each other as well as to reference solutions, which confirm the validity and applicability of the presented methods.