A phase‐field model of brittle fracture for an isogeometric Reissner‐Mindlin shell formulation

Abstract

AbstractOne of the biggest challenges in fracture modeling is the correct physical description of the fracture processes. Over the past decade, the well‐established phase‐field modeling framework has gained a lot of attention, due to its ability to predict the fracture phenomena adequately. It has shown very promising results for a three dimensional solid formulation and has been extended to an isogeometric Kirchhoff‐Love formulation in order to describe brittle fracture in plates and shells, see [1]. However, the Kirchhoff‐Love theory only describes shells in the thin regime. For thick shells, the deformation behavior and subsequently the fracture behavior additionally depends on the transverse shear strains which are not present in the Kirchhoff‐Love approach. In this work, the phase‐field fracture framework is extended to an isogeometric Reissner‐Mindlin shell formulation [2]. In this approach, the shell is described using the midsurface and a director vector field for the thickness direction. Subsequently, the phase‐field is also defined only on the midsurface. In order to distinguish the cracking behavior in tension and compression, as proposed in [1], the spectral decomposition of the strain for the tension‐compression split is done on the total strain, which varies through the thickness. The proposed method is tested for several numerical examples and compared to a three dimensional solid formulation and the Kirchhoff‐Love shell formulation in order to confirm its accuracy and efficiency.