Phase-field modeling of fracture in linear thin shells

•First phase field model for fracture in thin shells.•The method does not require complex track cracking procedures. The crack's topology is the natural outcome of the analysis.•Efficient meshfree method for complex geometries. We present a phase-field model for fracture in Kirchoff–Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantage over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected pipes.