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The phase field (PF) approach to fracture has emerged as a promising modeling tool that regularizes the variational fracture theory by Griffith via the introduction of a nonlocal damage-like field variable in the corresponding formulation. In this work, we outline a PF formulation for triggering brittle fracture phenomena in shell structures made of Functionally Graded Materials (FGMs). This model relies on the 6-parameter shell formulation complying with a solid shell kinematic description and incorporates the use of the Enhanced Assumed Strain (EAS) and Assumed Natural Strain (ANS) methods in order to alleviate different locking pathologies. The corresponding multi-field variational formalisms is consistently derived and discretized within the context of the Finite Element Method (FEM). Details regarding the implementation in the general purpose FE packages are outlined. The applicability of this model is demonstrated by means of several numerical applications.

Phase field model for fracture analysis of functionally graded power-based shell structures