Thermo-elastic solid shell formulation with phase field fracture for thin-walled FGMs

Thermo-elastic fracture is a matter of important concern for thin-walled structures made of functionally graded materials (FGMs). Based on this practical relevance, a thermodynamically consistent framework is herein proposed to solve the coupled thermo-mechanical phase-field fracture problem in thin-walled structures made of FGMs. The formulation of the current model is constructed via the evaluation of the phase-field in the Clausius–Duhem inequality leading in to first-order stability conditions in order to ensure thermodynamic consistency. The three-dimensional Kirchhoff–Saint–Venant constitutive model is modified to accommodate the functional grading in the material properties. The computational model is combined with Enhanced Assumed Strain (EAS) and Assumed Natural Strains (ANS) to alleviate locking pathologies concerning the solid shell formulation, leading to a coupled non-linear variational formulation. Several benchmark examples (straight and curved shells) are examined to assess the model capabilities. Moreover, crack deflection, and temperature distributions in the FGM structures are compared with their homogeneous surrogates, to show the importance of the technological solutions with two or even three FGM phases.