Fracture analysis of spatially graded piezoelectric-flexoelectric materials using XIGA

Dielectric Functionally Graded Materials (FGMs) exhibit superior flexoelectric properties. Gradual changes in material properties lead to large strain gradients and excellent flexoelectric responses. Cracks behave in a complex manner inside piezoelectric-flexoelectric FGMs subjected to electromechanical loading. An extended isogeometric analysis (XIGA)-based formulation is developed for flexoelectric FGMs with crack discontinuities. Ceramic-polymer FGMs of barium titanate (BTO) and polyvinylidene fluoride (PVDF) are selected for analysis since this material combination has shown better flexoelectric response solely due to gradation. A higher-order electromechanical J-integral is used to study the behavior of cracks. The fracture behavior of different crack geometries at various grading indices and levels of flexoelectricity is investigated. A crack interaction study is conducted with varying crack parameters. The length-scale effect on the energy release rate is also shown. A significant reduction in the energy release rate is observed in FGMs due to the flexoelectric effect.