Adaptive isogeometric analysis-based phase-field modeling of interfacial fracture in piezoelectric composites

This paper implements an adaptive phase-field model to investigate the interfacial fracture in transversely isotropic piezoelectric composites under different electromechanical loadings using an isogeometric framework based on polynomial splines over hierarchical T-meshes (PHTsplines). The model introduces the interface and crack phase-field parameters to regularize the sharp interface and crack topologies, respectively and the regularized energy terms are incorporated corresponding to crack and interface evading the need for line integration along them. It also modifies the energy functional to scrutinize the interaction between interfacial damage and crack propagation in piezocomposites and thus is capable of capturing the fracture patterns including interfacial debonding, matrix cracking and their interactions under different electric fields. An adaptive mesh refinement scheme using PHT-splines is implemented to efficiently resolve for interface and crack phase-fields and track the complex crack propagation paths without any ad hoc criteria. The efficacy and robustness of the proposed model are demonstrated using a set of examples simulating the electromechanical fracture in piezoelectric composites. Moreover, different fracture mechanisms in composite materials including the crack nucleation, interfacial debonding, matrix cracking, crack propagation and coalescence are found to be precisely captured using the present modeling technique.