Phase-field modeling of flexible piezoelectric composites incorporating interfacial failure

Within the finite-deformation framework, a unified modeling approach is developed for flexible piezoelectric composites based on the phase-field cohesive zone model (PF-CZM), accounting for both bulk fracture and interfacial failure. Unlike previous studies that primarily address brittle composites under small deformations, this work focuses on stretchable flexible piezoelectric materials exhibiting pronounced geometric and material nonlinearities, which lead to strongly coupled governing equations and increased computational complexity. An interface phase-field parameter is introduced to describe diffuse interfaces, while a crack phase-field parameter governs crack propagation. The model accommodates various cohesive softening laws to simulate interfacial failure and captures the influence of interface strength on overall fracture performance. The numerical framework is implemented in ABAQUS, with a HETVAL subroutine used for the diffuse interface modeling and UEL for fracture simulations. When damage is primarily localized within the matrix, neglecting the interface effects significantly reduces computational cost without compromising accuracy. In cases involving interfacial failure, the model effectively investigates the role of interface strength in crack propagation and fracture characteristics. Numerical results demonstrate the effects of interface strength, applied electric fields, and inclusion size on fracture behavior. Higher interface strength enhances peak load capacity and resistance to failure, with weaker interfaces favoring interfacial cracking and stronger interfaces promoting matrix cracking. Furthermore, in flexible piezoelectric materials bonded to soft substrates, interfacial debonding may be triggered by applied electric fields, a phenomenon supported by both numerical simulation and experimental observation.