An anisotropic phase-field framework for finite-deformation fracture and fatigue in flexible piezoelectric composites

Abstract

Flexible piezoelectric composites are increasingly used in wearable and adaptive structures. However, their geometric nonlinearity and pronounced anisotropy pose significant challenges for reliable prediction of fracture and fatigue under electromechanical loading. This work develops an anisotropic phase-field fracture model for flexible piezoelectric composites at finite strains, in which distinct softening laws are assigned to the isotropic matrix and anisotropic fibers. To eliminate unphysical fracture modes, the energy density is decomposed using the volumetric-stretch tension–compression scheme. This model is further extended to fatigue by introducing a cumulative history variable that captures the progressive degradation of fracture toughness under cyclic loading. Numerical results demonstrate that, with a large penalty parameter in anisotropic crack surface density function, the predicted crack path aligns with the fiber orientation, and the global responses are consistent with available experimental observations. For flexible piezoelectric composites, the fracture behavior is influenced by fiber orientation and applied electric fields. For composites with symmetric fiber families, enhanced mechanical performance and stabilized crack trajectories are observed. The proposed framework provides theoretical flexibility and computational robustness for predicting fracture and fatigue failure in flexible piezoelectric composites, enabling reliability-driven design of next-generation flexible piezoelectric devices.