A novel multiscale nonlocal damage model for simulating crack propagation in transversely isotropic piezoelectric materials

This study investigates the crack propagation behavior of transversely isotropic piezoelectric materials, with a particular focus on the influence of critical elongation anisotropy, applied electric field, and polarization angle on their fracture characteristics. Piezoelectric materials, known for their ability to interconvert mechanical and electrical energy, are widely utilized in sensors, transducers, and micro-electro-mechanical systems. However, their inherent brittleness and sensitivity to cracking make them prone to fracture under electro-mechanical coupling loads. To gain a deeper understanding of their fracture behavior, this paper introduces a nonlocal macro-meso-scale damage consistent model and employs numerical simulations based on the finite element method. We propose a new non-local influence domain and the corresponding integration strategy for the transversely isotropic materials. Besides, we define both the critical elongation and the brittleness index of the material as an elliptic function regarding the bond angle. The results demonstrate that the fracture resistance of piezoelectric materials increases significantly with an increase in the critical elongation ratio. Additionally, it was observed that a positive electric field promotes fracture, whereas a negative electric field inhibits it. These findings suggest that the fracture behavior of piezoelectric materials can be effectively regulated by adjusting the critical elongation ratio, applied electric field, and polarization angle. This provides a theoretical foundation for the design and application of piezoelectric materials in various engineering contexts.