A phase-field model for anisotropic brittle fracturing of piezoelectric ceramics

摘要

Piezoelectric ceramics are inherently brittle materials that show electromechanical coupling under electrical and mechanical stimuli. In the last decades piezoelectric materials have garnered significant attention due to their established applications as sensors and actuators. In this context the structural reliability of such materials under varied conditions is paramount. In the present work we propose a phase-field approach to model crack propagation in a coupled electromechanical setting. The proposed framework accounts for anisotropic crack propagation by employing appropriate structural tensors that enter the crack-surface-density function as additional arguments. Appropriate choices of degradation functions allow for the accommodation of varied electrical boundary conditions along cracks. Based on experimental results available in the literature, we employ a non-associative dissipative framework in which fracturing processes are driven by the mechanical part of the coupled electromechanical driving force alone. The modeling capabilities of the proposed framework are demonstrated by a set of numerical examples in two and three spatial dimensions.