Fracture Mechanics Analysis of Piezoelectric Materials Using an Efficient Collocation Element Differential Method

This paper presents a novel element differential method for modeling cracks in piezoelectric materials, aiming to simulate fracture behaviors and predict the fracture parameter known as the J-integral accurately. The method leverages an efficient collocation technique to satisfy traction and electric charge equilibrium on the crack surface, aligning internal nodes with piezoelectric governing equations without needing integration or variational principles. It combines the strengths of the strong form collocation and finite element methods. The J-integral is derived analytically using the equivalent domain integral method, employing Green's formula and Gauss's divergence theorem to transform line integrals into area integrals for solving two-dimensional piezoelectric material problems. The accuracy of the method is validated through comparison with three typical examples, and it offers fracture prevention strategies for engineering piezoelectric structures under different electrical loading patterns.