An Analysis of the Exponential Electric Displacement Saturation Model in Fracturing Piezoelectric Ceramics

Abstract

This paper presents a numerical analysis of a recently proposed exponential electric displacement saturation model to simulate crack initiation and crack propagation in piezoelectric ceramics. The motivation for the account of electric displacement saturation on a constitutive level can be found in the observed difference between theoretical predictions and the actual experimental obtained dependency of crack propagation onset on the applied electric field. Contrary to earlier accounts of electric displacement saturation, the exponential saturation of the electric displacement versus electric field relation allows for applications in problems like propagating cracks in fracturing piezoelectric ceramics where no analytical solutions exist. This requires the incorporation of strong discontinuities in the form of jumps in the displacement field and the electric potential for the electromechanical coupled solid within the individual finite elements. Based on two numerical examples for which experimental results are available the extension of such an advanced finite element framework to take into account electric displacement saturation is shown in this work to be independent of the finite element discretization and results in numerical solutions close to the experimentally observed results.