Three-dimensional finite elements with embedded strong discontinuities to model failure in electromechanical coupled materials

Abstract

This paper presents new finite elements with embedded strong discontinuities to model failure in three dimensional electromechanical coupled materials. Following the strong discontinuity approach for plane electromechanical problems, the coupled boundary value problem is decomposed into a continuous global part and into a discontinuous local part where strong discontinuities in the displacement field and electric potential are introduced. Those are incorporated into general three-dimensional brick finite elements through nine mechanical separation modes and three new electrical separation modes. All the local enhanced parameters related to those modes can be statically condensed out on the element level, yielding a computationally efficient framework to model failure in electromechanical coupled materials. Impermeable electric boundary conditions are assumed along the strong discontinuities. Their initiation and orientation is detected through a configurational force driven failure criterion. A marching cubes based crack propagation concept is used to obtain smooth failure surfaces in the three dimensional problems of interest. Several representative numerical simulations are included and compared with experimental results of failure in piezoelectric ceramics to outline the performance of the new finite elements.