Finite element implementation of nonlinear constitutive models for piezoceramic materials

Abstract

The objective of this work was the finite element implementation of constitutive material models for piezoceramic materials. A phenomenological material model was implemented by means of a customized radial return mapping algorithm into an open source finite element program, and the problem was reduced to the solution of a single nonlinear algebraic equation. This led to a significant reduction in computation time for simulations compared to an implementation by means of an explicit higher order integration scheme for the constitutive differential equations. Furthermore, a microscopically motivated material model was implemented by means of a radial return mapping algorithm based on the backward Euler scheme. Apart from simulations of the principal behavior of the material models and their finite element implementations, simulations of applied examples are discussed which demonstrate the properties of the models and the performance of the implementations. © 2010 Mathematical Sciences Publishers.