Vol. 5, No. 1, 2010

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ISSN: 1559-3959
Finite element implementation of nonlinear constitutive models for piezoceramic materials

Bernd Laskewitz and Marc Kamlah

Vol. 5 (2010), No. 1, 19–45
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.

Keywords
ferroelectrics, constitutive modeling, finite element analysis
Milestones
Received: 21 November 2008
Revised: 6 May 2009
Accepted: 6 July 2009
Published: 19 April 2010
Authors
Bernd Laskewitz
Karlsruhe Institute of Technology
Institute for Materials Research II
P.O. Box 3640
76021 Karlsruhe
Germany
http://www.fzk.de/imf2
Marc Kamlah
Karlsruhe Institute of Technology
Institute for Materials Research II
P.O. Box 3640
76021 Karlsruhe
Germany
http://www.fzk.de/imf2