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Finite element
implementation of nonlinear constitutive models for
piezoceramic materials
Bernd Laskewitz and Marc Kamlah |
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Vol. 5 (2010), No. 1, 19–45
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Abstract |
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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
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Milestones
Received: 21 November 2008
Revised: 6 May 2009
Accepted: 6 July 2009
Published: 19 April 2010
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Authors |
| Bernd Laskewitz | |
| Karlsruhe Institute of
Technology Institute for Materials Research II P.O. Box 3640 76021 Karlsruhe Germany |
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| http://www.fzk.de/imf2 | |
| Marc Kamlah | |
| Karlsruhe Institute of
Technology Institute for Materials Research II P.O. Box 3640 76021 Karlsruhe Germany |
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| http://www.fzk.de/imf2 | |
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