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A Complete Direct Approach to Modeling of Electrostrictive Polymer Plates as Electro-elastic Material Surfaces

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Contributions to Advanced Dynamics and Continuum Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 114))

Abstract

In this paper we present a first account towards the modeling of electro-elastic plates as electro-elastic material surfaces. A complete direct approach is developed without the need to involve the three-dimensional formulation. In particular, we consider the case of electrostrictive polymer plates, in which ponderomotive forces as well as constitutive coupling by means of electrostriction are accounted for. We propose a rational formulation for the augmented free energy of electro-elastic material surfaces incorporating electrostriction by a multiplicative decomposition of the surface stretch tensor and an additive decomposition of the surface curvature tensor into elastic and electrical parts. Moreover, we show that concepts such as the total stress, the electrostatic stress and the mechanical stress exist also for electro-elastic material surfaces. Results computed within the framework of this complete direct approach are compared to results based on a numerical integration of the plane stress three-dimensional augmented free energy. A very good agreement is found.

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Authors and Affiliations

  1. Institute of Mechanics and Mechatronics, TU Wien, Getreidemarkt 9, 1060, Vienna, Austria

    Michael Krommer & Elisabeth Hansy-Staudigl

Authors
  1. Michael Krommer
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  2. Elisabeth Hansy-Staudigl
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Correspondence to Michael Krommer .

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Editors and Affiliations

  1. Institut für Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Institut für Technische Mechanik, Johannes Kepler Universität Linz, Linz, Austria

    Hans Irschik

  3. Institute of Continuous Media Mechanics, Russian Academy of Sciences, Perm, Russia

    Valery P. Matveenko

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Krommer, M., Hansy-Staudigl, E. (2019). A Complete Direct Approach to Modeling of Electrostrictive Polymer Plates as Electro-elastic Material Surfaces. In: Altenbach, H., Irschik, H., Matveenko, V. (eds) Contributions to Advanced Dynamics and Continuum Mechanics. Advanced Structured Materials, vol 114. Springer, Cham. https://doi.org/10.1007/978-3-030-21251-3_9

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