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Nonlinear electroelastostatics: a variational framework

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Abstract.

Different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and two new variational principles for electroelastostatics are introduced. One is based on use of the electrostatic scalar potential and one on the vector potential, combined with the deformation function. In each case Lagrangian forms of the electric variables are used. Their connections with several formulations of nonlinear electroelasticity in the literature are established and some differences highlighted.

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Author notes

  1. R. Bustamante

    Present address: Departamento de Ingeniería Mecánica, Universidad de Chile, Torre Central, Piso 4, Beauchef 850, Santiago Centro, Santiago, Chile

Authors and Affiliations

  1. Department of Mathematics, University of Glasgow, University Gardens, Glasgow, G12 8QW, UK

    R. Bustamante & R. W. Ogden

  2. Department of Civil and Environmental Engineering, Tufts University, Medford, MA, 02155, USA

    A. Dorfmann

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  1. R. Bustamante
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  2. A. Dorfmann
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  3. R. W. Ogden
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Correspondence to R. W. Ogden.

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Bustamante, R., Dorfmann, A. & Ogden, R.W. Nonlinear electroelastostatics: a variational framework. Z. angew. Math. Phys. 60, 154–177 (2009). https://doi.org/10.1007/s00033-007-7145-0

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  • DOI: https://doi.org/10.1007/s00033-007-7145-0

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