Riv. Mat. Univ. Parma, Vol. 2, No. 2, 2011

Maurizio Romeo

Symmetric system of balance laws for a micromorphic continuum model of dielectrics

Pages: 255-271
Received: 8 April 2011   
Accepted in revised form: 14 September 2011
Mathematics Subject Classification (2010): 74A60, 74F15, 35L40, 74H55.

Keywords: Continuum theory of electroelastic solids, continuum micromechanics, wave stability.

Abstract: An electromechanical model for dielectric solids is formulated within the microcontinuum field theory. Electric dipole and quadrupole densities are introduced consistently with the microstructure and a set of non linear balance equations for micromorphic electroelasticity are derived. Constitutive assumptions are adopted accounting for additional internal variables compatibly with the second law of thermodynamics. It is shown that the differential system of balance laws can be given in a symmetric hyperbolic form. Stability conditions on wave motion superimposed to an undeformed polarized state are obtained in the form of suitable inequalities on constitutive parameters.

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