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14 June 2000 Analysis of deformable electroelastic devices: cumulative effects of weak electric conduction
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This paper presents the governing equations for small deformation electroelastic continua with electric conduction, consistently derived from the general continuum physics theory for electromagnetics and thermomechanics of deformable continua. The resulting small deformation equations are exactly the classical piezoelectric equations with additional electric body force and electric conduction terms. Furthermore, the paper presents weak forms of the small deformation equations and a corresponding finite element formulation suitable for nonlinear material constitutive equations. The response of highly electrically insulating devices can be dominated by the cumulative effects of weak electric conduction currents. Much of the engineering analysis literature is concerned with perfect electrically insulating deformable bodies, but the perfect insulator approximation is only accurate provided the time scales of loading are sufficiently fast compared to the time scales of electric conduction currents. Device designs based on perfect insulator analysis are likely to fail when subjected to sufficiently slow time scale loadings. A finite element example is presented for the transient response of a nonlinear repolarizable piezoelectric material embedded in an epoxy matrix, subject to an electric voltage step loading.
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John E. Harper and Nesbitt W. Hagood "Analysis of deformable electroelastic devices: cumulative effects of weak electric conduction", Proc. SPIE 3992, Smart Structures and Materials 2000: Active Materials: Behavior and Mechanics, (14 June 2000);

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