11 July 2001 Symmetric constitutive laws for polycrystalline ferroelectric ceramics
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A class of fully coupled, symmetric, multi-axial, ferroelectric constitutive laws is presented. The foundation of the theory is an assumed form for the Helmholtz free energy of the material. Yield surfaces and associated flow rules are postulated in a modified stress and electric field space such that a positive dissipation rate during switching is guaranteed. The resulting tangent moduli relating increments of stress and electric field to increments of strain and electric displacement are symmetric since changes in the linear elastic, dielectric and piezoelectric properties of the material are included in the switching surface and flow law. Symmetry is further investigated with a simple one-dimensional loading situation comparing the thermodynamically consistent framework to a more ad hoc theory.
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Chad M. Landis "Symmetric constitutive laws for polycrystalline ferroelectric ceramics", Proc. SPIE 4333, Smart Structures and Materials 2001: Active Materials: Behavior and Mechanics, (11 July 2001); doi: 10.1117/12.432765; https://doi.org/10.1117/12.432765

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