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Saint-Venant’s principle for antiplane shear deformations of linear piezoelectric materials. (English) Zbl 1047.74019

This paper is concerned with antiplane shear deformations in the context of linear theory of piezoelectricity. The authors study the extent of Saint-Venant end effects in homogeneous piezoelectric solids, and examine how they differ from the mechanical case. Energy decay estimates are used to investigate the axial decay of solutions on a semi-infinite strip with sides traction-free and subjected to zero surface charge and self-equilibrated conditions at the end. The problem is investigated in detail for two classes of materials: hexagonal 6mmm and cubic 43m. It is shown that for the first class the mechanical and electrical fields decouple, and that the decay rate end effects coincide with those for isotropic elastic materials. The authors show that for the second class the problem involves a full coupling of mechanical and electrical effects. The energy-decay inequality methods are applied to obtain an explicit estimate for the exponential decay rate of end effects. For this class of materials, the piezoelectric end effects are predicted to penetrate further into the strip than their elastic counterparts.

MSC:

74G50 Saint-Venant’s principle
74F15 Electromagnetic effects in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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