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Orthotropic rescaling for crack tip fields in linear piezoelectric materials. (English) Zbl 1119.74560

Summary: Analysis of stress fields in a linear elastic-piezoelectric-dielectric medium requires use of anisotropic elasticity theory. Many researchers employ the Stroh formalism, which requires the solution of a sixth order characteristic equation involving material coefficients. This equation must be solved numerically for each material composition to obtain the eigenvalues and eigenvectors that give the resulting field quantities. The focus of this work is the development of a closed form solution for the electro-mechanical crack tip fields in piezoelectric materials using orthotropic rescaling to reduce the governing field equations to the biharmonic equation and the Poisson equation. Solutions for an isotropic linear elastic material are utilized to obtain solutions for the anisotropic piezoelectric material. This leads to closed form solutions for the fields in terms of ratios of certain elastic, dielectric, and piezoelectric coefficients. Orthotropic rescaling and the Stroh formalism are compared and recommendations are made for when and when not to use the orthotropic rescaling approach.

MSC:

74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
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