Uniform asymptotic solutions for lamellar inhomogeneities in piezoelectric solids

Dascalu, Cristian; Homentcovschi, Dorel

doi:10.1090/qam/2019617

Authors: Cristian Dascalu and Dorel Homentcovschi
Journal: Quart. Appl. Math. 61 (2003), 657-682
MSC: Primary 74F15; Secondary 74B05, 74G10, 74G70, 78A30
DOI: https://doi.org/10.1090/qam/2019617
MathSciNet review: MR2019617
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Abstract: We study the problem of a lamellar inhomogeneity of arbitrary shape embedded in a piezoelectric matrix of infinite extent. Uniform asymptotic solutions for the equations of elastostatics and electrostatics on this configuration are obtained. The first order terms, in the inhomogeneity thickness, are explicitly determined for piezoelectric inclusions, rigid inclusions of electric conductor, impermeable cracks, and cracks with inside electric field. We give real-form expressions of mechanical and electric fields at the interface and on the inhomogeneity axis. Detailed first order solutions are obtained for elliptic and lemon-shaped inhomogeneities. It is found that, while for elliptic piezoelectric inclusions the perturbation stresses and electric displacements at the inclusion ends have the same order as those given at infinity, for a lemon-shaped inclusion they are an order-of-magnitude smaller. Intensity factors are calculated for lemon-shaped cavities. It is shown that, when inside electric fields are considered, the stress intensity coefficients are influenced by the material anisotropy.

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