Interface crack problems for metallic–piezoelectric composite structures

Abstract

AbstractWe investigate three‐dimensional interface crack problems (ICP) for metallic–piezoelectric composite bodies. We give a mathematical formulation of the physical problem when the metallic and piezoelectric bodies are bonded along some proper part of their boundaries where an interface crack occurs. By potential methods the ICP is reduced to an equivalent strongly elliptic system of pseudodifferential equations on manifolds with boundary. We study the solvability of this system in different function spaces and prove uniqueness and existence theorems for the original ICP. We analyse the regularity properties of the corresponding electric and mechanical fields near the crack edges and near the curves where the boundary conditions change. In particular, we characterize the stress singularity exponents and show that they can be explicitly calculated with the help of the principal homogeneous symbol matrices of the corresponding pseudodifferential operators. We present some numerical calculations that demonstrate that the stress singularity exponents essentially depend on the material parameters. Copyright © 2009 John Wiley & Sons, Ltd.