Interface Cracks Problems in Composites With Piezoelectric and Thermal Effects

Abstract

We investigate three–dimensional interface crack problems (ICP) for metallic-piezoelectric composite bodies with regard to thermal effects. We give a mathematical formulation of the physical problem when the metallic and piezoelectric bodies are bonded along some proper parts of their boundaries where interface cracks occur. By potential methods the ICP is reduced to an equivalent strongly elliptic system of pseudodifferential equations (ψDEs) on overlapping manifolds with boundary, which have no analogues in mathematical literature. We study the solvability of obtained ψDEs on overlapping manifolds with boundary by reduction to ψDEs on non-overlapping manifolds with boundary in different function spaces. These general results are applied to prove the uniqueness and the existence theorems for the original ICP-Problem.