T. Buchukuri, O. Chkadua, R. Duduchava, and D. Natroshvili

Interface Crack Problems for Metallic-Piezoelectric Composite Structures

abstract:
In the monograph we investigate three--dimensional interface crack problems for metallic-piezoelectric composite bodies with regard to thermal effects. We give a mathematical formulation of the physical problems when the metallic and piezoelectric bodies are bonded along some proper parts of their boundaries where interface cracks occur. By the potential method the interface crack problems are reduced to equivalent strongly elliptic systems of pseudodifferential equations on manifolds with boundary. We study the solvability of these systems in appropriate function spaces and prove uniqueness and existence theorems for the original interface crack problems. We analyse the regularity properties of the corresponding thermo-mechanical and electric fields near the crack edges and near the curves where the different boundary conditions collide. 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 expose some numerical calculations which demonstrate that the stress singularity exponents depend on the material parameters essentially.

Mathematics Subject Classification: 35J55, 74F05, 74F15, 74B05

Key words and phrases: Strongly elliptic systems, potential theory, thermoelasticity theory, thermopiezoelasticity, boundary-transmission problems, crack problems, interface crack, stress singularities, pseudodifferential equations