Tengiz Buchukuri, Otar Chkadua, David Natroshvili

Mixed and Crack Type Problems of the Thermopiezoelectricity Theory without Energy Dissipation

In this paper, we study mixed and crack type boundary value problems of the linear theory of thermopiezoelectricity for homogeneous isotropic bodies possessing the inner structure and containing interior cracks. The model under consideration is based on the Green-Naghdi theory of thermopiezoelectricity without energy dissipation. This theory permits propagation of thermal waves at finite speed. Using the potential method and the theory of pseudodifferential equations on manifolds with boundary we prove existence and uniqueness of solutions and analyze their smoothness and asymptotic properties. We describe an efficient algorithm for finding the singularity exponents of the thermo-mechanical and electric fields near the crack edges and near the curves where different types of boundary conditions collide. By explicit calculations it is shown that the stress singularity exponents essentially depend on the material parameters, in general.

Mathematics Subject Classification: 35B65, 35S15, 45M05, 47G30, 74A15, 74F05, 74F15, 74G40, 74G70

Key words and phrases: Thermopiezoelectricity without energy dissipation, bodies with microstructure, mixed boundary value problem, crack problem, potential method, pseudodifferential equations, stress singularities