**Tengiz Buchukuri, Otar Chkadua, David Natroshvili**

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

**abstract:**

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