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