T. Buchukuri, O. Chkadua, D. Natroshvili, A.-M. Sändig

Interaction Problems of Metallic and Piezoelectric Materials with Regard to Thermal Stresses

We investigate linear three-dimensional boundary transmission problems related to the interaction of metallic and piezoelectric ceramic media with regard to thermal stresses. Such type of physical problems arise, e.g., in the theory of piezoelectric stack actuators. We use the Voigt's model and give a mathematical formulation of the physical problem when the metallic electrodes and the piezoelectric ceramic matrix are bonded along some proper parts of their boundaries. The mathematical model involves different dimensional physical fields in different sub-domains, occupied by the metallic and piezoceramic parts of the composite. These fields are coupled by systems of partial differential equations and appropriate mixed boundary transmission conditions. We investigate the corresponding mixed boundary transmission problems by variational and potential methods. Existence and uniqueness results in appropriate Sobolev spaces are proved. We present also some numerical results showing the influence of thermal stresses.

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

Key words and phrases: Thermoelasticity, thermopiezoelasticity, boundary transmission problems, variational methods, potential method