Solvability and regularity results to boundary-transmission problems for metallic and piezoelectric elastic materials

• Published in: Mathematische Nachrichten 2009-08, Vol.282 (8), p.1079-1110
• Main Authors: Buchukuri, T., Chkadua, O., Natroshvili, D., Sändig, A.-M.
• Format: Article
• Language: English
• Subjects: boundary-transmission problems; elasticity theory; Elliptic systems; piezoelectricity; potential theory
• ISSN: 0025-584X; 1522-2616
• DOI: 10.1002/mana.200610790

We investigate three‐dimensional transmission problems related to the interaction of metallic and piezoelectric ceramic bodies. We give a mathematical formulation of the physical problem when the metallic and ceramic sub‐domains are bonded along some proper parts of their boundaries. The corresponding nonclassical mixed boundary‐transmission problem is reduced by the potential method to an equivalent nonselfadjoint strongly elliptic system of pseudo‐differential equations on manifolds with boundary. We investigate the solvability of this system in different function spaces. On the basis of these results we prove uniqueness and existence theorems for the original boundary‐transmission problem. We study also the regularity of the electrical and mechanical fields near the curves where the boundary conditions change and where the interfaces intersect the exterior boundary. The electrical and mechanical fields can be decomposed into singular and more regular terms near these curves. A power of the distance from a reference point to the corresponding edge‐curves occurs in the singular terms and describes the regularity explicitly. We compute these complex‐valued exponents and demonstrate their dependence on the material parameters (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)