Derivation of the localization and homogenization conditions for electro-mechanically coupled problems

The challenges in high-performance mechatronics and micromechatronics are the modeling, analysis and design of electro-mechanical systems. Piezoceramics are the prototype of materials which exhibit characteristic electro-mechanical coupling effects used in a wide range of industrial applications. In complex designs of piezoceramic devices concentrations of stresses and electric field occur, which may lead to nonlinear electro-mechanical responses, typical for the large signal range. The challenge in the field of ferroelectric ceramics is the modeling of the complicated interactions between electrical and mechanical quantities on the macroscale, which are caused by switching processes on the microscale. In this paper we derive the basic equations for a possible direct two-scale homogenization procedure of electro-mechanically coupled boundary value problems.