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Computational Mechanics

, Volume 50, Issue 2, pp 229–244 | Cite as

Two-scale homogenization of electromechanically coupled boundary value problems

Consistent linearization and applications
  • Jörg SchröderEmail author
  • Marc-André Keip
Original Paper

Abstract

The contribution addresses a direct micro-macro transition procedure for electromechanically coupled boundary value problems. The two-scale homogenization approach is implemented into a so-called FE2-method which allows for the computation of macroscopic boundary value problems in consideration of microscopic representative volume elements. The resulting formulation is applicable to the computation of linear as well as nonlinear problems. In the present paper, linear piezoelectric as well as nonlinear electrostrictive material behavior are investigated, where the constitutive equations on the microscale are derived from suitable thermodynamic potentials. The proposed direct homogenization procedure can also be applied for the computation of effective elastic, piezoelectric, dielectric, and electrostrictive material properties.

Keywords

Homogenization FE2-method Effective properties Electromechanical coupling Piezoelectricity Electrostriction 

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Civil Engineering, Faculty of EngineeringInstitute of MechanicsEssenGermany

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