Advertisement

A Generalized Framework and a Multiplicative Formulation of Electro-Mechanical Coupling

  • Carlo Sansour
  • Sebastian Skatulla
  • A. Arunachalakasi
Chapter
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)

Abstract

Electro-active polymers (EAP) recently attracted much interest because, upon electrical loading, EAP exhibit a large amount of deformation while sustaining large forces. On the other hand, generalized continuum frameworks are relevant to electro-mechanical coupled problems as they naturally incorporate couples or higher order stresses and can describe scale effects. Here, we want to adopt a strain gradient approach based on the generalized continuum framework as formulated in (Sansour in J. Phys. IV, Proc. 8:341–348, 1998; Sansour and Skatulla in Geomech. Geoeng. 2:3–15, 2007) and extend it to encompass the electro-mechanically coupled behavior of EAP. A new aspect of the electro-mechanical formulation relates to the multiplicative decomposition of the deformation gradient, well known from plasticity, into a purely elastic part and a further part which relates to the electric field. The formulation is elegant, makes for clarity and is numerically efficient. A numerical example of coupled large deformations is presented as well.

Keywords

Deformation Gradient Electric Displacement Move Least Square Multiplicative Decomposition Constitutive Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arruda, E.M., Boyce, M.C.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41(2), 389–412 (1993) CrossRefGoogle Scholar
  2. 2.
    Griffiths, D.: Introduction to Electrodynamics. Prentice-Hall, New Jersey (1999) Google Scholar
  3. 3.
    Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1999) MATHGoogle Scholar
  4. 4.
    Kovetz, A.: Electromagnetic Theory. Oxford Science Publications, New York (2000) MATHGoogle Scholar
  5. 5.
    Maugin, G.A.: Continuum Mechanics of Electromagnetic Solids. North-Holland, Amsterdam (1988) MATHGoogle Scholar
  6. 6.
    Sansour, C.: A unified concept of elastic-viscoplastic Cosserat and micromorphic continua. J. Phys. IV Proc. 8, 341–348 (1998) Google Scholar
  7. 7.
    Sansour, C., Skatulla, S.: A higher gradient formulation and meshfree-based computation for elastic rock. Geomech. Geoeng. 2, 3–15 (2007) CrossRefGoogle Scholar
  8. 8.
    Sansour, C., Skatulla, S., Arunachalakasi, A.: A multiplicative formulation for electromechanical coupling at finite strains (2009, to appear) Google Scholar
  9. 9.
    Skatulla, S., Arunachalakasi, A., Sansour, C.: A nonlinear generalized continuum approach for electro-elasticity including scale effects. J. Mech. Phys. Solids 57, 137–160 (2009) MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Vu, D.K., Steinmann, P., Possart, G.: Numerical modelling of non-linear electroelasticity. Int. J. Numer. Methods Eng. 70, 685–704 (2007) CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Carlo Sansour
    • 1
  • Sebastian Skatulla
    • 2
  • A. Arunachalakasi
    • 3
  1. 1.Division of Materials, Mechanics, and StructuresThe University of NottinghamNottinghamUK
  2. 2.CERECAM, Department of Civil EngineeringThe University of Cape TownRondeboschSouth Africa
  3. 3.Department of Applied MechanicsIndian Institute of Technology MadrasChennaiIndia

Personalised recommendations