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Electro-sensitive (ES) Materials

Nonlinear Electroelastic Deformations
Electro-sensitive (ES) elastomers form a class of smart materials whose mechanical properties can be changed rapidly by the application of an electric field. These materials have attracted considerable interest recently because of their potential for providing relatively cheap and light replacements for mechanical devices, such as actuators, and also for the development of artificial muscles. In this project we are concerned with a theoretical framework for the analysis of boundary-value problems that underpin the applications of the associated electromechanical interactions. We confine attention to the static situation and summarize the governing equations for a solid material capable of large electroelastic deformations. The general constitutive laws for the Cauchy stress tensor and the electric field vectors for an isotropic electroelastic material are developed in a compact form following recent work by the authors. The equations are then applied, in the case of an incompressible material, to the solution of a number of representative boundary-value problems. Specifically, we consider the influence of a radial electric field on the azimuthal shear response of a thick-walled circular cylindrical tube, the extension and inflation characteristics of the same tube under either a radial or an axial electric field (or both fields combined), and the effect of a radial field on the deformation of an internally pressurized spherical shell.


  • Dorfmann L, Ogden RW (2019) Instabilities of soft dielectrics. Phil Trans R Soc A 377:20180077.
  • Dorfmann L, Ogden RW (2019) Electroelastic plate instabilities based on the Stroh method in terms of the energy function Ω*(F, DL). Mech Res Commun 96:67-74.

  • Dorfmann L, Ogden RW (2018) The effect of deformation dependent permittivity on the elastic response of a finitely deformed dielectric tube. Mech Res Commun 93:47-57.
  • Dorfmann L, Saccomandi G, Salvatori MC (2018) On the use of universal relations in modeling nonlinear electro-elastic materials. Int J Mech Sci 149:577-582.
  • Fu Y, Xie Y-X, Dorfmann L (2018) A reduced model for electrodes-coated dielectric plates. Int J Nonlinear Mech 106:60-69.
  • Fu Y, Dorfmann L, Xie Y (2018) Localized necking of a dielectric membrane. Extreme Mechanics Letters 21:44-48.
  • Dorfmann L, Ogden RW (2017) Nonlinear electroelasticity: materials, continuum theory and applications. Proc R Soc A 473:20170311.
  • Dorfmann L, Ogden RW (2015) Corrigendum to: Instabilities of an electroelastic plate. Int J Eng Sci 92:95-96.
  • Dorfmann L, Ogden RW (2014) Nonlinear response of an electroelastic shell. Int J Eng Sci 85:163-174.
  • Dorfmann L, Ogden RW (2014) Instabilities of an electroelastic plate. Int J Eng Sci 77:79-101.
  • Dorfmann A, Ogden RW (2010) Electroelastic waves in a finitely deformed electroactive material. IMA J Appl Math 75:603-636.
  • Dorfmann A, Ogden RW (2010) Nonlinear Electroelasticity: Incremental Equations and Stability, Int J Eng Sci 48:1-14.
  • Bustamante R, Dorfmann A, Ogden RW (2009) On Electric Body Forces and Maxwell Stresses in nonlinearly Electroelastic Solids. Int J Eng Sci 47:1131-1141.
  • Bustamante R, Dorfmann A, Ogden RW (2009) Nonlinear Electroelastostatics: A Variational Framework. Z Angew Math Phys 60:154-177.
  • Dorfmann A, Ogden RW (2006) Nonlinear Electroelastic Deformations. J Elast 82:99-127.
  • Dorfmann A, Ogden RW (2005) Nonlinear Electroelasticity. Acta Mech 174 (2005), 167-183.