Abstract
A continuum model for dielectric elastomers is proposed on the basis of a micromorphic theory of electroelasticity. A biaxial microstretch deformation is considered to describe macrostretch and electric polarization due to applied mechanical loads and electric fields. A statistical isotropic condition is exploited to express the dependence of strain tensors on microstretch, and the equilibrium balance laws are given for micro- and macrodeformation and the electric potential. A one-dimensional problem is formulated to model a layer of dielectric elastomer subject to electric potential and mechanical traction. Some numerical results are obtained, which show consistence with the expected electroelastic physical behavior of such structures.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dorfmann, L., Ogden, R.W.: Nonlinear electroelasticity. Acta Mech. 174, 167–183 (2005)
Jimenez, S.M.A., McMeeking, R.M.: Deformation dependent dielectric permittivity and its effects on actuator performance and stability. Int. J. Nonlinear Mech. 57, 183–191 (2013)
Dorfmann, L., Ogden, R.W.: Nonlinear electroelasticity: material properties, continuum theory and applications. Proc. R. Soc. A 473, 20170311 (2017)
Cohen, N., deBotton, G.: The electromechanical response of polymer networks with long-chain molecules. Math. Mech. Solids 20, 721–728 (2014)
Cohen, N., Dayal, K., deBotton, G.: Electroelasticity of polymer networks. J. Mech. Phys. Solids 92, 105–126 (2016)
Itskov, M., Khiêm, V., Waluyo, S.: Electroelasticity of dielectric elastomers based on molecular chain statistics. Math. Mech. Solids 24, 862–873 (2019)
Eringen, A.C.: Microcontinuum Field Theories I—Foundations and Solids. Springer, New York (1999)
Romeo, M.: Micromorphic continuum model for electromagnetoelastic solids. Z.A.M.P. 62, 513–527 (2011)
Romeo, M.: A microstructure continuum approach to electromagneto-elastic conductors. Contin. Mech. Thermodyn. 28, 1807–1820 (2016)
Romeo, M.: Polarization in dielectrics modeled as micromorphic continua. Z.A.M.P. 66, 1233–1247 (2015)
Romeo, M.: A microstretch description of electroelastic solids with application to plane waves. Math. Mech. Solids 24, 2181–2196 (2019)
Romeo, M.: A variational formulation for electroelasticity of microcontinua. Math. Mech. Solids 20, 1234–1250 (2015)
Chen, Y., Lee, J.D.: Determining material constants in micromorphic theory through phonon dispersion relations. Int. J. Eng. Sci. 41, 871–886 (2003)
Villanueva-García, M., Robles, J., Martínez-Richa, A.: Quadrupolar moment calculations and mesomorphic character of model dimeric liquid crystals. Comput. Mater. Sci. 22, 300–308 (2001)
Schlögl, T., Leyendecker, S.: A polarization based approach to model the strain dependent permittivity of dielectric elastomers. Sens. Actuators A 267, 156–163 (2017)
Zhao, X., Hong, W., Suo, Z.: Electromechanical hysteresis and coexistent states in dielectric elastomers. Phys. Rev. B 76, 134113 (2007)
Zhao, X., Suo, Z.: Electrostriction in elastic dielectrics undergoing large deformations. J. Appl. Phys. 104, 123530 (2008)
Wissler, M., Mazza, E.: Electromechanical coupling in dielectric elastomer actuators. Sens. Actuators A 138, 384–393 (2007)
Li, B., et al.: Effects of mechanical pre-stretch on the stabilization of dielectric elastomer actuation. J. Phys. D Appl. Phys. 44, 155301 (2011)
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Romeo, M. A microstretch continuum approach to model dielectric elastomers. Z. Angew. Math. Phys. 71, 44 (2020). https://doi.org/10.1007/s00033-020-1266-0
Received:
Published:
DOI: https://doi.org/10.1007/s00033-020-1266-0