Abstract
We give a concise treatment of the interaction of a nonlinear elastic membrane with an electrostatic field. The focus is on the generation of reduced dimension model equations for continuum electrodynamics based on the methodology used by (2007) in the purely mechanical context. We formulate the background theory for reduced dimension models pertaining to continuum electrostatics and implement the resulting equations numerically for an example problem of practical interest.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Y. Bar-Cohen. Electroactive Polymer (EAP) Actuators as Artificial Muscles — Reality, Potential and Challenges. SPIE Press, 2004.
F. Carpi, A. Migliore, and G. Serra. Helical dielectric elastomer actuators. Smart Mater. Struct. 14:1210–1216, 2005.
F. Carpi, C. Salaris, and D. De Rossi. Folded dielectric elastomer actuators. Smart Mater. Struct. 16:S300–S305, 2007.
D. Griffiths. Introduction to Electrodynamics. Pearson Education Inc., 1999.
A. Kovetz. Electromagnetic Theory. Oxford University Press, 2000.
I.-S. Liu. Continuum Mechanics. Springer, 2002.
E. Mockensturm and N. Goulbourne. Dynamic response of dielectric elastomers. Int. J. Non-Linear Mech. 41:388–395, 2005.
R. E. Pelrine, R. D. Kornbluh, and J. P. Joseph. Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation. Sensors and Actuators A: Physical 64:77–85, 1998.
M. Shahinpoor, Y. Bar-Cohen, J. O. Simpson, and J. Smith. Ionic polymer-metal composites (IPMCs) as biomimetic sensors, actuators and artificial muscles — a review. Smart Mater. Struct. 7:15–30, 1998.
D. J. Steigmann. Equilibrium theory for magnetic elastomers and magnetoelastic membranes. Int. J. Non-Linear Mech. 39:1193–1216, 2004.
D. J. Steigmann. Thin-plate thoery for large elastic deformations. Int. J. Non-Linear Mech. 42:233–240, 2007.
D. J. Steigmann. On the formulation of balance laws for electromagnetic continua. Math. Mech. Solids 14:390–402, 2009.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 CISM, Udine
About this chapter
Cite this chapter
Edmiston, J., Steigmann, D. (2011). Analysis of Nonlinear Electrostatic Membranes. In: Ogden, R.W., Steigmann, D.J. (eds) Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials. CISM International Centre for Mechanical Sciences, vol 527. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0701-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-7091-0701-0_4
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-0700-3
Online ISBN: 978-3-7091-0701-0
eBook Packages: EngineeringEngineering (R0)