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Computational Nonlinear Electro-Elasticity — Getting Started —

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Mechanics and Electrodynamics of Magneto- and Electro-elastic Materials

Part of the book series: CISM International Centre for Mechanical Sciences ((CISM,volume 527))

Abstract

The intention of this contribution is to provide the basic ingredients needed for the formulation and computation of nonlinear problems in electro-elasticity. Thus, firstly the underlying variational setting of nonlinear electro-elasticity is outlined. Then, secondly the appropriate discretization in terms of the finite element method combined with the boundary element method together with the corresponding solution method are discussed in much detail. Finally the solution of some nonlinear boundary value problems demonstrates the applicability of the derived methods and highlights the characteristic features of coupled problems in nonlinear electro-elasticity.

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Bibliography

  • Y. Bar-Cohen. Electro-active polymers: current capabilities and challenges. Proc. SPIE — Smart Structures and Materials: Electroactive Polymer Actuators and Devices 4695:1–7, 2002.

    Google Scholar 

  • I. A. Brigdanov and A. Dorfmann. Mathematical modeling of magneto-sensitive elastomers. Int. J. Solids Struct. 40:4659–4674, 2003.

    Article  Google Scholar 

  • F. Carpi, P. Chiarelli, A. Mazzoldi, and D. Rossi. Electromechanical characterisation of dielectric elastomer planar actuators: comparative evaluation of different electrode materials and different counterloads. Sens. Actuators A 107: 85–95, 2003.

    Article  Google Scholar 

  • A. Dorfmann and I. A. Brigdanov. Constitutive modelling of magneto-sensitive Cauchy elastic solids. Comp. Mater. Sci. 29:270–282, 2004.

    Article  Google Scholar 

  • A. Dorfmann and R. W. Ogden. Magnetoelastic modelling of elastomers. Eur. J. Mech. A/Solids 22:497–507, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  • A. Dorfmann and R. W. Ogden. Nonlinear magnetoelastic deformations of elastomers. Acta Mech. 167:13–28, 2004.

    Article  MATH  Google Scholar 

  • A. Dorfmann and R. W. Ogden. Nonlinear magnetoelastic deformations. Q. J. Mech. Appl. Math. 57:599–622, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  • A. Dorfmann and R. W. Ogden. Nonlinear electroelasticity. Acta Mech. 174:167–183, 2005.

    Article  MATH  Google Scholar 

  • A. Dorfmann and R. W. Ogden. Some problems in nonlinear magnetoelasticity. ZAMP 56:718–745, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  • J. Eckerle, J. S. Stanford, J. Marlow, R. Schmidt, S. Oh, T. Low, and V. Shastri. A biologically inspired hexapedal robot using field-effect electroactive elastomer artificial muscles. Proc. SPIE — Smart Structures and Materials: Industrial and Commercial Applications of Smart Structures Technologies 4332:269–280, 2001.

    Google Scholar 

  • A. C. Eringen and G. A. Maugin. Electrodynamics of Continua. Springer, New York, 1990.

    Google Scholar 

  • N. Goulbourne, M. Frecker, E. Mockensturm, and A. Snyder. Modeling of a dielectric elastomer diaphragm for a prosthetic blood pump. Proc. SPIE — mart Structures and Materials: Electroactive Polymer Actuators and Devices 5051:319–331, 2003.

    Google Scholar 

  • D. J. Griffiths. Introduction to Electrodynamics, 3rd edition. Prentice Hall, New Jersey, 1998.

    Google Scholar 

  • R. Heydt, R. Kornbluh, R. Pelrine, and V. Mason. Design and performance of an electrostrictive-polymer-film acoustic actuator. J. Sound Vib. 215:297–311, 1998.

    Article  Google Scholar 

  • J. D. Jackson. Classical Electrodynamics, 3rd edition John Wiley & Sons, New York, 1999.

    MATH  Google Scholar 

  • H. Kim, S. Oh, K. Hwang, H. Choi, J. W. Jeon, and J. D. Nam. Actuator model of electrostrictive polymers (EPs) for microactuators. Proc. SPIE — Smart Structures and Materials: Electroactive Polymer Actuators and Devices 4329:482–490, 2001.

    Google Scholar 

  • G. Kofod. Dielectric Elastomer Actuators, PhD Thesis, Riso-R-1286 (EN), Technical University of Denmark, 2001.

    Google Scholar 

  • G. Kofod and P. Sommer-Larsen. Silicone dielectric elastomer actuators: Finite-elasticity model of actuation. Sens. Actuators A 122:273283, 2005.

    Google Scholar 

  • G. Kofod G, P. Sommer-Larsen, R. Kornbluh, and R. Pelrine. Actuation response of polyacrylate dielectric elastomers. Proc. SPIE — Smart Structures and Materials: Electroactive Polymer Actuators and Devices 4329:141–147, 2001.

    Google Scholar 

  • A. Kovetz. Electromagnetic Theory. Oxford University Press, 2000.

    Google Scholar 

  • S. P. Lacour, H. Prahlad, R. Pelrine, and S. Wagner. Mechatronic system of dielectric elastomer actuators addressed by thin film photoconductors on plastic. Sens. Actuators A 111:288–292, 2004.

    Article  Google Scholar 

  • J. Loverich, I. Kanno, and H. Kotera. Concepts for a new class of all-polymer micropumps. Lab Chip 6:1147–1154, 2006.

    Article  Google Scholar 

  • G. A. Maugin. Continuum Mechanics of Electromagnetic Solids. North-Holland, Amsterdam, 1988.

    MATH  Google Scholar 

  • R. M. McMeeking and C. M. Landis. Electrostatic forces and stored energy for deformable dielectric materials. ASME J. Appl. Mech. 72:581–590, 2005.

    Article  MATH  Google Scholar 

  • Q. Pei, R. Pelrine, S. Stanford, R. Kornbluh, and M. Rosenthal. Electroelastomer rolls and their application for biomimetic walking robots. Synth. Met. 135/136:129–131, 2003.

    Article  Google Scholar 

  • R. Pelrine, R. Kornbluh, Q. Pei, S. Stanford, S. Oh, and J. Eckerle. Dielectric elastomer artificial muscle actuators: Toward biomimetic motion. Proc. SPIE — Smart Structures and Materials: Electroactive Polymer Actuators and Devices 4332:269–280, 2002.

    Google Scholar 

  • P. Sommer-Larsen, G. Kofod, M. Shridhar, M. Benslimane, and P. Gravesen. Performance of dielectric elastomer actuators and materials. Proc. SPIE — Smart Structures and Materials: Electroactive Polymer Actuators and Devices 4695:158–166, 2002.

    Google Scholar 

  • R. Trujillo, J. Mou, P. E. Phelan, and D. S. Chau. Investigation of electrostrictive polymers as actuators for mesoscale devices. Int. J. Adv. Manuf. Tech. 23:176–182, 2004.

    Article  Google Scholar 

  • D. K. Vu and P. Steinmann. A 2d coupled BEM-FEM simulation of electro-elastostatics at large strain. Comp. Meth. Appl. Mech. Engng. 199:1124–1133, 2010.

    Article  MathSciNet  Google Scholar 

  • D. K. Vu, P. Steinmann, and G. Possart. Numerical modelling of nonlinear electroelasticity. Int. J. Num. Meth. Engng. 70:685–704, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  • A. Wingert, M. D. Lichter, and S. Dubowsky. On the design of large degree-of-freedom digital mechatronic devices based on bistable dielectric elastomer actuators. IEEE/ASME Transactions on Mechatronics 11:448–456, 2006.

    Article  Google Scholar 

  • A. Wingert, M. D. Lichter, S. Dubowsky, and M. Hafez. Hyper-redundant robot manipulators actuated by optimized binary-dielectric polymers. Proc. SPIE — Smart Structures and Materials: Electroactive Polymer Actuators and Devices 4695:415–423, 2002.

    Google Scholar 

  • R. Zhang, P. Lochmatter, A. Kunz, and G. Kovacs. Spring roll dielectric elastomer actuators for a portable force feedback glove. Proc. SPIE — Electroactive Polymer Actuators and Devices (EAPAD) 6168:505–516, 2006.

    Google Scholar 

  • X. Zhang, C. Löwe, M. Wissler, B. Jähne, and G. Kovacs. Dielectric elastomers in actuator technology. Adv. Eng. Mater. 7:361–367, 2005.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Erlangen-Nuremberg, Germany

    Paul Steinmann (Chair of Applied Mechanics)

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  1. Paul Steinmann
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Editor information

Editors and Affiliations

  1. University of Glasgow, UK

    Ray W. Ogden

  2. University of California at Berkeley, USA

    David J. Steigmann

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Steinmann, P. (2011). Computational Nonlinear Electro-Elasticity — Getting Started —. 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_5

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  • DOI: https://doi.org/10.1007/978-3-7091-0701-0_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-0700-3

  • Online ISBN: 978-3-7091-0701-0

  • eBook Packages: EngineeringEngineering (R0)

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