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Theoretical and Numerical Modeling of Nonlinear Electromechanics with applications to Biological Active Media

Published online by Cambridge University Press:  28 November 2014

Alessio Gizzi ,
Christian Cherubini ,
Simonetta Filippi  and
Anna Pandolfi
Alessio Gizzi
Affiliation:
Nonlinear Physics and Mathematical Modeling Laboratory
Christian Cherubini*
Affiliation:
Nonlinear Physics and Mathematical Modeling Laboratory International Center for Relativistic Astrophysics Network, I.C.R.A.Net, University Campus Bio-Medico of Rome, Via A. del Portillo 21, 00128 Rome, Italy
Simonetta Filippi
Affiliation:
Nonlinear Physics and Mathematical Modeling Laboratory International Center for Relativistic Astrophysics Network, I.C.R.A.Net, University Campus Bio-Medico of Rome, Via A. del Portillo 21, 00128 Rome, Italy
Anna Pandolfi
Affiliation:
Civil and Environmental Engineering Department Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
*
*Email addresses:[email protected](A. Gizzi), [email protected](C. Cherubini), [email protected](S. Filippi), [email protected](A. Pandolfi)
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Abstract

We present a general theoretical framework for the formulation of the nonlinear electromechanics of polymeric and biological active media. The approach developed here is based on the additive decomposition of the Helmholtz free energy in elastic and inelastic parts and on the multiplicative decomposition of the deformation gradient in passive and active parts. We describe a thermodynamically sound scenario that accounts for geometric and material nonlinearities. In view of numerical applications, we specialize the general approach to a particular material model accounting for the behavior of fiber reinforced tissues. Specifically, we use the model to solve via finite elements a uniaxial electromechanical problem dynamically activated by an electrophysiological stimulus. Implications for nonlinear solid mechanics and computational electrophysiology are finally discussed.

Keywords

46.25.Hf05.70.Ce62.20.F-81.40.Jj87.10.PqActive electromechanical mediaHelmholtz free energymultiplicative decomposition of the deformation gradientactive deformationactive stress
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 1 , January 2015 , pp. 93 - 126
Copyright
Copyright © Global Science Press Limited 2015 

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