Electrostrictive polymer plates as electro-elastic material surfaces: Modeling, analysis, and simulation

2020 ◽  
pp. 1045389X2093564
Author(s):  
Elisabeth Hansy-Staudigl ◽  
Michael Krommer
Keyword(s):  
Free Energy ◽  
Elastic Material ◽  
Three Dimensional ◽  
Direct Approach ◽  
Multiplicative Decomposition ◽  
Additive Decomposition ◽  
Material Surfaces ◽  
Modeling Analysis ◽  
Ponderomotive Forces ◽  
Electrostrictive Polymer

In this article we discuss modeling of electrostrictive polymer plates as electro-elastic material surfaces. A complete direct approach is developed without the need to involve the three-dimensional formulation. Ponderomotive forces and couples as well as constitutive coupling by means of electrostriction are accounted for. We propose a rational formulation for the augmented free energy of electro-elastic material surfaces incorporating electrostriction by a multiplicative decomposition of the surface stretch tensor and an additive decomposition of the surface curvature tensor into elastic and electrical parts. Numerical results computed within the framework of this complete direct approach are compared to results computed with a method that requires the numerical integration of the three-dimensional augmented free energy through the thickness of the plate and to alternative formulations reported in the literature.

scholarly journals A complete direct approach to nonlinear modeling of dielectric elastomer plates

2019 ◽  
Vol 230 (11) ◽  
pp. 3923-3943 ◽  
Author(s):  
Elisabeth Hansy-Staudigl ◽  
Michael Krommer ◽  
Alexander Humer
Keyword(s):  
Free Energy ◽  
Nonlinear Modeling ◽  
Three Dimensional ◽  
Direct Approach ◽  
Thin Plates ◽  
Elastic Behavior ◽  
Dielectric Elastomers ◽  
Novel Approach ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

Abstract In this paper, we present a complete direct approach to nonlinear modeling of thin plates, which are made of incompressible dielectric elastomers. In particular, the dielectric elastomers are assumed to exhibit a neo-Hookean elastic behavior, and the effect of electrostatic forces is incorporated by the purely electrical contribution to the augmented Helmholtz free energy. Our approach does not involve any extraction-type procedure from the three-dimensional energy to derive the plate augmented free energy, but directly postulates the form of this energy for the structural plate problem treated in this paper. Results computed within the framework of this novel approach are compared to results available in the literature as well as to our own three-dimensional finite element solutions. A very good agreement is found.

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

2014 ◽  
Vol 17 (1) ◽  
pp. 93-126 ◽  
Author(s):  
Alessio Gizzi ◽  
Christian Cherubini ◽  
Simonetta Filippi ◽  
Anna Pandolfi
Keyword(s):  
Free Energy ◽  
Solid Mechanics ◽  
Helmholtz Free Energy ◽  
Deformation Gradient ◽  
Material Model ◽  
Multiplicative Decomposition ◽  
Additive Decomposition ◽  
Active Media ◽  
Nonlinear Solid Mechanics ◽  
Computational Electrophysiology

AbstractWe 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.

scholarly journals On the Kirchhoff-Love Hypothesis (Revised and Vindicated)

2021 ◽  
Author(s):  
Olivier Ozenda ◽  
Epifanio G. Virga
Keyword(s):  
Free Energy ◽  
Dimension Reduction ◽  
Three Dimensional ◽  
Energy Functional ◽  
The Other ◽  
Variational Model ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Kinematic Constraint ◽  
Free Energy Functional

AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard $\varGamma $ Γ -convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard $\varGamma $ Γ -convergence also appears to be removed in the cases where contact with that method and ours can be made.

scholarly journals Boundary conditions in topological AdS4/CFT3

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Pietro Benetti Genolini ◽  
Matan Grinberg ◽  
Paul Richmond
Keyword(s):  
Field Theory ◽  
Free Energy ◽  
Boundary Conditions ◽  
Smooth Solution ◽  
Three Dimensional ◽  
Field Theories ◽  
Legendre Transformation ◽  
Generating Functional ◽  
Holographic Duals

Abstract We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional $$ \mathcal{N} $$ N = 4 field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

scholarly journals Multi-Funnel Landscape of the Fold-Switching Protein RfaH-CTD

2017 ◽  
Author(s):  
Nathan A. Bernhardt ◽  
Ulrich H.E. Hansmann
Keyword(s):  
Free Energy ◽  
Transcription Factor ◽  
Biological Function ◽  
Double Helix ◽  
Energy Landscape ◽  
Three Dimensional ◽  
Conversion Process ◽  
Free Energy Landscape ◽  
Enhanced Sampling ◽  
Helix Bundle

AbstractProteins such as the transcription factor RfaH can change biological function by switching between distinct three-dimensional folds. RfaH regulates transcription if the C-terminal domain folds into a double helix bundle, and promotes translation when this domain assumes a β-barrel form. This fold-switch has been also observed for the isolated domain, dubbed by us RfaH-CTD, and is studied here with a variant of the RET approach recently introduced by us. We use the enhanced sampling properties of this technique to map the free energy landscape of RfaH-CTD and to propose a mechanism for the conversion process.TOC Image

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