Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space

Pelteret, Jean-Paul; Davydov, Denis; McBride, Andrew; Vu, Duc Khôi; Steinmann, Paul

doi:10.1002/nme.5254

Cited by 57 publications

(49 citation statements)

References 110 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tri-linear approximations are used for the (scalar) electric potential ϕ h . This is a non-standard choice for the problem of E-Elasticity where equal-order approximations are typically used for ϕ h and ϕ h [34]. We choose to break with convention to ensure that the flexoelectric contribution to the energy in Eq.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In a key contribution, Yvonnet and Liu [32] extended the nonlinear theory of electroelasticity [see e.g. [33][34][35], and references therein] to account for the coupling between polarization and the gradient of the deformation gradient G -a third-order tensor. A non-standard, C 1 -continuous, Argyris-triangle-based finite element formulation was used.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modelling the flexoelectric effect in solids

McBride¹,

Davydov²,

Steinmann³

2019

Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications

View full text Add to dashboard Cite

Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate resulting higher-order gradient contributions arising in this highly-nonlinear and coupled problem within a classical finite element setting. The formulation accounts for all material and geometric nonlinearities, as well as the coupling between the mechanical, electrical and micromorphic fields. The highly-nonlinear system of governing equations are derived using the Dirichlet principle and solved using the finite element method. A series of numerical examples serve to elucidate the theory and to provide insight into this fascinating effect.1 Flexo and Piezo derive from the latin words flecto -to bend -and piezein -to squeeze.

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling the flexoelectric effect in solids

McBride¹,

Davydov²,

Steinmann³

2019

Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications

View full text Add to dashboard Cite

show abstract

“…The more standard four (and three) displacement-potential-Jacobianpressure [90] (and displacement-potential-pressure) [65] variational principles and new more sophisticated extended Hu-Washizu mixed variational principles obtained following the ideas in Reference [1] will be presented in this Section.…”

Section: Variational Formulationsmentioning

confidence: 99%

“…Some authors [90] advocate for a four-field mixed variational principle where the geometry, the electric potential, the Jacobian and the pressure are the unknown variables, defined as…”

Section: Standard Displacement and Electric Potential Based Variationmentioning

confidence: 99%

A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Ortigosa

Gil

Lee

2016

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Please cite this article as: R. Ortigosa, A.J. Gil, C.H. Lee, A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies, Comput. Methods Appl. Mech. Engrg. (2016), http://dx.doi.org/10. 1016/j.cma.2016.06.025 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies. AbstractThe series of papers published by Gil and Ortigosa [1-3] introduced a new convex multi-variable variational and computational framework for the numerical simulation of Electro Active Polymers (EAPs) in scenarios characterised by extreme deformations and/or extreme electric fields. Building upon this body of work, five key novelties are incorporated in this paper. First, a generalisation of the concept of multi-variable convexity to energy functionals additively decomposed into isochoric and volumetric components. This decomposition is typical of nearly and truly incompressible materials, group which represents the majority of the most relevant EAPs. Second, convexification or regularisation strategies are applied to a priori non-convex multi-variable isochoric functionals to yield physically meaningful convex multi-variable functionals. Third, based on the mixed variational principles introduced in Reference [1] in the context of compressible electro-elasticity, a novel extended Hu-Washizu mixed variational principle for nearly and truly incompressible scenarios is presented. From the computational standpoint, a static condensation procedure is applied in order to condense out the element-wise extra fields, the resulting formulation having a comparable cost to the more standard three-field displacement-potential-pressure mixed formulation. Fourth, the computational framework for the three-field mixed variational principle in nearly and truly incompressible scenarios is also presented. In this case, the novelty resides in the consideration of convex multi-

show abstract

“…To accurately characterize the transient magnetic field distribution over the domains covering the magnetic hydrogel and its surrounding solvent, the magnetic intensity vector H is employed as the independent variable. If the linear magnetic behavior of the magnetic hydrogel is considered, the augmented free energy dentistry  in reference configuration is given by [233] )] det( At the inlet of the fluid channel, we have…”

Section: Long-time Scalementioning

confidence: 99%

Computational investigation of magnetic hydrogels and elastomers

Liu¹

View full text Add to dashboard Cite

Computational electro‐elasticity and magneto‐elasticity for quasi‐incompressible media immersed in free space

Cited by 57 publications

References 110 publications

Modelling the flexoelectric effect in solids

Modelling the flexoelectric effect in solids

A computational framework for large strain nearly and truly incompressible electromechanics based on convex multi-variable strain energies

Computational investigation of magnetic hydrogels and elastomers

Contact Info

Product

Resources

About