A new framework for large strain electromechanics based on convex multi-variable strain energies: conservation laws, hyperbolicity and extension to electro-magneto-mechanics

DOI10.1016/j.cma.2016.05.019zbMath1439.74122OpenAlexW2409937901MaRDI QIDQ2308619

Rogelio Ortigosa, Antonio J. Gil

Publication date: 3 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://cronfa.swan.ac.uk/Record/cronfa28513

zbMATH Keywords

conservation lawshyperbolicitypolyconvexitydielectric elastomersnonlinear electro-elasticitymagneto active polymers

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Electromagnetic effects in solid mechanics (74F15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A computational framework for polyconvex large strain elasticity for geometrically exact beam theory
• A vertex centred finite volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics
• A new mixed finite element based on different approximations of the minors of deformation tensors
• Riemann solutions and spacetime discontinuous Galerkin method for linear elastodynamic contact
• A multiplicative approach for nonlinear electro-elasticity
• On electric body forces and Maxwell stresses in nonlinearly electroelastic solids
• Existence theorems in intrinsic nonlinear elasticity
• On simple constitutive restrictions for transversely isotropic nonlinearly elastic materials and isotropic magneto-sensitive elastomers
• Anisotropic polyconvex energies on the basis of crystallographic motivated structural tensors
• A nonlinear field theory of deformable dielectrics
• Development of a stabilised Petrov-Galerkin formulation for conservation laws in Lagrangian fast solid dynamics
• On uniqueness and stability in the theory of finite elastic strain
• \(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
• Transversely isotropic nonlinear electro-active elastomers
• Fiber-constrained, dielectric-elastomer composites: finite-strain response and stability analysis
• Nonlinear electroelastostatics: a variational framework
• A new finite element formulation for computational fluid dynamics. I: Symmetric forms of the compressible Euler and Navier-Stokes equations and the second law of thermodynamics
• A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Convexity conditions and existence theorems in nonlinear elasticity
• Systems of conservation laws of mixed type
• An iterative Riemann solver for systems of hyperbolic conservation laws, with application to hyperelastic solid mechanics.
• A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
• A first order hyperbolic framework for large strain computational solid dynamics. I: Total Lagrangian isothermal elasticity
• A computational framework for polyconvex large strain elasticity
• Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure
• Nonlinear electroelasticity
• A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function
• Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions.
• An upwind vertex centred finite volume solver for Lagrangian solid dynamics
• A variational approach for materially stable anisotropic hyperelasticity
• A first order hyperbolic framework for large strain computational solid dynamics. II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
• A new framework for large strain electromechanics based on convex multi-variable strain energies: variational formulation and material characterisation
• A new framework for large strain electromechanics based on convex multi-variable strain energies: finite element discretisation and computational implementation
• Nonlinear electroelastic deformations
• On the thermostatics of continuous media
• Quasi-convexity and the lower semicontinuity of multiple integrals
• Nonlinear Elasticity
• Computational structural and material stability analysis in finite electro-elasto-statics of electro-active materials
• Electrostatic Forces and Stored Energy for Deformable Dielectric Materials
• Electromechanical instabilities in fiber-constrained, dielectric-elastomer composites subjected to all-around dead-loading
• Electroelastic waves in a finitely deformed electroactive material
• A First Course in Continuum Mechanics
• Nonlinear Solid Mechanics for Finite Element Analysis: Statics
• Direct methods in the calculus of variations

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