A new framework for large strain electromechanics based on convex multi-variable strain energies: Variational formulation and material characterisation

[1]  Rodney Hill,et al.  On uniqueness and stability in the theory of finite elastic strain , 1957 .

[2]  Walter Noll,et al.  On the thermostatics of continuous media , 1959 .

[3]  J. Ball.  Convexity conditions and existence theorems in nonlinear elasticity , 1976 .

[4]  T. Belytschko,et al.  A uniform strain hexahedron and quadrilateral with orthogonal hourglass control , 1981 .

[5]  Reint Boer,et al.  Vektor- und Tensorrechnung für Ingenieure , 1982 .

[6]  J. Ball,et al.  W1,p-quasiconvexity and variational problems for multiple integrals , 1984 .

[7]  J. C. Simo,et al.  Variational and projection methods for the volume constraint in finite deformation elasto-plasticity , 1985 .

[8]  R. Rogers.  Nonlocal variational problems in nonlinear electromagneto-elastostatics , 1988 .

[9]  R. Stenberg.  A family of mixed finite elements for the elasticity problem , 1988 .

[10]  B. Dacorogna.  Direct methods in the calculus of variations , 1989 .

[11]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[12]  J. C. Simo,et al.  Geometrically non‐linear enhanced strain mixed methods and the method of incompatible modes , 1992 .

[13]  Robert L. Taylor,et al.  Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems☆ , 1993 .

[14]  Javier Bonet,et al.  A uniform deformation gradient hexahedron element with artificial hourglass control , 1995 .

[15]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[16]  R. Pelrine,et al.  Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation , 1998 .

[17]  Qin Tiehu,et al.  Symmetrizing Nonlinear Elastodynamic System , 1998 .

[18]  Clark R. Dohrmann,et al.  Uniform Strain Elements for Three-Node Triangular and Four-Node Tetrahedral Meshes , 1999 .

[19]  Michael A. Puso,et al.  A highly efficient enhanced assumed strain physically stabilized hexahedral element , 2000 .

[20]  Q. Pei,et al.  High-speed electrically actuated elastomers with strain greater than 100% , 2000, Science.

[21]  Robert L. Taylor,et al.  A mixed-enhanced formulation tetrahedral finite elements , 2000 .

[22]  Ron Pelrine,et al.  Actuation Response of Polyacrylate Dielectric Elastomers , 2001, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[23]  T. Böhlke,et al.  Graphical representation of the generalized Hooke's law , 2001 .

[24]  Ron Pelrine,et al.  Dielectric elastomer artificial muscle actuators: toward biomimetic motion , 2002, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[25]  Alan Weinstein,et al.  Geometry, Mechanics, and Dynamics , 2002 .

[26]  P. Neff,et al.  Invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions , 2003 .

[27]  M. Chial,et al.  in simple , 2003 .

[28]  Mikhail Itskov,et al.  A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function , 2004 .

[29]  Alessandro Reali,et al.  A stability study of some mixed finite elements for large deformation elasticity problems , 2005 .

[30]  R. Ogden,et al.  Nonlinear electroelasticity , 2005 .

[31]  P. Neff,et al.  A variational approach for materially stable anisotropic hyperelasticity , 2005 .

[32]  R. McMeeking,et al.  Electrostatic Forces and Stored Energy for Deformable Dielectric Materials , 2005 .

[33]  A. E. Ehret,et al.  A polyconvex anisotropic strain–energy function for soft collagenous tissues , 2006, Biomechanics and modeling in mechanobiology.

[34]  Ray W. Ogden,et al.  Nonlinear Electroelastic Deformations , 2006 .

[35]  P. Steinmann,et al.  Numerical modelling of non‐linear electroelasticity , 2007 .

[36]  Mikhail Itskov,et al.  A polyconvex hyperelastic model for fiber-reinforced materials in application to soft tissues , 2007 .

[37]  P. Neff,et al.  Anisotropic polyconvex energies on the basis of crystallographic motivated structural tensors , 2008 .

[38]  P. McHugh,et al.  A review on dielectric elastomer actuators, technology, applications, and challenges , 2008 .

[39]  R. Bustamante,et al.  Transversely isotropic non-linear electro-active elastomers , 2009 .

[40]  Z. Suo,et al.  A nonlinear field theory of deformable dielectrics , 2008 .

[41]  Zhigang Suo,et al.  Electrostriction in elastic dielectrics undergoing large deformation , 2008 .

[42]  Andrew M. Stuart,et al.  A First Course in Continuum Mechanics: Bibliography , 2008 .

[43]  Z. Suo,et al.  Propagation of instability in dielectric elastomers , 2008 .

[44]  David H. Wagner,et al.  SYMMETRIC-HYPERBOLIC EQUATIONS OF MOTION FOR A HYPERELASTIC MATERIAL , 2009 .

[45]  R. Ogden,et al.  Nonlinear electroelastostatics: a variational framework , 2009 .

[46]  Ray W. Ogden,et al.  On electric body forces and Maxwell stresses in nonlinearly electroelastic solids , 2009 .

[47]  P. Ciarlet,et al.  Existence theorems in intrinsic nonlinear elasticity , 2010 .

[48]  Paul Steinmann,et al.  A 2-D coupled BEM―FEM simulation of electro-elastostatics at large strain , 2010 .

[49]  P. Neff,et al.  Polyconvex Energies for Trigonal, Tetragonal and Cubic Symmetry Groups , 2010 .

[50]  A. W. Richards,et al.  Constitutive Modeling of Electrostrictive Polymers using a Hyperelasticity-Based Approach , 2010 .

[51]  Jörg Schröder,et al.  Anisotropie polyconvex energies , 2010 .

[52]  R. Bustamante,et al.  On simple constitutive restrictions for transversely isotropic nonlinearly elastic materials and isotropic magneto-sensitive elastomers , 2010 .

[53]  F. Auricchio,et al.  The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations , 2010 .

[54]  R. Ogden,et al.  Electroelastic waves in a finitely deformed electroactive material , 2010 .

[55]  José Merodio,et al.  Constitutive structure in coupled non-linear electro-elasticity: Invariant descriptions and constitutive restrictions , 2011 .

[56]  Peter Wriggers,et al.  A new Mixed Finite Element based on Different Approximations of the Minors of Deformation Tensors , 2011 .

[57]  Zhigang Suo,et al.  Extension limit, polarization saturation, and snap-through instability of dielectric elastomers , 2011 .

[58]  Paul Steinmann,et al.  On 3-D coupled BEM–FEM simulation of nonlinear electro-elastostatics , 2012 .

[59]  Paul Steinmann,et al.  On some mixed variational principles in electro-elastostatics , 2012 .

[60]  Carlo Sansour,et al.  A multiplicative approach for nonlinear electro-elasticity , 2012 .

[61]  C. Keplinger,et al.  Giant voltage-induced deformation in dielectric elastomers near the verge of snap-through instability , 2013 .

[62]  Antonio J. Gil,et al.  Development of a cell centred upwind finite volume algorithm for a new conservation law formulation in structural dynamics , 2013 .

[63]  Koichi Masuda,et al.  Consistent ocean wave energy harvesting using electroactive polymer (dielectric elastomer) artificial muscle generators , 2013 .

[64]  Antonio J. Gil,et al.  Development of a stabilised Petrov–Galerkin formulation for conservation laws in Lagrangian fast solid dynamics , 2014 .

[65]  Miquel Font.  A vertex centred finite volume method for solid dynamics. , 2014 .

[66]  Antonio J. Gil,et al.  A two-step Taylor-Galerkin formulation for fast dynamics , 2014 .

[67]  Antonio J. Gil,et al.  A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics , 2014 .

[68]  Antonio J. Gil,et al.  A vertex centred Finite Volume Jameson-Schmidt-Turkel (JST) algorithm for a mixed conservation formulation in solid dynamics , 2014, J. Comput. Phys..

[69]  P. P. Castañeda,et al.  Fiber-constrained, dielectric-elastomer composites: Finite-strain response and stability analysis , 2014 .

[70]  Rogelio Ortigosa,et al.  A computational framework for polyconvex large strain elasticity for geometrically exact beam theory , 2015, Computational Mechanics.

[71]  Reza Avazmohammadi,et al.  Electromechanical instabilities in fiber-constrained, dielectric-elastomer composites subjected to all-around dead-loading , 2015 .

[72]  Antonio J. Gil,et al.  An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics , 2015, J. Comput. Phys..

[73]  B. Carnes,et al.  A simple, stable, and accurate linear tetrahedral finite element for transient, nearly, and fully incompressible solid dynamics: a dynamic variational multiscale approach , 2016 .

[74]  Rogelio Ortigosa,et al.  A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity , 2015 .

[75]  Christian Miehe,et al.  Computational structural and material stability analysis in finite electro‐elasto‐statics of electro‐active materials , 2015 .

[76]  Mikhail Itskov,et al.  A polyconvex anisotropic free energy function for electro- and magneto-rheological elastomers , 2016 .

[77]  Rogelio Ortigosa,et al.  A new framework for large strain electromechanics based on convex multi-variable strain energies: Finite Element discretisation and computational implementation , 2016 .

[78]  Rogelio Ortigosa,et al.  A computational framework for polyconvex large strain elasticity for geometrically exact beam theory , 2016 .

[79]  Rogelio Ortigosa,et al.  On a tensor cross product based formulation of large strain solid mechanics , 2016 .

[80]  Rogelio Ortigosa,et al.  A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity , 2016 .