Constitutive Modeling of Electrostrictive Polymers using a Hyperelasticity-Based Approach

The use of constitutive equations to describe the electro-mechanical behavior of electrostrictive materials began over 100 years ago. While these equations have been used to model a host of ceramic-based and polymer-based electroactive materials, a fully-characterized model has not yet been developed to predict the response of transversely-isotropic polymer electrostrictives. A constitutive model is developed within a thermodynamic and hyperelastic framework that incorporates the transversly-isotropic material symmetry that is present in many polymer-based electrostrictives. The resulting constitutive model is characterized for three electrostrictive polymer systems using empirical data that is available in the literature. The model has a relatively simple functional form that is easily adaptable to other polymer electrostrictive material systems.

[1]  J. Swinburne.  Electromagnetic Theory , 1894, Nature.

[2]  Sur un cas particulier de déformation électrique d'un diélectrique solide isotrope , 1901 .

[3]  L. T. More.  I. On electrostriction , 1903 .

[4]  Note on the End Effect in the Electrostriction of Cylindrical Condensers , 1916 .

[5]  L'électrostriction dans les liquides très peu biréfringents , 1924 .

[6]  Sur la thorie de l'lectrostriction dans les liquides isolants , 1925 .

[7]  Ny Tsi Ze.  Étude expérimentale des déformations et des changements de propriétés optiques du quartz sous l'influence du champ électrique , 1928 .

[8]  Electroelastic and Pyro-Electric Phenomena , 1930, Proceedings of the Institute of Radio Engineers.

[9]  W. P. Mason,et al.  Piezoelectric Crystals and Their Applications to Ultrasonics , 1951 .

[10]  A. F. Devonshire.  Theory of ferroelectrics , 1954 .

[11]  R. Toupin.  The Elastic Dielectric , 1956 .

[12]  J. Nye.  Physical Properties of Crystals: Their Representation by Tensors and Matrices , 1957 .

[13]  C. Truesdell,et al.  The Classical Field Theories , 1960 .

[14]  E. M. Lifshitz,et al.  Electrodynamics of continuous media , 1961 .

[15]  A. Cemal Eringen,et al.  Nonlinear theory of continuous media , 1962 .

[16]  A. Hippel,et al.  Dielectrics and Waves , 1966 .

[17]  A. Cemal Eringen,et al.  Mechanics of continua , 1967 .

[18]  A.J.M. Spencer,et al.  Theory of invariants , 1971 .

[19]  H. F. Tiersten,et al.  On the nonlinear equations of thermo-electroelasticity , 1971 .

[20]  L. G. Suttorp,et al.  Foundations of electrodynamics , 1972 .

[21]  H. F. Tiersten,et al.  Nonlinear electroelastic equations for small fields superposed on a bias , 1973 .

[22]  Y. Pao.  IV – Electromagnetic Forces in Deformable Continua , 1978 .

[23]  Z. Meng,et al.  Determination of the electrostriction tensor components in single‐crystal CaF2 from the uniaxial stress dependence of the dielectric permittivity , 1985 .

[24]  Lallit Anand,et al.  Moderate deformations in extension-torsion of incompressible isotropic elastic materials , 1986 .

[25]  Gérard A. Maugin,et al.  Continuum Mechanics of Electromagnetic Solids , 1989 .

[26]  Gérard A. Maugin,et al.  Electrodynamics of Continua II: Fluids and Complex Media , 1989 .

[27]  Gérard A. Maugin,et al.  Electrodynamics of Continua I: Foundations and Solid Media , 1989 .

[28]  A. C. Eringen,et al.  Electrodynamics of continua. Volume 1. Foundations and solid media. Volume 2 - Fluids and complex media , 1990 .

[29]  Measurement of the electrostrictive tensor of eight alkali halides , 1991 .

[30]  R. Newnham,et al.  Electrostriction and polarization , 1992 .

[31]  C. Truesdell,et al.  The Non-Linear Field Theories Of Mechanics , 1992 .

[32]  Dragan Damjanovic,et al.  FERROELECTRIC, DIELECTRIC AND PIEZOELECTRIC PROPERTIES OF FERROELECTRIC THIN FILMS AND CERAMICS , 1998 .

[33]  Daniel J. Klingenberg,et al.  Electrostriction of polarizable materials: Comparison of models with experimental data , 1998 .

[34]  J. Harrison,et al.  Ferroelectric and Piezoelectric Properties of Blends of Poly(Vinylidene-Trifluoroethylene) and Graft Elastomer , 1999 .

[35]  A. Eringen.  Microcontinuum Field Theories , 2020, Advanced Continuum Theories and Finite Element Analyses.

[36]  Measurement of electrostrictive coefficients of polymer films , 2001 .

[37]  F. Xia,et al.  An all-organic composite actuator material with a high dielectric constant , 2002, Nature.

[38]  E. Balizer,et al.  Electrostrictive effect in polyurethanes , 2003 .

[39]  M. Dadras,et al.  Microactuators based on ion-implanted dielectric electroactive polymer membranes (EAP) , 2005, The 13th International Conference on Solid-State Sensors, Actuators and Microsystems, 2005. Digest of Technical Papers. TRANSDUCERS '05..

[40]  F. Santoyo,et al.  Modal vibration analysis of a metal plate by using a laser vibrometer and the POD method , 2005 .

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

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

[43]  I. Diaconu,et al.  Electrostriction of a Polyurethane Elastomer-Based Polyester , 2006, IEEE Sensors Journal.

[44]  Samuel Rosset,et al.  Microactuators based on ion implanted dielectric electroactive polymer (EAP) membranes , 2006 .

[45]  J. Scheinbeim,et al.  Dielectric properties of a hydrated sulfonated poly(styrene–ethylene/butylenes–styrene) triblock copolymer , 2006 .

[46]  S. Tadigadapa,et al.  Relaxor Ferroelectric Polymers, Thin Film Devices, and Ink-Jet Microprinting for Thin Film Device Fabrication , 2006 .

[47]  Q.M. Zhang,et al.  Recent advances in highly electrostrictive P(VDF-TrFE-CFE) terpolymers , 2006, IEEE Transactions on Dielectrics and Electrical Insulation.

[48]  B. Steinberger,et al.  Electrically actuated elastomers for electro–optical modulators , 2006 .

[49]  Haedo Jeong,et al.  Preparation and properties of polyurethane/MMT nanocomposite actuators , 2006 .

[50]  Zhongyang Cheng,et al.  Electromechanical properties of poly(vinylidene-fluoride-chlorotrifluoroethylene) copolymer , 2006 .

[51]  Srinivas Tadigadapa,et al.  Electroactive polymer based microfluidic pump , 2006 .

[52]  F. Xia,et al.  High Performance Electroactive Polymers and Nano-composites for Artificial Muscles , 2007 .

[53]  R. McMeeking,et al.  A principle of virtual work for combined electrostatic and mechanical loading of materials , 2007 .

[54]  Heath Hofmann,et al.  An active energy harvesting scheme with an electroactive polymer , 2007 .

[55]  Y. Suzuki,et al.  Microelectrostrictive Actuator With Large Out-of-Plane Deformation for Flow-Control Application , 2007, Journal of Microelectromechanical Systems.

[56]  W. Y. Cheung,et al.  Characterization of proton irradiated copolymer thin films for microelectromechanical system applications , 2007 .

[57]  Qiming Zhang,et al.  Structural and ferroelectric response in vinylidene fluoride/trifluoroethylene/hexafluoropropylene terpolymers , 2007 .

[58]  C. Spillmann,et al.  Anisotropic actuation in electroclinic liquid crystal elastomers , 2007 .

[59]  Tushar K. Ghosh,et al.  Electroactive Nanostructured Polymers as Tunable Actuators , 2007 .

[61]  Nonlinear capacitance dilatometry for investigating elastic and electromechanical properties of ferroelectrets , 2007 .

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

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

[64]  C. Cho,et al.  Modified boundary layer analysis of an electrode in an electrostrictive material , 2008 .

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

[66]  K. Hutter,et al.  Electromagnetic Field Matter Interactions in Thermoelastic Solids and Viscous Fluids , 2010 .

[67]  Déformations électriques des diélectriques solides isotropes , .