Thermodynamical formulation for coupled electromechanical hysteresis effects—I. Basic equations

Abstract In this work we present a thermodynamical phenomenological formulation of a theory capable of displaying electromechanical hysteresis effects in continous media, which should apply to ferroelectric ceramics. This is built within the scheme of the thermodynamical theory of internal variables. This theory produces both plastic and electric-hysteresis effects in the form of “plasticity”, i.e. rate-independent, evolution equations for the plastic strain, the residual electric polarization and both mechanical and electric “hardenings”. This paper develops in detail the electric hardening effects through the residual polarization vector and an internal variable representing an electric polarization. An electric version of Drucker's inequality of plasticity has been derived. Several examples of loading functions are studied including the influence of piezoelectric and electrostrictive couplings. In particular, the purely electric loading function has been studied in greater detail and the first polarization curve either based on experimental data or theoretically displayed is discussed. In all the paper provides all ingredients for a future discussion of more specific cases.

[1]  G. Haertling.  Improved Hot-Pressed Electrooptic Ceramics in the (Pb,La)(Zr,Ti)O3 System , 1971 .

[2]  B. Jiménez,et al.  Poling strategy of PLZT ceramics , 1984 .

[3]  G. Maugin,et al.  Electroacoustic equations for one‐domain ferroelectric bodies , 1980 .

[4]  A. Hopfinger,et al.  Kink propagation as a model for poling in poly(vinylidene fluoride) , 1980 .

[5]  G. Schmidt,et al.  Influence of uniaxial pressure on the properties of PLZT ceramics , 1984 .

[6]  G. Maugin,et al.  Basic equations for shocks in nonlinear electroelastic materials , 1989 .

[7]  R. Hill.  The mathematical theory of plasticity , 1950 .

[8]  M. Lax,et al.  Electrodynamics of elastic pyroelectrics , 1976 .

[9]  N. Schmidt,et al.  Coercive force and 90° domain wall motion in ferroelectric PLZT ceramics with square hysteresis loops , 1981 .

[10]  D. F. Nelson,et al.  Linear elasticity and piezoelectricity in pyroelectrics , 1976 .

[11]  D. F. Nelson,et al.  Theory of nonlinear electroacoustics of dielectric, piezoelectric, and pyroelectric crystals , 1978 .

[12]  Gérard A. Maugin,et al.  The method of virtual power in continuum mechanics: Application to coupled fields , 1980 .

[13]  M. Lax,et al.  Linear and Nonlinear Electrodynamics in Elastic Anisotropic Dielectrics , 1971 .

[14]  E. W. Jacobs,et al.  Correlation of ferroelectric hysteresis with 33 ferroelastic hysteresis in polyvinylidene fluoride , 1984 .

[15]  G. Haertling.  PLZT electrooptic materials and applications: a review , 1987 .

[16]  A. Bogomolov,et al.  Study of the pyroelectric properties of PLZT ceramics by dynamic method , 1987 .

[17]  Takeo Furukawa,et al.  Switching process in composite systems of PZT ceramics and polymers , 1986 .

[18]  P. S. Peercy,et al.  One dimensional dynamic electromechanical constitutive relations of ferroelectric materials , 1979 .

[19]  Charles F. Pulvari,et al.  Phenomenological Theory of Polarization Reversal in BaTiO3 Single Crystals , 1958 .

[20]  C. Yoon,et al.  Ferroelectric hysteresis effects in poly(vinylidene fluoride) films , 1980 .

[21]  J. Grindlay,et al.  An Introduction to the Phenomenological Theory of Ferroelectricity: International Series of Monographs In: Natural Philosophy , 1970 .

[22]  R. Toupin,et al.  A dynamical theory of elastic dielectrics , 1963 .

[23]  On the behavior of shock waves in deformable dielectric materials , 1983 .

[24]  D. F. Nelson,et al.  Maxwell equations in material form , 1976 .

[25]  G. Kluitenberg.  On dielectric and magnetic relaxation phenomena and vectorial internal degrees of freedom in thermodynamics , 1977 .

[26]  L. Kachanov,et al.  Fundamentals of the Theory of Plasticity , 1974 .

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

[28]  Kunihiro Nagata,et al.  Effects of Grain Size and Porosity on Electrical and Optical Properties of PLZT Ceramics , 1973 .

[29]  Peter J. Chen.  Three dimensional dynamic electromechanical constitutive relations for ferroelectric materials , 1980 .