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.