This chapter presents a thermodynamically consistent approach to the modeling of ferroelectric materials such as piezoceramics of PZT type. The material’s state and response are described in the sense of continuum physics, employing fields such as strain and stress, electric field intensity and electric polarization. Dissipative behavior is modeled introducing internal electric polarization and internal ferroelastic strain as independent unknowns. Based on the principles of thermodynamics, the derivation of characteristic relationships and evolution equations from energy, enthalpy and dissipation densities is shown. A specific choice of potentials for the description of ferroelectric materials is discussed. Variational formulations suitable for computational treatment are derived. Two finite element schemes are presented and compared with respect to their accuracy for an exemplary problem.

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Thermodynamically Consistent Modeling of Ferroelectricity and Finite Element Formulations

  • Astrid Pechstein,
  • Alexander Humer,
  • Michael Krommer

摘要

This chapter presents a thermodynamically consistent approach to the modeling of ferroelectric materials such as piezoceramics of PZT type. The material’s state and response are described in the sense of continuum physics, employing fields such as strain and stress, electric field intensity and electric polarization. Dissipative behavior is modeled introducing internal electric polarization and internal ferroelastic strain as independent unknowns. Based on the principles of thermodynamics, the derivation of characteristic relationships and evolution equations from energy, enthalpy and dissipation densities is shown. A specific choice of potentials for the description of ferroelectric materials is discussed. Variational formulations suitable for computational treatment are derived. Two finite element schemes are presented and compared with respect to their accuracy for an exemplary problem.