Caloric aspects of nonlinear ferroelectric constitutive behavior: modeling and simulation

Wingen, Marius; Ricoeur, Andreas

doi:10.1007/s00161-018-0711-1

Cited by 8 publications

(14 citation statements)

References 25 publications

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“…Starting from equation 7, Figure 2 shows the results for the temperature development vs. load cycles compared to the experimental results and those of the FEM. The result from the simulation of a polyristal, solid blue line, is in a good agreement with the experimental result [3] and those obtained by the FEM [4]. Due to the lack of internal grain stresses, the heating of a single crystal is larger than that of a polycrystal.…”

Section: Homogeneus Distribution Of Temperature Changesupporting

confidence: 82%

“…ξ := The result from the simulation of a polyristal, solid blue line, is in a good agreement with the experimental result [3] and those obtained by the FEM [4]. ξ := The result from the simulation of a polyristal, solid blue line, is in a good agreement with the experimental result [3] and those obtained by the FEM [4].…”

Section: Homogeneus Distribution Of Temperature Changesupporting

confidence: 71%

“…The rate-dependant formulation emanates from the local form of the first law of thermodynamics and the GIBB's fundamental equation of the thermodynamical potential [4]: The rate-dependant formulation emanates from the local form of the first law of thermodynamics and the GIBB's fundamental equation of the thermodynamical potential [4]:…”

Section: Basic Equationsmentioning

confidence: 99%

“…where σ ij describes the mechanical stress, D i the electric displacement and s the specific entropy and the electromechanical balance laws σ ij,j = 0 and D i,i = 0, an energy balance is required to compute the distribution of temperature change due to irreversible domain wall motions. The rate-dependant formulation emanates from the local form of the first law of thermodynamics and the GIBB's fundamental equation of the thermodynamical potential [4]:…”

Section: Basic Equationsmentioning

confidence: 99%

“…For this purpose, the CM is extended by the nonlinear bilateral caloric-electromechanical couplings. In addition, a comparison of the results by this work and those of the FEM according to [4] is presented. For verification, the theoretical results from the CM and FEM are compared to experimental results in [3].…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Nonlinear bilateral caloric–electromechanical couplings in polycrystalline ferroelectrics

Warkentin

Lange

Wingen

et al. 2019

Proc Appl Math and Mech

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Section: Homogeneus Distribution Of Temperature Changesupporting

confidence: 82%

Section: Homogeneus Distribution Of Temperature Changesupporting

confidence: 71%

Section: Basic Equationsmentioning

confidence: 99%

Section: Basic Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Nonlinear bilateral caloric–electromechanical couplings in polycrystalline ferroelectrics

Warkentin

Lange

Wingen

et al. 2019

Proc Appl Math and Mech

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Experimental investigations of viscoelastic and ferroelectric heating in PZT–5H

Warkentin

Ricoeur

2021

Proc Appl Math and Mech

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This contribution focuses on the separation of two effects causing a temperature change in experiments with electrically loaded ferroelectrics. These materials are often subjected to cyclic loading, where viscoelasticity prevails at lower electric fields, whereas dissipative heating by domain switching governs the heating above the coercive field. Different frequencies and load amplitudes are investigated experimentally.

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A monolithic approach toward coupled electrodynamic–thermomechanical problems with regard to weak formulations

Ricoeur

Wingen

2021

Acta Mech

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Weak formulations of boundary value problems are the basis of various numerical discretization schemes. They are classically derived applying the method of weighted residuals or a variational principle. For electrodynamical and caloric problems, variational approaches are not straightforwardly obtained from physical principles like in mechanics. Weak formulations of Maxwell’s equations and of energy or charge balances thus are frequently derived from the method of weighted residuals or tailored variational approaches. Related formulations of multiphysical problems, combining mechanical balance equations and the axioms of electrodynamics with those of heat conduction, however, raise the additional issue of lacking consistency of physical units, since fluxes of charge and heat intrinsically involve time rates and temperature is only included in the heat balance. In this paper, an energy-based approach toward combined electrodynamic–thermomechanical problems is presented within a classical framework, merging Hamilton’s and Jourdain’s variational principles, originally established in analytical mechanics, to obtain an appropriate basis for a multiphysical formulation. Complementing the Lagrange function by additional potentials of heat flux and electric current and appropriately defining generalized virtual powers of external fields including dissipative processes, a consistent formulation is obtained for the four-field problem and compared to a weighted residuals approach.

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Caloric aspects of nonlinear ferroelectric constitutive behavior: modeling and simulation

Cited by 8 publications

References 25 publications

Nonlinear bilateral caloric–electromechanical couplings in polycrystalline ferroelectrics

Nonlinear bilateral caloric–electromechanical couplings in polycrystalline ferroelectrics

Experimental investigations of viscoelastic and ferroelectric heating in PZT–5H

A monolithic approach toward coupled electrodynamic–thermomechanical problems with regard to weak formulations

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