A hybrid phenomenological model for ferroelectroelastic ceramics. Part II: Morphotropic PZT ceramics

Stark, S.; Neumeister, Peter; Balke, Herbert

doi:10.1016/j.jmps.2016.03.003

Cited by 7 publications

(8 citation statements)

References 57 publications

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“…Concerning this initial state, Stark et al (2016b) point out that it is not consistent if θ ≠ 0 ° , 180 ° , as then surface charges of size ρ P = P i · n occur at the non-electroded boundaries. In this work, we assume one of their remedy proposals, where these charges are modeled as non-moveable surface charges.…”

Section: Numerical Resultsmentioning

confidence: 96%

“…This example has been widely used as a benchmark example for non-proportional loading e.g. by McMeeking and Landis (2002); Landis (2002); Arockiarajan et al (2009); Stark et al (2016b). In our computations, we assume the cube to be of size 5 mm .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…They observed very fast convergence of the Newton-Raphson iteration. Stark et al (2016aStark et al ( , 2016b combine a phenomenological and micro-mechanically motivated model in their work.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials

Pechstein

Meindlhumer

Humer

2020

Journal of Intelligent Material Systems and Structures

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An energy-based model of the ferroelectric polarization process is presented in the current contribution. In an energy-based setting, dielectric displacement and strain (or displacement) are the primary independent unknowns. As an internal variable, the remanent polarization vector is chosen. The model is then governed by two constitutive functions: the free energy function and the dissipation function. Choices for both functions are given. As the dissipation function for rate-independent response is non-differentiable, it is proposed to regularize the problem. Then, a variational equation can be posed, which is subsequently discretized using conforming finite elements for each quantity. We point out which kind of continuity is needed for each field (displacement, dielectric displacement and remanent polarization) is necessary to obtain a conforming method, and provide corresponding finite elements. The elements are chosen such that Gauss’ law of zero charges is satisfied exactly. The discretized variational equations are solved for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve.

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Section: Numerical Resultsmentioning

confidence: 96%

Section: Numerical Resultsmentioning

confidence: 99%

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High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials

Pechstein

Meindlhumer

Humer

2020

Journal of Intelligent Material Systems and Structures

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“…Zouari et al (2011) proposed a quadratic element realizing a constitutive law, similar to the one proposed by Kamlah (2001). A hybrid phenomenological model for ferroelectric ceramics is presented by Stark et al (2016aStark et al ( , 2016b. Comments on the stability of ferroelectric constitutive models were given by Stark et al (2016c) and Bottero and Idiart (2018).…”

Section: Introductionmentioning

confidence: 99%

“…A hybrid phenomenological model for ferroelectric ceramics is presented by Stark et al (2016a, 2016b). Comments on the stability of ferroelectric constitutive models were given by Stark et al (2016c) and Bottero and Idiart (2018).…”

Section: Introductionmentioning

confidence: 99%

Variational inequalities for ferroelectric constitutive modeling

Meindlhumer

Pechstein

Humer

2020

Journal of Intelligent Material Systems and Structures

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This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of free energy as well as switching and saturation conditions in form of inequalities. Thermodynamically consistent models naturally lead to variational formulations. We propose to use the concept of variational inequalities. We aim at combining the different phenomenological conditions into one variational inequality. In our formulation we use one Lagrange multiplier for each condition (the onset of domain switching and saturation), each satisfying Karush-Kuhn-Tucker conditions. An update for reversible and remanent quantities is then computed within one, in general nonlinear, iteration.

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Theoretical modeling and experimental characterization of rate and temperature dependent electromechanical behavior of piezocomposites

Jayendiran

Arockiarajan

2018

European Journal of Mechanics - A/Solids

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A hybrid phenomenological model for ferroelectroelastic ceramics. Part II: Morphotropic PZT ceramics

Cited by 7 publications

References 57 publications

High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials

High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials

Variational inequalities for ferroelectric constitutive modeling

Theoretical modeling and experimental characterization of rate and temperature dependent electromechanical behavior of piezocomposites

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