High-order mixed finite elements for an energy-based model of the polarization process in ferroelectric materials
| Autor: | Astrid S. Pechstein, Alexander Humer, Martin Meindlhumer |
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| Rok vydání: | 2020 |
| Předmět: |
FOS: Computer and information sciences
Materials science Condensed matter physics Mechanical Engineering 02 engineering and technology Dielectric Numerical Analysis (math.NA) 021001 nanoscience & nanotechnology Ferroelectricity Finite element method Computational Engineering Finance and Science (cs.CE) 020303 mechanical engineering & transports 0203 mechanical engineering Energy based Variational inequality FOS: Mathematics General Materials Science Mathematics - Numerical Analysis High order 0210 nano-technology Polarization (electrochemistry) Computer Science - Computational Engineering Finance and Science |
| DOI: | 10.48550/arxiv.2001.07105 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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