Project
AA2-21
Strain Engineering for Functional Heterostructures: Aspects of Elasticity
Project Heads
Annegret Glitzky, Matthias Liero, Barbara Zwicknagl
Project Members
Kateryna Buryachenko
Project Duration
01.01.2024 − 31.12.2025
Located at
HU Berlin
Description
Strain engineering for semiconductor devices or lithium-ion batteries requires a good understanding of elastic effects that strongly influence their functional properties. We consider some problems in the modelling of such material systems, related to the choice of the free energy density and dimension reduction for lower-dimensional structures such as plates and rods.
In the latter, mathematical challenges arise due to the coupling of the mechanical deformation to other physical effects such as electrostatics. To tackle such problems, variational techniques, e.g. Gamma-convergence, combined with modern tools for nonlinear partial differential equations are used.
Related Publications
- Annegret Glitzky, Matthias Liero, and Grigor Nika. Dimension reduction of thermistor models for large-area organic light-emitting diodes. Discr. Cont. Dynam. Systems Ser. S, 14:3953–3971, 2021. https://www.aimsciences.org/article/doi/10.3934/dcdss.2020460
- Lukas Abel, Janusz Ginster, and Barbara Zwicknagl. A scaling law for a model of epitaxially strained elastic films with dislocations. Archive for Rational Mechanics and Analysis 249 (59), 2025. https://doi.org/10.1007/s00205-025-02117-9
- Sergio Conti, Martin Lenz, Martin Rumpf, Jan Verhülsdonk, and Barbara Zwicknagl. Microstructure of macrointerfaces in shape-memory alloys. Journal of the Mechanics and Physics of Solids, 179, 2023, https://www.sciencedirect.com/science/article/abs/pii/S0022509623001473?via%3Dihub
- Sergio Conti, Martin Lenz, Martin Rumpf, Jan Verhülsdonk, and Barbara Zwicknagl. Geometry of Needle-Like Microstructures in Shape-Memory Alloys. Shape Memory and Superelasticity, 9, 2023, https://link.springer.com/article/10.1007/s40830-023-00442-0
- Yiannis Hadjimichael, Christian Merdon, Matthias Liero, and Patricio Farrell. An energy-based finite-strain model for 3d heterostructured materials and its validation by curvature analysis. International Journal for Numerical Methods in Engineering, 2024. https://onlinelibrary.wiley.com/doi/abs/10.1002/nme.7508
- Dilara Abdel, Annegret Glitzky, and Matthias Liero. Analysis of a drift-diffusion model for perovskite solar cells. Discrete and Continuous Dynamical Systems – B, 2024. 10.3934/dcdsb.2024081
- Kateryna Buryachenko and Yuliia Andreieva. Qualitative analysis of fourth-order hyperbolic equations. Front. Appl. Math. Stat., 10, 2024, https://doi.org/10.3389/fams.2024.1467199
- Annegret Glitzky and Matthias Liero. Uniqueness and regularity of weak solutions of a drift-diffusion system for perovskite solar cells. Journal of Evolution Equations (JEEQ), 25, 2025. https://doi.org/10.1007/s00028-025-01117-2
- Annegret Glitzky. On a drift-diffusion model for perovskite solar cells. PAMM Proc. Appl. Mech., page
202300017, 2024. doi:https://doi.org/10.1002/pamm.202400017 - Kateryna Buryachenko, Annegret Glitzky, Matthias Liero, and Barbara Zwicknagl. Dimension reduction for a coupled
electro-elastic saddle-point problem at finite strains. Preprint 3230, Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, 2025. https://doi.org/10.20347/WIAS.PREPRINT. - Tamara Fastovska, Janusz Ginster, and Barbara Zwicknagl. Derivation of the Reissner–Mindlin model from nonlinear elasticity. Preprint 3216, Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, 2025. https://doi.org/10.20347/WIAS.PREPRINT.3216
- Moritz Immanuel Gau and Matthias Liero. Derivation of a thermo-visco-elastic plate model at small strains. Preprint 3209, Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin, 2025. https://doi.org/10.20347/WIAS.PREPRINT.3209
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