- AutorIn
- Max Griehl Technische Universität Dresden, Institut für wissenschaftliches Rechnen
- Titel
- Bending models of nematic liquid crystal elastomers
- Untertitel
- Gamma-convergence results in nonlinear elasticity
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:14-qucosa2-915614
- Übersetzter Titel (DE)
- Biegemodelle von nematischen Flüssigkristall-Elastomeren : Gamma-Konvergenz-Resultate in nichtlinearer Elastizität
- Erstveröffentlichung
- 2024
- Datum der Einreichung
- 16.08.2023
- Datum der Verteidigung
- 25.03.2024
- Abstract (EN)
- We consider thin bodies made from elastomers and nematic liquid crystal elastomers. Starting from a nonlinear 3d hyperelastic model, and using the Gamma-convergence method, we derive lower dimensional models for 2d and 1d. The limit models describe the interplay between free liquid crystal orientations and bending deformations.
- Verweis
- A nonlinear bending theory for nematic LCE plates
Kapitel 4 basiert auf diesem Artikel
Link: https://www.worldscientific.com/doi/10.1142/S0218202523500331
DOI: https://doi.org/10.1142/S0218202523500331 - Modeling and simulation of nematic LCE rods
Kapitel 3 basiert auf diesem Preprint
Link: https://arxiv.org/abs/2205.15174
DOI: https://doi.org/10.48550/arXiv.2205.15174 - Freie Schlagwörter (DE)
- nichtlineare Elastizität, Gamma-Konvergenz, Biegemodelle, Dimensionsreduktion
- Freie Schlagwörter (EN)
- nonlinear elasticity, Gamma-convergence, bending models, dimension reduction
- Klassifikation (DDC)
- 510
- Klassifikation (RVK)
- SK 950
- GutachterIn
- Prof. Dr. Stefan Minsu Neukamm
- Prof. Dr. Bernd Schmidt
- BetreuerIn Hochschule / Universität
- Prof. Dr. Stefan Minsu Neukamm
- BetreuerIn - externe Einrichtung
- Prof. Dr. Sören Bartels
- Den akademischen Grad verleihende / prüfende Institution
- Technische Universität Dresden, Dresden
- Förder- / Projektangaben
- Deutsche Forschungsgemeinschaft Vector- and Tensor-Valued Surface PDEs
(FOR 3013)
ID: 417223351 - Version / Begutachtungsstatus
- aktualisierte Version
- URN Qucosa
- urn:nbn:de:bsz:14-qucosa2-915614
- Veröffentlichungsdatum Qucosa
- 22.05.2024
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch
- Lizenz / Rechtehinweis
CC BY 4.0
- Inhaltsverzeichnis
1 Introduction 1.1 Main results and structure of the text 1.2 Survey of the literature 1.2.1 Dimension reduction in nonlinear elasticity 1.2.2 Relation to other bending regime results in detail 1.2.3 Relation to other Gamma-convergence results of LCEs 2 Liquid crystal elastomers 2.1 Properties 2.2 Modeling 3 Rods 3.1 Setup and statement of analytical main results 3.1.1 The 3d-model and assumptions 3.1.2 The effective 1d-model 3.1.3 The Gamma-convergence result without boundary conditions 3.1.4 Boundary conditions for y 3.1.5 Weak and strong anchoring of n 3.1.6 Definition and properties of the effective coefficients 3.2 Numerical 1d-model exploration 3.3 Dimensional analysis and scalings 3.3.1 Non-dimensionalization and rescaling 3.3.2 Scaling assumptions 3.3.3 Dimensional analysis and applicability of the 1d-model 3.4 Smooth approximation of framed curves 3.5 Proofs 3.5.1 Compactness: proofs of Theorem 3.1.3 (a) and Proposition 3.1.4 (a) 3.5.2 Lower bound: proof of Theorem 3.1.3 (b) . . . . . . . . . . . . 68 3.5.3 Upper bound: proofs of Theorem 3.1.3 (c) and Proposition 3.1.4 (b) 3.5.4 Anchoring: proof of Proposition 3.1.5 3.5.5 Properties of the effective coefficients 4 Plates 4.1 Setup and statement of analytical main results 4.1.1 The 3d-model and assumptions 4.1.2 The effective 2d-model 4.1.3 The Gamma-convergence result without boundary conditions 4.1.4 Definition and properties of the effective coefficients 4.1.5 Boundary conditions for y 4.1.6 Weak and strong anchoring of n 4.2 Analytical and numerical 2d-model exploration 4.2.1 Analytical 2d-model exploration 4.2.2 Numerical 2d-model exploration 4.3 Dimensional analysis and scalings 4.3.1 Non-dimensionalization and rescaling 4.3.2 Scaling assumptions 4.3.3 Dimensional analysis and applicability 4.4 Geometry and approximation of bending deformations 4.4.1 Proofs of the geometric properties in the smooth case 4.4.2 Proof for the smooth approximations 4.5 Proofs 4.5.1 Compactness: proofs of Theorems 4.1.1 (a) and 4.1.8 (a) 4.5.2 Lower bound: proof of Theorem 4.1.1 (b) 4.5.3 Upper bound: proofs of Theorem 4.1.1 (c) and Theorem 4.1.8 (b) 4.5.4 Properties of the effective coefficients 4.5.5 Anchorings 4.5.6 Approximation of nonlinear strains: proof of Proposition 4.5.4 5 Conclusions and outlooks Bibliography