Eintrag in der Universitätsbibliographie der TU Chemnitz
Volltext zugänglich unter
URN: urn:nbn:de:bsz:ch1-qucosa2-235462
Schmidt, Hansjörg
Tobiska, Lutz ; Apel, Thomas (Gutachter)
Anisotropic Viscoelasticity at Large Strain Deformations
Kurzfassung in englisch
The aim of this thesis is the fast and exact simulation of modern materials like fibre reinforced thermoplastics and fibre reinforced elastomers. These simulations are in the scope of large strain deformations and contain anisotropic and viscoelastic behaviour. The chapter Differential geometry outlines the necessary tensor analysis and differential geometry. We present the weak formulation in the undeformed domain and use Newton’s method to approximate the solution of this formulation, cf. Section 3.1 and Chapter 4, respectively. For the viscoelasticity we use a special ansatz for the internal variable. Next, we compute all necessary derivations for the Newton system, cf. Sections 4.2 and 4.3. We also investigate the symmetry of the material tensors in Section 4.4. Further, we present three methods to improve the convergence of Newton’s method, cf. Section 4.5. With these three methods we are able to consider more problems, compute them faster and in a more robust way. In Chapter 5 we concisely discuss the FEM and show the appearing matrices in detail. The aim of Chapter 6 is the application of the a posteriori error estimator to this complex material behaviour. We present some numerical examples in Chapter 7. In Chapter 8 the problems that arise in the simulation of fibre-reinforced elastomers are analysed and tackled with help of mixed formulations. We derive a symmetric mixed formulation from a reduced form of the energy density. Also, we reformulate the mixed variable for inextensibility to avoid the numerical cancellation in Section 8.3. The Section 8.4 is about a joined mixed formulation to solve problems with inextensible fibres in an incompressible matrix, like fibre-reinforced rubber. The succeeding section Section 8.5 deals with the arising indefinite block matrix system.
| Universität: | Technische Universität Chemnitz | |
| Institut: | Professur Numerische Mathematik | |
| Fakultät: | Fakultät für Mathematik | |
| Dokumentart: | Dissertation | |
| Betreuer: | Meyer, Arnd (Prof. Dr. rer. nat. habil.) | |
| URL/URN: | http://nbn-resolving.de/urn:nbn:de:bsz:ch1-qucosa2-235462 | |
| SWD-Schlagwörter: | Finite-Elemente-Methode , Funktionalanalysis , Kontinuumsmechanik | |
| Freie Schlagwörter (Englisch): | finite element method , newtons method , continuum mechanics , mixed formulation , viscoelasticity , anisotropy | |
| DDC-Sachgruppe: | Mathematik, Ingenieurwissenschaften | |
| Tag der mündlichen Prüfung | 19.06.2018 |
