Consistent Higher Order Accurate Time Discretization Methods for Inelastic Material Models

Schröder, Bettina Anna Barbara

kassel university press, ISBN: 978-3-7376-0772-8, 2019, 257 Seiten
(Schriftenreihe Institut für Baustatik und Baudynamik 2019-2)

URN: urn:nbn:de:0002-407733

DOI: 10.19211/KUP9783737607735

Zugl.: Kassel, Univ., Diss. 2019

| Preis und lieferbare Formen -->

Inhalt: The present thesis investigates the usage of higher order accurate time integrators together with appropriate error estimators for small and finite dynamic (visco)plasticity. Therefore, a general (visco)plastic problem is defined which serves as a basis to create closed-form solution strategies. A classical access towards small and finite (visco)plasticity is integrated into this concept. This approach is based on the idea, that the balance of linear momentum is formulated in a weak sense and the material laws are included indirectly. Thus, separate time discretizations are implemented and an appropriate coupling between them is necessary. Limitations for the usage of time integrators are the consequence. In contrast, an alternative multifield formulation is derived, adapting the principle of Jourdain. The idea is to assume that the balance of energy - taking into account a pseudopotential representing dissipative effects – resembles a rate-type functional, whose stationarity condition leads to the equations
describing small or finite dynamic (visco)plasticity. Accordingly, the material laws and the balance of linear momentum can be solved on the same level and only one single time discretization has to be performed. A greater freedom in the choice of time integrators is obtained and the application of higher order accurate schemes - such as Newmark’s method, fully implicit as well as diagonally implicit Runge-Kutta schemes, and continuous as well as discontinuous Galerkin methods - is facilitated. An analysis and a comparison of the classical and the multifield formulation is accomplished by means of distinct examples. In this context, a dynamic benchmark problem is developed, which allows to focus on the effect of different time integrators. For this investigation, a variety of time discretization error estimators are formulated, evaluated, and compared.

Die Publikation ist in folgenden Formen erhältlich:

Volltext (pdf-Datei, ausdruckbar, Open Access - 16.00 MB)
PDF ansehen (view)

Das e-book ist lizenziert unter einer Creative Commons Namensnennung - Weitergabe unter gleichen Bedingungen 4.0 International Lizenz.