Klawonn, Axel; Neff, Patrizio; Rheinbach, Oliver; Vanis, Stefanie:
Solving geometrically exact micromorphic elasticity with a staggered algorithm
2010
In: GAMM-Mitteilungen, Jg. 33 (2010), Heft 1, S. 57 - 72
Artikel/Aufsatz in Zeitschrift / Fach: Mathematik
Titel:
Solving geometrically exact micromorphic elasticity with a staggered algorithm
Autor(in):
Klawonn, Axel im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen; Neff, Patrizio im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen; Rheinbach, Oliver im Online-Personal- und -Vorlesungsverzeichnis LSF anzeigen; Vanis, Stefanie
Erscheinungsjahr
2010
Erschienen in:
GAMM-Mitteilungen, Jg. 33 (2010), Heft 1, S. 57 - 72
ISSN
DOI

Abstract:

A minimization problem modeling geometrically exact generalized continua of micromorphic type is considered. The solution consists of two fields, the elastic deformation φ of a given body and a tensorial field P which can model different additional features needed for a more reliable description of solids. For the solution of this minimization problem, a staggered algorithm is introduced which decouples the original problem into two separate problems. In each of these subproblems, one of the variables, φ or P, respectively, is kept fixed and the subproblem is solved for the remaining variables, i.e., P or φ, respectively. Each of the problems is discretized with finite elements. Numerical results are presented for a cubic and a cylindrical geometry.