Summary
In frictional geomaterials, shear bands occur as a result of local concentrations of plastic strains in small bands of finite width. Since in practice as well as in numerical simulations both the location of the onset and the direction of shear bands are generally unknown, time- and space-adaptive methods are an excellent tool to detect and to solve shear band problems. In the present contribution, the ill-posedness of the numerical computation of shear band phenomena is overcome by extending the standard continuum mechanical approach by the inclusion of micropolar degrees of freedom in the sense of the Cosserat brothers.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
R. M. Bowen. Incompressible porous media models by use of the theory of mixtures. Int. J. Engnq. Sci., 18:1129–1148, 1980.
R. de Boer and W. Ehlers. Theorie der Mehrkomponentenkontinua mit Anwendung auf bodenmechanische Probleme. Forschungsberichte aus dem Fachbereich Bauwesen, Heft 40, Universität-GH-Essen, 1986.
S. Diebels, P. Ellsiepen, and W. Ehlers. Error-controlled Runge-Kutta time integration of a viscoplastic hybrid two-phase model. Technische Mechanik, 19:19–27, 1999.
W. Ehlers. Poröse Medien — ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsberichte aus dem Fachbereich Bauwesen, Heft 47, Universität-GH-Essen, 1989.
W. Ehlers. Constitutive equations for granular materials in geomechanical context. In K. Hutter, editor, Continuum Mechanics in Environmental Sciences and Geophysics, CISM Courses and Lectures No. 337, pages 313–402. SpringerVerlag, Wien, 1993.
W. Ehlers. Grundlegende Konzepte in der Theorie Poröser Medien. Technische Mechanik, 16:63–76, 1996.
W. Ehlers and W. Volk. On theoretical and numerical methods in the theory of porous media based on polar and non-polar elasto-plastic solid materials. Int. J. Solids Structures, 35:4597–4617, 1998.
P. Ellsiepen. Zeit- und ortsadaptive Verfahren angewandt auf Mehrphasenprobleme poröser Medien. Dissertation, Bericht Nr. II-3 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart. 1999.
I. Kossaczký. A recursive approach to local mesh refinement in two and three dimensions. J. Comp. Appl. Math., 55:275–288, 1994.
W. F. Mitchell. Adaptive refinement for arbitrary finite-element spaces with hierarchical bases. J. Comp. Appl. Math., 36:65–78, 1991.
W. Volk. Untersuchung des Lokalisierungsverhaltens mikropolarer poröser Medien mit Hilfe der Cosserat- Theorie. Dissertation, Bericht Nr. II-2 aus dem Institut für Mechanik (Bauwesen), Universität Stuttgart. 1999.
O. C. Zienkiewicz and J. Z. Zhu. A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Methods Eng., 24:337– 357, 1987.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Ehlers, W., Ellsiepen, P. (2000). On the Adaptive Computation of Shear Bands in Frictional Geomaterials. In: Sändig, AM., Schiehlen, W., Wendland, W.L. (eds) Multifield Problems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04015-7_15
Download citation
DOI: https://doi.org/10.1007/978-3-662-04015-7_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08693-9
Online ISBN: 978-3-662-04015-7
eBook Packages: Springer Book Archive