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Constitutive models for static granular systems and focus to the Jiang-Liu hyperelastic law

  • Granular systems in solid-like state exhibit properties like stiffness dependence on stress, dilatancy, yield or incremental non-linearity that can be described within the continuum mechanical framework. Different constitutive models have been proposed in the literature either based on relations between some components of the stress tensor or on a quasi-elastic description. After a brief description of these models, the hyperelastic law recently proposed by Jiang and Liu [1] will be investigated. In this framework, the stress-strain relation is derived from an elastic strain energy density where the stable proper- ties are linked to a Drucker-Prager yield criteria. Further, a numerical method based on the finite element discretization and Newton- Raphson iterations is presented to solve the force balance equation. The 2D numerical examples presented in this work show that the stress distributions can be computed not only for triangular domains, as previoulsy done in the literature, but also for more complex geometries. If the slope of the heap is greater than a critical value, numerical instabilities appear and no elastic solution can be found, as predicted by the theory. As main result, the dependence of the material parameter Xi on the maximum angle of repose is established.

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Author:Clement Zemerli, Arnulf Latz, Heiko Andrä
URN (permanent link):urn:nbn:de:hbz:386-kluedo-29912
Serie (Series number):Berichte des Fraunhofer-Instituts für Techno- und Wirtschaftsmathematik (ITWM Report) (215)
Document Type:Report
Language of publication:English
Publication Date:2012/04/18
Year of Publication:2012
Publishing Institute:Fraunhofer-Institut für Techno- und Wirtschaftsmathematik
Date of the Publication (Server):2012/04/19
Number of page:46
Faculties / Organisational entities:Fraunhofer (ITWM)
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 15.02.2012