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Cosserat Parameter Identification within the Frame of the Discrete Element Method
Author(s) -
Wessels Nicola,
Hackl Klaus
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210212
Subject(s) - discrete element method , homogenization (climate) , quadrilateral , moduli , shear (geology) , element (criminal law) , mathematics , classical mechanics , mathematical analysis , finite element method , physics , mechanics , materials science , thermodynamics , composite material , biodiversity , ecology , quantum mechanics , political science , law , biology
One of the main challenges using the Discrete Element Method is that there is no direct compliance to the well known continuum parameters such as elastic moduli. In this article we show how homogenization procedures using representative volume elements composed of discrete particles lead to Cosserat continua. Simulating a shear test with discrete elements it becomes obvious, that the evolving microstructure is mainly composed of contact chains that form triangles and quadrilaterals. For these contact chains we set up contact energies in normal and shear directions and combine those to derive the effective energy of the material. By comparison of this energy to a Cosserat energy we can derive formulas for the Lamé and Cosserat parameters. They are now only dependent on the interaction energies and radii of the particles. To show the validity of our assumptions and derivations we present some discrete element simulations of shear tests. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)