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A constitutive model for granular materials with microstructures using the concept of energy relaxation
Author(s) -
Khan Muhammad Sabeel,
Hackl Klaus
Publication year - 2013
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201310089
Subject(s) - constitutive equation , finite element method , granular material , relaxation (psychology) , displacement field , field (mathematics) , classical mechanics , continuum mechanics , displacement (psychology) , variational principle , physics , mechanics , materials science , mathematics , thermodynamics , psychology , social psychology , pure mathematics , psychotherapist , quantum mechanics
In this paper, we present a constitutive model for granular materials exhibiting microstructures using the concept of energy relaxation. Within the framework of Cosserat continuum theory the free energy of the material is enriched with an interaction energy potential taking into account the counter rotations of the particles. The enhanced energy potential fails to be quasiconvex. Energy relaxation theory is employed to compute the relaxed energy which yields all possible displacement and micro‐rotations field fluctuations as minimizers. Based on a two‐field variational principle the constitutive response of the material is derived. The developed constitutive model is then implemented in a finite element analysis program using the finite element method. Numerical simulations are presented to observe the localized deformation phenomenon in a granular medium. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)