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Finite strain formulation of a strain space multiple mechanism model for granular materials
Author(s) -
Iai Susumu,
Ueda Kyohei,
Tobita Tetsuo,
Ozutsumi Osamu
Publication year - 2012
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2084
Subject(s) - infinitesimal strain theory , finite strain theory , strain rate tensor , hyperelastic material , cauchy stress tensor , eulerian path , strain energy density function , mathematics , tensor (intrinsic definition) , material derivative , kinematics , mathematical analysis , viscous stress tensor , stress (linguistics) , finite element method , classical mechanics , geometry , physics , lagrangian , structural engineering , engineering , linguistics , philosophy
SUMMARY This paper presents the finite strain formulation of a strain space multiple mechanism model for granular materials. Because the strain space multiple mechanism model has an appropriate micromechanical background in which the branch and complementary vectors are defined in the material (or referential) coordinate, the finite strain formulation is carried out by following the change in these vectors, in direction and magnitude, associated with deformation in the material. By applying the methodology for compressible materials established in the finite strain continuum mechanics, decoupled formulation that decomposes the kinematic mechanisms into volumetric and isochoric components is adopted for the strain space multiple mechanism model. Lagrangian (material) description of integrated form is given by a relation between the second Piola–Kirchhoff effective stress tensor and the Green–Lagrange strain tensor; Eulerian (spatial) description by a relation between the Cauchy effective stress tensor and the Euler–Almansi strain tensor. In particular, the volumetric strain is defined as a logarithm of Jacobian determinant. Lagrangian (material) description of incremental form is derived through the material time derivative of the integrated form. The counterpart in the spatial description is derived through the Lie time derivative, given as a relation between the Oldroyd stress rate of Kirchhoff stress and the rate of deformation tensor (sometimes called stretching in the literatures). An example is shown to discuss the applicability of the finite strain formulation. Copyright © 2012 John Wiley & Sons, Ltd.