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Uniqueness and localization analysis of elastic–plastic saturated porous media
Author(s) -
Zhang H. W.,
Schrefler B. A.
Publication year - 2001
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 - 10.1002/1096-9853(200101)25:1<29::aid-nag116>3.0.co;2-s
Subject(s) - uniqueness , porous medium , finite element method , permeability (electromagnetism) , shear band , mechanics , moduli , materials science , hardening (computing) , shear modulus , mathematical analysis , plasticity , mathematics , porosity , geotechnical engineering , geology , physics , structural engineering , composite material , engineering , chemistry , biochemistry , layer (electronics) , quantum mechanics , membrane
Conditions for localization of deformation into a planar (shear) band in the incremental response of elastic–plastic saturated porous media are derived in the case of small strains and rotations. The critical modulus for localization of both undrained and drained conditions are given in terms of the discontinuous bifurcation analysis of the problem. Loss of uniqueness of the response of coupled problems is investigated by means of positiveness of the second‐order work density. From the discussion of drained conditions, it is shown that there are two critical hardening moduli, i.e. lower and upper hardening moduli which, respectively, correspond to single phase material (large permeability) and to undrained conditions (small permeability). In analogy to one‐dimensional results, it is shown that there exists a domain of permeability values where we have loss of stability, but the waves can still propagate. In this domain finite element results do not show pathological mesh dependence, and permeability will play the role of an internal length parameter in dynamic models. The length scale prediction is thus given for multi‐dimensional problems. Copyright © 2001 John Wiley & Sons, Ltd.