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A consistent formulation of a dilatant interface element
Author(s) -
Snyman M. F.,
Martin J. B.
Publication year - 1992
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.1610160703
Subject(s) - finite element method , constitutive equation , discretization , dilatant , nonlinear system , mathematics , classification of discontinuities , tangent , stiffness matrix , mathematical analysis , structural engineering , geometry , mechanics , engineering , physics , quantum mechanics
The paper considers a plane joint or interface element suitable for implementation into a standard non‐linear finite element code. The element is intended to model discontinuities with rough contact surfaces, such as rock joints, where dilatant behaviour is present. Of particular concern is the formulation of a constitutive model which fully caters for all possible histories of opening, closing and sliding (accompained by dilation or contraction) in any direction. The non‐linear incremental constitutive equations are formulated in a manner appropriate for a back‐ward difference discretization in time along the path of loading. The advantage of such an approach is that no essential distinction need be drawn between opening, closing and sliding. Further, a convenient formulation of the constitutive equations is facilitated by representing the different contact conditions in relative displacement space. The state diagram in relative displacement space, however, changes from one time step to the next, and evolution equations for the updating must be formulated. These concepts are illustrated for two rock‐joint models: a sawtooth asperity model and a limited dilation model. The models are based on a penalty formulation to enforce the contact constraints, and explicit equations for the tangent stiffness matrix and for the corrector step of the standard Newton–Raphson iterative algorithm are derived. These equations have been implemented as an user element into the finite element code ABAQUS 7 . Three examples are presented to illustrate the predictions of the formulation.