Finite Element Modelling of Material Instability via an Enriched Elastoplastic Model
Geomaterials are dissipative particulate systems due to internal forces that arise from intergranular friction or viscosity. As such, their mechanical behaviour is highlighted by various forms of failure with either localization of deformations or diffuse deformations. Intriguingly, the latter failure mode, which does not involve any localized deformations or discontinuities, is normally observed well before plastic limit conditions are met. This work examines failure as a material (constitutive) instability phenomenon giving way to a bifurcation problem whereby a multiplicity of material response is possible for the same initial loading history. We use a rate-independent elastoplastic constitutive model with plastic strain softening and non-associativity of plastic flow through a micromechanically derived stress-dilatancy equation. The dependencies of the latter on density, stress, and fabric provide essential mathematical sources of material instability to promote the capturing of discontinuous response. An example problem involving diffuse and localization deformations in a water saturated sand sample as a boundary value problem is presented.
KeywordsSecond order work Diffuse failure Localized failure Stress dilatancy Non-associated flow rule
This work has been undertaken under funding provided by the Natural Science and Engineering Research Council of Canada. The first author is grateful to several colleagues, notably F. Darve, F. Nicot, and A. Daouadji, for various discussions of ideas on the central theme of second-order work. The finite element effort in this work originated from lab work performed by A. Daouadji.
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