Large-scale modeling of localized dissipative mechanisms in a local continuum: applications to the numerical simulation of strain localization in rate-dependent inelastic solids

This paper presents a general framework for the formulation of constitutive models that incorporate a localized dissipative mechanism. The formalism o f strong discontinuities is employed, allowing for the decoupling of the co nstitutive characterization of the continuum and localized responses of the material. A procedure for incorporating the localized small-scale effects of the material response in the large-scale problem characterized by the st andard local continuum is described in detail. The resulting large-scale mo del is able to capture objectively the localized dissipation observed in lo calized failures of solids and structures. A localized viscous slip model i s presented as a model example. The finite element implementation of the pr oposed formulation arises naturally as a local element enhancement of the f inite element interpolations, with no regularization of the discontinuities . The above considerations are formulated first in the infinitesimal range, and then extended to the finite strain regime. Furthermore, it is shown th at the proposed framework allows for the development of effective finite el ement methods capturing in the large scale the localized dissipation observ ed in the failure of rate-dependent materials, avoiding the resolution of s mall length scales associated to the localization bands in these regularize d models. Several representative numerical simulations are presented to ill ustrate these ideas. Copyright (C) 1999 John Wiley & Sons, Ltd.