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

Abstract

This paper presents a general framework for the formulation of constitutive models that incorporate a localized dissipative mechanism. The formalism of strong discontinuities is employed, allowing for the decoupling of the constitutive 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 standard local continuum is described in detail. The resulting large-scale model is able to capture objectively the localized dissipation observed in localized failures of solids and structures. A localized viscous slip model is presented as a model example. The finite element implementation of the proposed formulation arises naturally as a local element enhancement of the finite 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 that the proposed framework allows for the development of effective finite element methods capturing in the large scale the localized dissipation observed in the failure of rate-dependent materials, avoiding the resolution of small length scales associated to the localization bands in these regularized models. Several representative numerical simulations are presented to illustrate these ideas. Copyright © 1999 John Wiley & Sons, Ltd.