Objective localization criterion and behavior for finite deformation plasticity - a Lagrangian formulation

Abstract

In this paper, the condition for strain localization bifurcation is studied using Lagrangian description. The localization criterion with respect to the reference con®guration is obtained by relating the rate of the second Piola-Kirchoff stress to the rate of Cauchy-Green deformation tensor. When transferred to the present con®guration, it is equivalent to the one which is obtained when Truesdell rate of Cauchy stress is used in the rate problem. An example for the localization response for a set of triaxial extensions is presented using a speci®c ®nite-deformation thermo-elastic-plastic model.When a small-deformation based localization criterion is used, i.e. when some terms in the localization criterion are neglected, the localization response, at some loading paths, becomes signi®cantly different from that obtained in the presence of these terms. It is therefore concluded that ®nite deformation tools should be employed when localization analysis is performed even when the small deformation hypothesis is otherwise considered as valid.

A Cartesian parametrization for the numerical analysis of material instability

“…whereˇm D 1 if the damage of the matrix evolves within the time increment orˇm D 0 otherwise, f i D 1 if the damage of the ith fiber evolves within the time increment orˇf i D 0 otherwise, m0 and f i 0 are the derivatives of the damage parameters defined in (28) with respect to the maximum thermodynamic force defined in (29), and S m and S f i are the effective (undamaged) second Piola-Kirchhoff stresses for the matrix and the ith fibers given by the following:…”

“…The algorithm was applied to the bifurcation analysis of a small deformation isotropic elastoplastic material model. Khen et al , formulated the localization criterion for finite deformation plasticity in a Lagrangian formulation and searched the bifurcation direction using two characteristic angles in a spherical coordinate system. Boussaa and Aravas proposed an alternative approach where numerical and symbolic computations were combined to detect the loss of strong ellipticity and applied this approach to a Gurson‐type porous material.…”

Study of evolution of shear band systems in sand retained by flexible wall

“…A detailed presentation of various theoretical models of shear band generation lies beyond the scope of this paper. We only mention some important papers and books such as Vardoulakis and Sulem [1], Khen et al [2], Imposimato and Nova [3], Schae!er and Shearer [4], Vardoulakis [5,6], Papamichos and Vardoulakis [7], Zienkiewicz et al [8], MroH z and Maciejewski [9], Bigoni and Hueckel [10], MuK lhaus and Vardoulakis [11], Micha"owski [12].…”