A Gradient-Dependent Flow Theory of Plasticity: Application to Metal and Soil Instabilities

Abstract

We propose a gradient-dependent flow theory of plasticity for metals and granular soils and apply it to the problems of shear banding and liquefaction. We incorporate higher order strain gradients either into the constitutive equation for the flow stress or into the dilantancy condition. We examine the effect of these gradients on the onset of instabilities in the form of shear banding in metals or shear banding and liquefaction in soils under both quasi-static and dynamic conditions. It is shown that the higher order gradients affect the critical conditions and allow for a wavelength selection analysis leading to estimates for the width or spacing of shear bands and liquefying strips. Finally, a nonlinear analysis is given for the evolution of shear bands in soils deformed in the post-localization regime.