Shear softening and localization: Modelling the evolutionof the width of the shear zone

摘要

In this paper, the question of shear localizationinside a band is revisited. Using simplified constitutiveequations we look at a 1D layer in a classical medium. Eventhough the example is simple, we show once more the lossof uniqueness of the solution. By studying the initialboundary value problem we also show that the width of thelocalization zone stays constant or decreases. A secondgradient model is then introduced and the evolution of thewidth of the localization zone is studied. Analytical solu-tions are derived for a quasi-brittle material and estimationsmade for a ductile constitutive law. It is shown that thewidth of the localization zone stays constant for the quasi-brittle material and decreases for the ductile one. Numericalsimulations are finally provided to validate the approach andto get more precise numerical results for the ductile case.