Loss of ellipticity analysis in non-smooth plasticity

Abstract

This work is concerned with the influence of non-smooth yield functions on material instabilities. Using Rice's criterion, the conditions for loss of ellipticity are determined in the case of a family of non-smooth yield functions in principal stress space. It is found that the presence of corners on the yield surface allows for postponing or advancing loss of ellipticity. A procedure for the numerical detection of loss of ellipticity in multisurface plasticity is proposed. An explicit expression of the subdifferential of the non-smooth yield function is obtained, thereby extending existing results in the literature for the Tresca and Mohr-Coulomb criteria. Structural computations show that the use of non-smooth yield functions can lead to much earlier failure prediction than in the case of a commonly used von Mises criterion.