Nonlocal continuum effects on bifurcation in the plane strain tension-compression test

Abstract

The paper examines nonlocal effects on bifurcation phenomena. A gradient plasticity model is used where a characteristic length is introduced in the yield criterion. Hill's well known framework of bifurcation theory is shown to hold in the presence of normality and a sufficient condition for uniqueness is given. Further, the regularizing effects of nonlocality are underlined. It is also shown that the underlying local continuum, obtained when the length scale goes to zero, always provides a lower bound for bifurcation stresses for the nonlocal continuum. Detailed analysis of bifurcation phenomena in the plane strain tension-compression test is carried out and compared to the results of Hill and Hutchinson for the local continuum. The results are qualitatively the same in the long wavelength domain while they differ markedly in the short wavelength domain. In this last case and in the elliptic regime, bifurcation modes disappear in tension while the corresponding stresses are significantly increased in the compressive regime.