NONLOCAL CONTINUUM EFFECTS ON BIFURCATION IN THE PLANE-STRAIN TENSION- COMPRESSION TEST

The paper examines nonlocal effects on bifurcation phenomena. A gradie nt plasticity model is used where a characteristic length is introduce d in the yield criterion. Hill's well known framework of bifurcation t heory is shown to hold in the presence of normality and a sufficient c ondition for uniqueness is given. Further, the regularizing effects of nonlocality are underlined. It is also shown that the underlying loca l continuum, obtained when the length scale goes to zero, always provi des a lower bound for bifurcation stresses for the nonlocal continuum. Detailed analysis of bifurcation phenomena in the plane strain tensio n-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 t he short wavelength domain. In this last case and in the elliptic regi me, bifurcation modes disappear in tension while the corresponding str esses are significantly increased in the compressive regime.