It is well known that, due to the absence of an intrinsic length scale, conventional rate-independent plasticity theories fail to explain the size effects observed in problems such as shear-flow localization, nanoindentation tests and precipitate hardening. Consequently, several new nonlocal/gradient constitutive theories with a preferred-length scale have been proposed recently.
One such gradient dependent J-2 flow theory of plasticity that preserves the classical structure of incremental boundary value problem has been proposed in Reference 27. The key feature of this theory that allows for the preservation of the classical structure of the incremental problem is the fact that the gradient measures enter the constitutive relations only through the hardening moduli and no higher-order stresses enter the formulation.
This paper deals with a preliminary evaluation of the above theory in the context of two simple problems. The first problem considers quasistatic rate-independent motions of an infinite 1-D bar that is at the point of incipient softening at all points along its length. An analytical solution is provided to this problem and the stabilizing effect of the nonlocal theory is illustrated. The second problem considers 1-D, dynamic, simple-shearing motions of an infinite plate of finite thickness. Numerical results for both the nonclassical theory and the corresponding classical theory are presented. Comparisons show that the non-classical theory predicts a stabilizing trend in the motions and mesh-size insensitivity of the results.