C0 solid elements for materials with strain gradient effects

Experiments conducted by various researchers in the past few decades have shown that materials display strong size effects when the material and characteristic length scales associated with nonuniform plastic deformation are of the same order at micron and submicron levels. The state of stress under such a condition was observed to be a function of both strain and strain gradient. The meso-scale constitutive relation taking into account Taylor dislocation theory is briefly described. The conventional theory of mechanism-based strain-gradient (CMSG) plasticity incorporating the intrinsic material length scale is adopted in the formulation of a series of C0 solid elements of 20–27 nodes. The model is implemented in ABAQUS, a finite element package via a user subroutine. Convergent studies have been carried for the series of elements with classical as well as CMSG plasticity theories. Numerical results on a bar under constant body force and indentation at submicron level reinforce the observation that materials are significantly strengthened for deformation at micron and submicron levels and the effects of strain gradient cannot be ignored without significant loss of the accuracy of the results