An alternative decomposition of the strain gradient tensor

An alternative decomposition of the strain gradient tensor is proposed in this paper in order to ensure that the deviatoric strain gradient vanishes for an arbitrary volumetric strain field, which is consistent with the physical picture of plastic deformation. The theory of mechanism-based strain gradient (MSG) plasticity is then modified accordingly based on this new decomposition. The numerical study of the crack-tip field based on the new theory shows that the crack tip in MSG plasticity has the square-root singularity, and the stress level is much higher than the HRR field in classical plasticity.