Bridging strain gradient elasticity and plasticity toward general loading histories

• The total number of elastic characteristic lengths reduced from 5 to 3.
• Anti-symmetric part of rotational gradient does not influence SGP.
• Study of unloading behavior using higher order SGP.

The Fleck–Hutchinson theory on strain gradient plasticity (SGP), proposed in Fleck and Hutchinson (1997), has been reformulated by adopting the strategy of decomposing the second order strain presented by Lam et al. (2003). This study attempts to build a SGP framework for general loading histories which has yet been well addressed. The main features of this study include: (1) The total number of the elastic characteristic length scales has been reduced from 5 to 3; (2) The anti-symmetric part of the rotational gradient has been found to have no influence on SGP; (3) The established SGP flow theory is characterized by its strict correspondence to the conventional J2 plasticity. This thermodynamically acceptable reformulation has been proven to satisfy the nonnegativity of plastic dissipation, which is still an outstanding issue in other SGP theories. It explicitly shows how elastic strain gradients and corresponding elastic characteristic length scales come into play in general elastic–plastic loading histories. Another feature of the present SGP formation is the exclusion of plastic strain-related boundary conditions which believably will facilitate SGP applications significantly.