Strain gradient elasto-plasticity with a new Taylor-based yield function

For micron-scale elasto-plastic deformations, a theory of strain gradient elasto-plasticity (SGEP) has been established to explain some phenomena that have recently attracted intensive investigations, which include size effects around the elastic limit and in plastic hardening, the anomalous Bauschinger effect, plastic softening, and the unconventional load–unload hysteresis loops. Based on the fact that for most materials the elastic length scale is far smaller than the plastic length scale, our dimensional analysis reveals that the elastic strain gradient is generally dominant over the plastic strain gradient, which indicates the significant role of elasticity. Therefore, a more rigorous consideration of the elastic deformation is implemented within the proposed SGEP framework, featured by a new Taylor plasticity-based yield function and the elasto-plastic decompositions of both strain and strain gradient. The proposed yield function emphasizes the reversibility of elastic deformation-related dislocations, which has been frequently observed experimentally. This proposed SGEP not only does satisfy the principle of nonnegative plastic dissipation for material hardening, but also allows for the existence of material softening which has been observed in recent experiments. The wire torsion and foil bending problems are used as examples, to validate the SGEP’s capability in interpreting the above-mentioned phenomena by comparison with experimental data in the literature.