Open issues in strain gradient continuum plasticity and other approaches to address size effects

Abstract This book addresses the enhanced continuum theory to assess the thermomechanical response of instabilities such as shear bands and necking in materials as well as small-scale metallic compounds. Historically, the determination of the model parameters, including material length scale and its physical interpretation is exhaustively discussed. In addition, whether the additional strengthening caused by plastic strain gradients is mainly energetic or dissipative is one of the open issues in the strain gradient plasticity. The elastic stress jump is also receiving significant attention from the strain gradient plasticity community. This chapter will thoroughly discuss the three aforementioned issues. Apart from the strain gradient plasticity, there are several other approaches such as strain gradient crystal plasticity, discrete dislocation dynamics, and molecular dynamics that can account for the size, boundary, and rate effect in microscale materials. Such techniques will be briefly discussed at the end.