Comparison of the Strain Localization Approaches: Viscoplasticity Theory and Gradient Dependent Theory

This work is focused on the comparison between the two strain localization techniques namely, the viscoplasticity and the gradient dependent theory. In the first approach a length-scale parameter is introduced implicitly through viscosity in order to address strain localization and material instability in the (initial) boundary value problems. The second approach is the enhanced nonlocal gradient-dependent theory which formulates a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical theories and the classical (local) continuum. It is successful in explaining the size effects encountered at the micron scale and in preserving the well-posedeness of the (initial) boundary value problems governing the solution of material instability triggering strain localization. This is due to the explicit incorporation of an intrinsic material length scale parameter in the constitutive description. These numerical examples prove the excellent performance of the present frameworks in describing the strain localization problem.