Shear band localization in finite strain deformation theory with strain gradient effects

Abstract

Shear band localization is investigated for a class of incompressible, isotropic, nonlinear elastic material models known as finite strain deformation theories that incorporate a dependence on strain gradients. These models mimic some of the important features of monotonically increasing plastic deformation. By invoking a nonlinear elastic solid, one can employ mathematical tools to analyze localization which cannot be used for other plasticity models. It will be seen that these tools lead to methods which provide new insights into localization and are readily implemented for numerical computation. Detailed localization and post-localization results are presented for power-law materials subject to simple shear and plane strain tension. The width of the localization band is found to be roughly ten to fifteen times the material length parameter characterizing the strain gradient effect. In a uniform block of material, the onset of localization occurs as a bifurcation. An initial non-uniformity, such as a slight reduction in strength in some region of the block, initiates growth of an incipient band which develops into the localized shear band. Bifurcation and imperfection-seeded localizations will be analyzed, revealing the possibility of size dependent imperfection-sensitivity of the localization process.