ON THE ROLE OF GRADIENTS IN THE LOCALIZATION OF DEFORMATION AND FRACTURE

A brief account on the role of higher order strain gradients in the localization of plastic flow, the formation and propagation of deformation bands, and the determination of the structure of the crack tip is given. In the case of shear localization, the higher order gradients provide a mechanism for capturing the evolution of plastic flow in the "material softening" regime, deriving estimates for the width or spacing of the localized zones, and obtaining expressions for the velocity of propagating deformation bands. In the case of determination of the structure of the crack tip, the higher order gradients provide a mechanism for eliminating the strain singularity and deriving a displacement profile which satisfies the smooth closure condition and substantiates Barenblatt's cohesive zone concept.