Deformation of strain softening materials Part II: Modelling of strain softening response

Abstract

This paper is an extension of the research reported by the authors in ref. [1]. The emphasis is placed on the modelling of unstable strain softening response. The inception of softening is viewed as a bifurcation problem. Necessary conditions for bifurcation corresponding to strain localization are first reviewed, followed by the description of post bifurcation behaviour. The approach advocated herein regards strain softening as a local phenomenon occurring in a “smeared” sense at a material point. Two alternative techniques for incorporating strain softening response into phenomenological frameworks are discussed: a “smeared” shear band approach employing an internal variable (the thickness of the shear band), and a method based on direct incorporation of “size effect”.