A size-dependent constitutive modelling framework for localised failure analysis

Abstract

Localised deformation of materials usually takes place in thin bands during the nonlinear phase of the deformation process. The orientation and size of these localisation bands are important properties characterising the post-localisation behaviour of the materials, and hence should be taken into account in constitutive modelling. In this research, a new approach is proposed for the integration of both size and orientation of a localisation band in the constitutive description beyond the onset of localisation. Since a length scale related to the size of the localisation band appears in the model description, its post-localisation response then scales with both the band size and the size of the volume element containing it. Therefore, size effects are intrinsically included and post-localisation behaviour is correctly captured, which helps ensure convergence of numerical solutions upon discretisation refinement in numerical analysis of boundary value problems. The concept together with implementation features of the framework and its performances at constitutive level and in the analysis of boundary value problems are presented in this paper.