Modelling Localisation and Spatial Scaling of Constitutive Behaviour: a Kinematically Enriched Continuum Approach

TL;DR

This paper introduces a kinematically enriched continuum model that captures localised failure and size effects in quasi-brittle materials by embedding a localisation band, improving upon classical models that fail post-peak.

Contribution

It presents a novel approach with intrinsic length scale modeling localisation and size effects, addressing limitations of classical continuum models in failure analysis.

Findings

Models capture size effects automatically.

Behavior scales with localisation band width.

Improved representation of post-peak failure.

Abstract

It is well known that classical constitutive models fail to capture the post-peak material behaviour, due to localisation of deformation. In such cases the concept of Representative Volume Element (RVE) on which classical continuum models rest ceases to exist and hence the smearing out of local inhomogeneities over the whole RVE is no longer correct. This paper presents a new approach to capturing localised failure in quasi-brittle materials, focusing on the kinematic enrichment of the constitutive model to describe correctly the behaviour of a volume element with an embedded localisation band. The resulting models possess an intrinsic length scale which in this case is the width of the embedded localisation band. The behaviour therefore scales with both the width of the localisation band and the size of the volume on which the model is defined. As a consequence, size effects are automatically captured in addition to the model capability in capturing behaviour at the scale of the localisation zone.