A constitutive modelling framework featuring two scales of behaviour: Fundamentals and applications to quasi-brittle failure

• A new approach to bridge the scales in modelling localised failure is proposed.
• We enrich the kinematics of constitutive models with localised mode of deformation.
• The resulting constitutive models possess two different scales of behaviour.
• Size effects induced by localised failure are properly captured with models based on this approach.

We propose a constitutive modelling framework with enhanced kinematics to capture localised mode of deformation. The total strain is decomposed into two components to reflect an inelastic localisation band embedded in an elastic bulk. This is the usual case in numerical analysis of localised failure in geomaterials, when the size of the localisation band is very small compared to an element of the discretised domain under consideration. The proposed framework takes into account the sizes and corresponding behaviours of the two inelastic and elastic zones and hence gives derived constitutive models a length scale. This is an essential feature in dealing with size effect issues as a consequence of localised failure in geomaterials. The proposed framework is applied to a constitutive model for the failure analysis of quasi-brittle materials. The implementation algorithms are developed and novel features are illustrated through numerical examples.