An enriched constitutive modelling framework for localised failure of geomaterials
Localised failure in geomaterials is preceded and accompanied by intensive deformation and irreversible micro-structural changes of the material in a small but finite size region. Shear, compaction, and dilation bands observed in soils and porous rocks are typical examples of phenomena that lead to localised failure. The width h of the localisation band has been experimentally shown to be a physical quantity related to the microstructure of the material. On the other hand, numerical methods for the solution of boundary value problems usually introduce another length scale H, as a result of the spatial discretisation of the considered domain into smaller ones over which the constitutive response of the material is defined in terms of incremental stress-strain relationships. While h, as a physical quantity, is fixed, H varies with the resolution of the numerical discretisation. Since h scales with the material microstructure and therefore is usually much smaller than the resolution of the numerical discretisation, the case H > h is considered in this study, e.g. failure behaviour governed by a localisation band of width h embedded in an elastic bulk of nominal side H. We present a general constitutive modelling framework to connect these two scales, and corresponding responses of the materials inside and outside the localisation zone. We demonstrate how this approach can help obtain physically meaningful solutions that are independent of the spatial discretisation in numerical analysis. Numerical analyses of localised failure in quasi-brittle materials are used to further highlight the features and applicability of the proposed approach.