A multiscale approach for investigating the effect of microstructural instability on global failure in granular materials

Abstract

This paper aims to develop a multiscale approach that has the ability to characterise the influence of microstructural instabilities on global failures in granular materials. For this purpose, the Chang-Hicher multiscale constitutive relation has been implemented into a finite element code, and the expression of the second-order work, as an indicator of the material instability, has been computed at the interparticle contact scale, at the representative element volume scale, and at the boundary value problem scale. At the global scale, the second-order work can be obtained through the integration of that obtained at interparticle contacts. Hence, it becomes possible to analyse the range of instability from the microstructure to the macrostructure. Drained and undrained triaxial tests were numerically simulated. With this method, it was demonstrated that the grain-scale origin of the specimen instability was well captured. Additionally, biaxial tests were conducted and the onsets of localised and diffuse failure in granular assemblies were successfully predicted. The transition from diffuse to localised failure was demonstrated at different scales, whereby the coincidence between the direction of local instabilities and the direction of the shear band became evident. The influence of the boundary conditions and of the heterogeneity of the initial porosity on the failure mode of granular materials was also analysed. All these examples demonstrate that the developed multiscale approach can characterise in a satisfactory manner the influence of instability at the inter-grain contacts upon the global failure of granular assemblies.