A coupled-volume approach to the multi-scale modelling of quasi-brittle materials

The hierarchical multi-scale procedure is analysed in this paper. The local multiscale model has been studied with respect to the macro-level mesh dependency and meso-level size dependency. The material behaviour has been analysed in case of linear-elasticity, hardening and softening. Though the results show no dependency in cases of linear-elasticity and hardening, the strong dependency on both macro-level mesh and meso-level size in case of softening has been found. In order to eliminate both macro-level mesh dependency and meso-level size dependency, a new multi-scale procedure has been proposed. This procedure uniquely links the numerical parameter (macro-level mesh size) and model parameter (meso-level size). The results of this coupled-volume multi-scale model show no dependency on the macro-level mesh or meso-level size in any regimes.