Coupled-volume multi-scale modelling of quasi-brittle material

The hierarchical multi-scale procedure is analysed in this paper. A local multi-scale model has been studied with respect to the macro-level mesh size and meso-level cell 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, a strong dependency on both macro-level mesh size and meso-level cell size in case of softening has been found. In order to eliminate both macro-level mesh size and meso-level cell size dependency, a new multi-scale procedure has been proposed. This procedure uniquely links the numerical parameter “macro-level mesh size” with the model parameter “meso-level cell size”. The results of this coupled-volume multi-scale model show no dependency on the macro-level mesh size or meso-level cell size.