Multi-scale Distinct Lattice Spring Model (m-DLSM)

Multi-scale modeling is regarded as an exciting and promising methodology which can provide powerful tool for the study of macroscopic mechanical response in geo-materials based on their microstructures. A new multi-scale numerical method: multi-scale Distinct Lattice Spring Model (m-DLSM) is presented, in which the micro model of material is represented by a system of discrete units (e.g. particles) interacting via springs, or, more generally, rheological elements and its macroscopic level model represented by Numerical Manifold Method (NMM). The proposed multi-scale model bears a structure of three layers corresponding to the NMM model, the DLSM model and a model for coupling, respectively. The model for coupling is based on a new developed Particle based Manifold Method (PMM) and is called as PMM model to bridge the DLSM with the NMM. The m-DLSM can reduce the computational resources needed for DLSM which is built totally from particles of small size. In this paper, the theoretical basis of the model as well as its application using several numerical examples is presented.