An introduction to Distinct Lattice Spring Model (DLSM)

The classical elasticity theory can provide an adequate description of the macroscopic mechanical response of most materials, even though they may be heterogeneous when viewed at a microscopic level. However, dynamic fracturing of heterogeneous materials such as rock and concrete cannot be modeled realistically without appealing to their microstructure. To capture such phenomena, a numerical method must be capable of considering not only the elastic range but also the formulation and evolution of micro discontinuities. In this paper, a new numerical method, Distinct Lattice Spring Model (DLSM), is presented in which the material is represented by a system of discrete units (e.g. particles) interacting via springs, or more generally, rheological elements. The model is a close relative of the common finite element method (FEM) when dealing with elastic problems. Yet, due to its discrete nature, it is suitable for simulation of complex fracturing of rocks and solids. Basic principles as well as the application of the model using several numerical examples are presented.