Elastic moduli of simple mass spring models

Mass spring models (MSMs) are a popular choice for representation of soft bodies in computer graphics and virtual reality applications. In this paper, we investigate physical properties of the simplest MSMs composed of mass points and linear springs. The nodes are either placed on a cubic lattice or positioned randomly within the system. We calculate the elastic moduli for such models and relate the results to other studies. We show that there is a well-defined relationship between the geometric characteristics of the MSM systems and physical properties of the modeled materials. It is also demonstrated that these models exhibit a proper convergence to a unique solution upon mesh refinement and thus can represent elastic materials with a high precision.