Maciej Kot

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.

Mass spring models with adjustable Poisson's ratio

In this paper we show how to construct mass spring models for the representation of homogeneous isotropic elastic materials with adjustable Poisson’s ratio. Classical formulation of elasticity on mass spring models leads to the result, that while materials with any value of Young’s modulus can be modeled reliably, only fixed value of Poisson’s ratio is possible. We show how to extend the conventional model to overcome this limitation. The technique is demonstrated on cubic lattice as well as disordered networks.

Verlet with Collisions for Mass Spring Model Simulations.

In this paper we study the problem of the interaction of soft bodies modeled with mass spring models (MSM) and static elements of the environment. We show that in such setup it is possible to couple standard time evolution of MSMs with collision responses in a way, that does not require complex processing for multi collision situations while successfully preventing object inter-penetration. Moreover we show how to achieve similar energy dissipation for models with different resolutions when the friction is present.