Integrating Tensile Parameters in 3D Mass-Spring System

Besides finite element method, mass-spring discrete modeling is widely used in computer graphics. This discrete model allows to perform very easily interactive deformations and to handle quite complex interactions with only a few equations. Thus, it is perfectly adapted to generate visually correct animations. However, a drawback of this simple formulation is the relative difficulty to control efficiently physically realistic behaviors. Indeed, none of the existing models has succeeded in dealing with this satisfyingly. Here, we propose a new general 3D formulation that reconstructs the geometrical model as an assembly of elementary "bricks". Each brick (or element) is then transformed into a mass-spring system. Edges are replaced by springs that connect masses representing the ele- ment vertices. The key point of our approach is the determination of the spring-stiffness to reproduce the correct mechanical properties (Young’s modulus, Poisson’s ratio, bulk and shear modulus) of the reconstructed object. We validate our methodology by performing some numerical experimentations, like shearing and loading, or beam deflection and then we evaluate the accuracy limits of our approach.