Deriving a particle system from continuum mechanics for the animation of deformable objects

Mass-spring and particle systems have been widely employed in computer graphics to model deformable objects because they allow fast numerical solutions. In this work, we establish a link between these discrete models and classical mathematical elasticity. It turns out that discrete systems can be derived from a continuum model by a finite difference formulation and approximate classical continuum models unless the deformations are large. In this work, we present the derivation of a particle system from a continuum model, compare it to the models of classical elasticity theory, and assess its accuracy. In this way, we gain insight into the way discrete systems work and we are able to specify the correct scaling when the discretization is changed. Physical material parameters that describe materials in continuum mechanics are also used in the derived particle system.