Determination of elasticity parameters in lumped element (mass-spring) models of deformable objects

Lumped element models, also known as, mass-spring-damper models, are widely used to simulate deformable objects because of their simplicity and computational efficiency. However, the parameters of lumped element models are typically determined in an ad hoc fashion through trial-and-error, as these models are not directly based on continuum mechanics of deformable objects. In this paper, an alternative method to determine the elasticity parameters of lumped element models of deformable objects is presented. The elasticity parameters are determined using an optimization that minimizes the matrix norm of the error between the stiffness matrices of the linear lumped element model and the linear finite element model of the same object. The method has been developed for two-dimensions and for three-dimensional volumetric objects with tetrahedral and hexahedral (brick) elements. The method has been validated by comparing deformation results of the lumped element models with the deformation results given by finite element models, under various tension, and compression loading conditions.