Parameter optimization for 3D mass-spring-damper models

In this paper, we investigate the physical accuracy of the 3D mass-spring-damper (MSD) model of an isotropic object. The isotropic object should have the same Poisson constant and Young's modulus in different directions, and so should its model. Based on these two properties, we derive a set of constraints on the parameters of the 3D MSD model. From these constraints, the parameters of the MSD model can be obtained by the constrained least square method. For the MSD model with tetrahedral meshes, we show that its tensile stiffness can be achieved very accurately, and the prone irregular Poisson effects can be suppressed below a tolerable level although its Poisson constant generally cannot be precisely achieved. For the MSD model with hexahedral meshes, we find that the parameters of the model can be obtained explicitly in terms of material properties and mesh geometry. In this case, we also demonstrate that both the tensile stiffness and the Poisson constant can be accurately achieved.