Identification of Spring Parameters for Deformable Object Simulation

Abstract

Mass spring models are frequently used to simulate deformable objects because of their conceptual simplicity and computational speed. Unfortunately, the model parameters are not related to elastic material constitutive laws in an obvious way. Several methods to set optimal parameters have been proposed, but so far only with limited success. We analyze the parameter identification problem and show the difficulties, which have prevented previous work from reaching wide usage. Our main contribution is a new method to derive analytical expressions for the spring parameters from an isotropic linear elastic reference model. The method is described and expressions for several mesh topologies are derived. These include triangle, rectangle and tetrahedron meshes. The formulae are validated by comparing the static deformation of the MSM with reference deformations simulated with the finite element method.

Pneumoperitoneum simulation based on mass-spring-damper models for laparoscopic surgical planning

“…The paper assumes that the tissue Young's modulus E is uniform. Therefore spring stiffness k is computed by a method proposed by Lloyd et al, 31 which estimates spring stiffness k from the Young's modulus E and Poisson's ratio ν based on a comparison between MSDMs and finite element models (FEMs) with tetrahedron elements. According to their paper, when Poisson's ratio ν is 0.25, spring stiffness k is given by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 3 ; 6 3 ; 3 1 7 …”

“…See their paper for a detailed explanation of the above equations. 31 Damping coefficient c is given by E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 4 ; 6 3 ; 2 1 2 c ¼ 2ζ…”

Resolution Scaling for Mass Spring Model Simulations

“…The basic and general case that we want to analyze is an MSM composed of mass points and linear springs. The description of such an MSM was given by Lloyd et al [15]; however, their equations are limited to models based on tetrahedral meshes. They obtained spring parameters by comparing MSM to a corresponding FEMbased model.…”

A Novel Approach for Modeling and Simulation of Helix Twisting Structure Based on Mass-Spring Model

“…As a simplified method, we assume that the material is linear, elastic, homogeneous, and isotropic. As proposed in [29], the spring stiffness is proportional to Young's modulus and the length of shared edge connected with mass point and mass point . In order to compute shared edge length, a fictitious length is proposed and the final stiffness can be calculated as follows:…”