Second Degree of Freedom of Elastic Objects - Adjustable Poisson’s Ratio for Mass Spring Models

Kot, Maciej; Nagahashi, Hiroshi

doi:10.5220/0005303601380142

Cited by 1 publication

(1 citation statement)

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“…With the same approach, Kot [22,20,21] presented a method for overcoming the limitation of fixed Poisson's ratio when simulating elastic homogeneous isotropic bodies. His approach is verified on a cubic and disordered lattice.…”

Section: Previous Workmentioning

confidence: 99%

Hybrid 3D mass-spring system for simulation of isotropic materials with any Poisson’s ratio

et al. 2019

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Mass-Spring Systems (MSS) simulating elastic materials obey constraints known in elasticity as the Cauchy relations, restricting the Poisson ratio of isotropic systems to be exactly ν = 1/4. We remind that this limitation is intrinsic to centrosymmetric spring systems (where each node is a center of symmetry), forbidding them for instance to simulate incompressible materials (with ν = 1/2). To overcome this restriction, we propose to supplement the spring deformation energy with an energy depending on the volume only, insensitive to change of shape, permitting MSS to simulate any real isotropic materials. In addition, the freedom in choosing the spring constants realizing a given elastic behavior allows to manage instabilities. The proposed hybrid model is evaluated by comparing its response to various deformation geometries with analytical model and/or Finite Element Model (FEM). The results show that the hybrid MSS model allows to simulate any compressible isotropic elastic material and in particular the nearly incompressible (Poisson ratio ν 1/2) biological soft tissues to which it is dedicated.

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Section: Previous Workmentioning

confidence: 99%