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Recommendations for Hyperelastic Materials

  • Use the NR (Newton-Raphson) iterative method.
  • Values of Poisson's ratio greater than or equal to 0.48 but less than 0.5 are acceptable. When the displacement-pressure formulation is used, Poisson's ratio is recommended in the range from 0.499 to 0.4999.
  • Rubber-like materials usually deform rapidly at low magnitudes of loads thus requiring a slow initial loading.
  • When dealing with rubber-like materials, due to the highly nonlinear behavior of the problem, rapid increase in loading will often result in either numerical instability (negative diagonal terms in the stiffness) or divergence during equilibrium iterations. The automatic-adaptive stepping algorithm can help in such cases.
  • The displacement or the arc-length control may prove to be more effective than force control when negative diagonal terms repeatedly occur under various loading rates.
  • For shell elements with thick formulation, the analysis is simplified since incompressibility does not result in unbounded terms. The formulation is derived assuming perfect incompressibility (Poisson's ratio of 0.5).
  • Constants A and B must be defined such that (A+B) > 0. For more information about how to determine the values of the A and B constants, refer to the work by Kao and Razgunas (Kao and Razgunas, L., "On the Determination of Strain Energy Functions of Rubbers," Proceedings VI of the International Conference on Vehicle Structural Mechanics, Detroit, pp. 124-154.).

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