Rubber FEA

[weisse]

Can reasonable FEA results for nearly incompressible materials be obtained by using an ordinary element type and a Poisson's ratio and Young's modulus from linear elasticity theory if the strain is "small?" Ignore any time dependent material behavior and, because of a small shape factor (i.e., elastomer isn’t highly constrained), the effect of bulk compression on the modulus. This is a general question, so I'm talking about compression or tension. Assume that the modulus is an average from the initial portion of the stress-strain curve if uniaxial test data were to exist. My question regards the limitation of using a Poisson’s ratio ≥ 0.49, not of using a constant modulus. A technical paper by MSC Marc says that using a value near 0.50 leads to very serious numerical errors because of division by approximately zero (www.mscsoftware.com-assets-103_elast_paper.pdf, p. 42). Too serious for a ballpark answer? Is this true no matter what the strain? If so, below what Poisson’s ratio is this no longer an issue? Does this depend on the software (I’m using ANSYS.)?

[Jorgen]

Hmm, I am not quite sure I understand your question. In general, if you have a virtually incompressible material, then you should use hybrid-type elements to avoid pressure locking.

If you want, you should be able to perform a parametric study with different Poisson's ratios and element types, in an effort to figure out in what range each element type gives accurate results.

- Jorgen

[hhspiny]

as you have said, when v -> 0.5, numerical problem occurs (i.e., hard to converge). thus, hybrid element uses lagrangian multiplier to impose the extra incompressible constraint to avoid the convergence problem. I don't remember exact number, but 0.49 should give your K/G over 100 or something, 0.48 gives probaby 20. a guess would be if less than 0.48, normal element might also work. on the otherhand, if you can get it to converge, normal element should give a ballpark number. best way, as Jorgen said, would to test yourselve in the code to see what difference it makes. but chances are, convergence is a problem with normal element.

[weisse]

Thank you both. The motivation for my question is to determine whether different elastomeric compounds with various hardnesses can be evaluated by rough linear FEA (small strain) before obtaining material test data for a hyperelastic model.

Is mesh locking an issue for only large compressive strain?

The quantity (1 - 2*nu) in Hooke’s law (stiffness form) for an isotropic material appears in the denominator, so I see how using a Poisson’s ratio near 0.50 could be problematic. Does the Marc paper's statement about “very serious numerical errors” refer to inaccuracy of a convergent solution or to solution divergence?

A figure at www.padtinc.com/epubs/focus/common/focus.asp?I=27&P=article2.htm graphs the relationship between Poisson’s ratio and K/G. Isn’t the wide variation in K/G at high Poisson’s ratios an issue for only bulk compression?

[sq]

You're right about the denominator, the equation actually quite simple to come by:

[TeX:7f65814b0a]\frac{K}{G}=\frac{2}{3}\frac{1 + \nu}{1 - 2 \nu}[/TeX:7f65814b0a]

The error is divergence, not convergence to an incorrect solution.

When I have had to run limiting cases, using an elasticity model with a Poisson's ratio of 0.49 has yielded acceptable results, just don't get too carried away with the 9's you paste on to the tail of that.

Of course, if the simulation you're doing has finite shear or material rotation components, you might want to avoid using any hypoelastic element formulation (as an integrated deformation rate tensor is not guaranteed to match the proper strain measure based on the deformation tensor).