Ogden (hyperelastic Model) - Ogden Material Model

Ogden Material Model

In the Ogden material model, the strain energy density is expressed in terms of the principal stretches, as:

$W\left( \lambda_1,\lambda_2,\lambda_3 \right) = \sum_{p=1}^N \frac{\mu_p}{\alpha_p}\left( \lambda_1^{\alpha_p} + \lambda_2^{\alpha_p} + \lambda_3^{\alpha_p} -3 \right)$

where, and are material constants. Under the assumption of incompressibility one can rewrite as

$W\left( \lambda_1,\lambda_2 \right) = \sum_{p=1}^N \frac{\mu_p}{\alpha_p}\left( \lambda_1^{\alpha_p} + \lambda_2^{\alpha_p} + \lambda_1^{-\alpha_p}\lambda_2^{-\alpha_p} -3 \right)$

In general the shear modulus results from

$2\mu = \sum_{p=1}^{N} \mu_p \alpha_{p}.$

With and by fitting the material parameters, the material behaviour of rubbers can be described very accurately. For particular values of material constants the Ogden model will reduce to either the Neo-Hookean solid (, ) or the Mooney-Rivlin material (, with the constraint condition ).

Using the Ogden material model, the three principal values of the Cauchy stresses can now be computed as

$\sigma_{j} = p + \lambda_{j}\frac{\partial W}{\partial \lambda_{j}}$

where use is made of .

Read more about this topic: Ogden (hyperelastic Model)

Famous quotes containing the words material and/or model:

“A second-class mind dealing with third-class material is hardly a necessity of life.”
—Harold Laski (1893–1950)

“Your home is regarded as a model home, your life as a model life. But all this splendor, and you along with it ... it’s just as though it were built upon a shifting quagmire. A moment may come, a word can be spoken, and both you and all this splendor will collapse.”
—Henrik Ibsen (1828–1906)