 ## Material Properties

#### How can I determine the Poisson’s ratio for Ogden Hyperfoam (TB,HYPER,,,,FOAM)?

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The Ogden hyperfoam model is a strain energy function which allows for large compressibility since the deviatoric and volumetric terms are actually coupled. The “beta” parameter can be related to the Poisson’s ratio as follows: For a linear elastic material: bulk_modulus = EX/3/(1-2*NUXY) shear_modulus = EX/2/(1+NUXY) Therefore, the ratio of bulk to shear modulus is: bulk/shear = 2*(1+NUXY)/(3*(1-2*NUXY)) Per the Elements Reference for Ogden Hyperfoam constants, the initial bulk and shear moduli are: initial_bulk_modulus = SUM(mu_i * alpha_i (1/3 + beta_i)) initial_shear_modulus = SUM(mu_i * alpha_i)/2 Therefore, the ratio of bulk to shear modulus is: bulk/shear = SUM(1/3+beta_i)*2 Assuming that beta_i is a constant (i.e., beta_1=beta_2=…=constant for all values of i), we can therefore relate Poisson’s ratio with beta_i: bulk/shear = 2*(1/3 + beta_i) = 2*(1+NUXY)/(3*(1-2*NUXY)) (1/3 + beta_i) * 3 * (1-2*NUXY) = (1+NUXY) -1+1+3*beta_i = NUXY + 2*NUXY + 6*NUXY*beta_i NUXY = 3*beta_i/(3+6*beta_i) NUXY = beta_i / (1+2*beta_i) Hence, for example, if beta_i = 0.5, then NUXY can be calculated as being 0.25. 