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Equivalent Young's Modulus

Posted Oct 6, 2023, 9:59 a.m. EDT Geomechanics, Materials, User Interface Version 6.1 3 Replies

B.T. Lee
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Hi,

I am trying to run an example simulation (Hyperelastic Materials) on the Video Gallery, especially 'user defined' function. I noticed that I need to add the equivalent Young's modulus to run a model. I noticed that there is a equation in the example but I cannot see the full equation from this video.

Anybody knows about this equation? "Eeq" in the figure (Red box)

Thanks in advance. B.T.

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3 Replies Last Post Oct 11, 2023, 7:13 a.m. EDT
Henrik Sönnerlind COMSOL Employee

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Posted: 1 year ago Oct 9, 2023, 2:25 a.m. EDT
Updated: 1 year ago Oct 10, 2023, 3:46 a.m. EDT

The equivalent Young's modulus, Eeq, is a non-essential quantity. For the hyperelastic material itself, it is not used. In some other features, for example in Contact, it is used as characteristic stiffness when defining a default penalty factor. If you have a situation where it is misssing, you can just replace it with any number that gives a correct order of magnitude of the stiffness of the material.

In the built-in hyperelastic materials, it is defined as the Young's modulus at infinitesimal strain.

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Henrik Sönnerlind
COMSOL
The equivalent Young's modulus, Eeq, is a non-essential quantity. For the hyperelastic material itself, it is not used. In some other features, for example in *Contact*, it is used as characteristic stiffness when defining a default penalty factor. If you have a situation where it is misssing, you can just replace it with any number that gives a correct order of magnitude of the stiffness of the material. In the built-in hyperelastic materials, it is defined as the Young's modulus at infinitesimal strain.
B.T. Lee
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Posted: 1 year ago Oct 9, 2023, 10:10 a.m. EDT
Updated: 1 year ago Oct 10, 2023, 3:49 a.m. EDT

Dear Henrik,

Thanks for the reply. Is there any way to get that equation? I am curious how to define the equivalent Young's modulus in especially that equation.

I found one in Storakers, Eeq = 9*((2/3+2*beta1)*mu1+(2/3+2*beta2)*mu2)*(mu1+mu2)/(3*((2/3+2*beta1)*mu1+(2/3+2*beta2)*mu2)+mu1+mu2), but the value is slightly off.

Thanks. B.T.

Dear Henrik, Thanks for the reply. Is there any way to get that equation? I am curious how to define the equivalent Young's modulus in especially that equation. I found one in Storakers, Eeq = 9\*((2/3+2\*beta1)\*mu1+(2/3+2\*beta2)\*mu2)\*(mu1+mu2)/(3\*((2/3+2\*beta1)\*mu1+(2/3+2\*beta2)\*mu2)+mu1+mu2), but the value is slightly off. Thanks. B.T.
Henrik Sönnerlind COMSOL Employee

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Posted: 1 year ago Oct 11, 2023, 7:13 a.m. EDT

Sorry, I am not certain that I understand the question. Are you asking about the derivation of the expression above for the Storakers material?

Basically, you compute the shear modulus (G) and bulk modulus (K) analytically from the strain energy density equation, linearized at zero strain. Then, E_equ=9K*G/(3K+G) using expressions from linear elasticity.

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Henrik Sönnerlind
COMSOL
Sorry, I am not certain that I understand the question. Are you asking about the derivation of the expression above for the Storakers material? Basically, you compute the shear modulus (G) and bulk modulus (K) analytically from the strain energy density equation, linearized at zero strain. Then, E_equ=9K\*G/(3K+G) using expressions from linear elasticity.

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