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Define Young's Modulus as a piecewise function dependent on strain

Posted Jul 16, 2012, 11:26 a.m. EDT Materials, Modeling Tools & Definitions, Parameters, Variables, & Functions, Structural Mechanics Version 4.3 4 Replies

J. C.
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I'd like to define a new material with a nonlinear Young's modulus as a piecewise function dependent on strain. I've defined the piecewise function under Global Definitions, but I'm confused as to what I should make the argument - does Comsol have a strain variable that is independent of direction? Right now all I can find are the principal strains (solid.ep1, solid.ep2, solid.ep3), and since the material should be isotropic, I just want to define E as one general function dependent on strain. Also, once I have this piecewise function defined with the argument as strain, can I just input this function as a user-defined Young's modulus (e.g. E = pw1(strain))? Please let me know if I am on the wrong track - if there is a different, simpler way of defining E.
4 Replies Last Post Jan 15, 2013, 1:02 p.m. EST
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Jul 16, 2012, 2:36 p.m. EDT
Hi

I though strain was a "tensor", hence there is no "one value".
Just as the Young and Poisson value are there to simplify the full stiffness tensor representation for isotropic material

--
Good luck
Ivar
Hi I though strain was a "tensor", hence there is no "one value". Just as the Young and Poisson value are there to simplify the full stiffness tensor representation for isotropic material -- Good luck Ivar
Mats Karlsson
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Posted: 1 decade ago Oct 24, 2012, 6:51 a.m. EDT
Hi,

you could define the bulk Modulus with respect to the volumtric strain (solid.evol in comsol in comsol 4.3a you could choose if you want the elastic part or the total part solid.eelvol = elastic part if you use an no elastic model) and then make use of a constant poissons ratio (nu) and you multiply with 3*(1-2nu).

it would probably be something like E=(-P0+P0*exp(-eelvol/k))/(eps-eelvol)*fac and make sure it cant be zero e.g. by adding a small value.

Cheers,

Mats
Hi, you could define the bulk Modulus with respect to the volumtric strain (solid.evol in comsol in comsol 4.3a you could choose if you want the elastic part or the total part solid.eelvol = elastic part if you use an no elastic model) and then make use of a constant poissons ratio (nu) and you multiply with 3*(1-2nu). it would probably be something like E=(-P0+P0*exp(-eelvol/k))/(eps-eelvol)*fac and make sure it cant be zero e.g. by adding a small value. Cheers, Mats
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago Oct 24, 2012, 10:53 a.m. EDT
Hi JC,

There is no single scalar strain quantity that is ideal for your purpose. You can use the volumetric strain as suggested by Mats or any other strain measure. The key is to find a strain measure that matches your experimental data. If your test data is Young’s modulus vs. strain in only uniaxial loading that is not enough since it does not tell you how the modulus will vary in say shear or biaxial loading.

That is why I recommend that checking if a hyperelastic material model suites your test data instead. That way when the loading mode is different from what you tested experimentally (which is very common) you will have the benefit of a robust continuum based material framework.

Nagi Elabbasi
Veryst Engineering
Hi JC, There is no single scalar strain quantity that is ideal for your purpose. You can use the volumetric strain as suggested by Mats or any other strain measure. The key is to find a strain measure that matches your experimental data. If your test data is Young’s modulus vs. strain in only uniaxial loading that is not enough since it does not tell you how the modulus will vary in say shear or biaxial loading. That is why I recommend that checking if a hyperelastic material model suites your test data instead. That way when the loading mode is different from what you tested experimentally (which is very common) you will have the benefit of a robust continuum based material framework. Nagi Elabbasi Veryst Engineering
N. D.
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Posted: 1 decade ago Jan 15, 2013, 1:02 p.m. EST
Hi everyone,

my aim is related to the issue of J.C.. I’d like to define a new “Elastoresistive coupling matrix” (structural mechanics, piezoresistivity, domain currents) as a function of strain (Young’s modulus remain constant). I think hyperelastic material is not suitable for my issue, because there is no coupling between deformation and resistance change. Can someone tell me how can I define the Elastoresistive coupling matrix as a function of strain or stress?

Thanks in advance
Hi everyone, my aim is related to the issue of J.C.. I’d like to define a new “Elastoresistive coupling matrix” (structural mechanics, piezoresistivity, domain currents) as a function of strain (Young’s modulus remain constant). I think hyperelastic material is not suitable for my issue, because there is no coupling between deformation and resistance change. Can someone tell me how can I define the Elastoresistive coupling matrix as a function of strain or stress? Thanks in advance

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