12 Replies Latest reply on Oct 29, 2014 3:23 PM by Jared Conway

Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?

Kyle Jin Oct 28, 2014 4:05 AM

I assume the Elastic Modulus in the isotropic material properties is Young's Modulus (G) so it should have a relation with Shear Modulus and Poisson's ratio as in the equation below:

E=2G(1+v)

I tried calculating several materials and none of them meets the above equation. I am wondering what Elastic Modulus stands for here? If it is not Young's Modulus, what is it?

Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?

Kyle Jin Oct 28, 2014 4:12 AM (in response to Kyle Jin)

One typo in my question: Young's Modulus (E)
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Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?

James Riddell Oct 28, 2014 9:39 AM (in response to Kyle Jin)

If the Shear Modulus is measured then it may not exactly match the relationship. That is just for homogeneous isotropic elastic materials. In practice, for some materials, they actually have been measured and end up in tables around the world. If you leave out 'G' then the FEA solver will calculate it from 'E' & 'nu'.
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- Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
  
  Kyle Jin Oct 28, 2014 10:07 AM (in response to James Riddell)
  
  Hi James,
  
  Thanks for your reply. The material properties in the clipped picture is linear elastic isotropic material from the solidworks library so I think they should fit into this eq. E=2G(1+v).
  
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Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?

Mike Pogue Oct 28, 2014 9:45 AM (in response to Kyle Jin)

You should only have two of those quantities; the third is constrained. If SW doesn't bonk when all three are entered, it must be programmed to ignore one of them.

EDIT: This is only true if SW knows the material is isotropic.
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- Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
  
  Kyle Jin Oct 28, 2014 9:57 AM (in response to Mike Pogue)
  
  The material properties are from the default solidworks library.I didn't change anything but the default parameters didn't fit into the formula. I am thinking mabye elastic modulus is not Young's modulus in solidworks library.
  It is better if someone from SWDWRKS can answer this question.
  
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  - Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
    
    Mike Pogue Oct 28, 2014 10:10 AM (in response to Kyle Jin)
    
    Elastic modulus is the Young's modulus.
    
    I know it was there when you found it. I'm just arguing that there is no way for the software to use all three of these numbers. In fact, I'm pretty sure shear modulus does not enter into the FEA calculations. It's just there like a reference dimension. Consider the shear modulus to be in parenthesis.
    
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    - Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
      
      James Riddell Oct 28, 2014 4:31 PM (in response to Mike Pogue)
      
      If you study continuum mechanics or have developed the compatiblity equations for three dimensional stress then you will see where the three values are used. Yes, there is a relation between them, yes, FEA is based on all three values.
      
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      - Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
        
        Mike Pogue Oct 28, 2014 5:23 PM (in response to James Riddell)
        
        Since it can't vary independently, it's a completely dead parameter. There are three quantities here but only two degrees of freedom. There is no need to track x, y and z if z = f(x,y).
        
        EDIT: It's worth mentioning that, in Nastran, you cannot enter all three of these. You can enter any two you choose
        
        EDIT: I shouldn't be so argumentative. Without looking it up, I'm certain that your right that it shows up. the takeaway was meant to be that you don't need to know it, since it's constrained.
        
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      - Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
        
        Shaun Densberger Oct 28, 2014 7:40 PM (in response to James Riddell)
        
        All three are needed only if you go outside of an isotropic material model (E = 2G(1+nu) is only for an isotropic material), such as transversely isotropic and orthotropic.
        
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    - Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
      
      Kyle Jin Oct 28, 2014 10:35 PM (in response to Mike Pogue)
      
      Hi Mike,
      
      I created a new material with the same properties except setting shear modulus, G to 0 and apply the two materials for simulation. The simulation results are exactly the same. It proves that shear modulus is only a reference value, which is not used in linear elastic isotropic material simulation.
      
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      - Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
        
        Jared Conway Oct 29, 2014 3:23 PM (in response to Kyle Jin)
        
        did you see the article i suggested taking a look at in the kb?
        
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  - Re: Why the the elastic modulus(E), shear modulus(G) and Poisson's ratio(v) don't fit into the formula E=2G(1+v)?
    
    Jared Conway Oct 28, 2014 7:18 PM (in response to Kyle Jin)
    
    i'm trying to figure out what your question is
    
    are you asking why the actual material property from the library may have values that don't match theory
    
    or are you asking how does solidworks use G
    
    i would recommend taking a peek in the solidworks KB as it covers the second question
    for the first question, i wouldn't recommend using default properties without validating them but when you see the answer for the second question your answer will be clear
    
    the basics are this:
    
    When the shear modulus is not explicitly defined by the user, COSMOS products use their normal values calculated using these formulas:
    
    GXY = EX /[2(1 + NUXY)] for isotropic materials, and GXY = (EX.EY) / (EX + EY + 2.EY.NUXY) for orthotropic materials
    
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