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Radial variation in Poisson's ratio 
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#1
Jan1013, 12:06 PM

P: 4

Hi,
I am wondering why radial variation in Poisson's ratio exists when a cylinder is compressed? Ie, Poisson's ratio toward the center is lower than what is measured at the circumferential edge. Thanks M 


#2
Jan1013, 05:08 PM

P: 5,462

Perhaps you could elaborate further, particularly clarifying the axes in relation to the cylinder and the loads.
Say the cylinder axis is in the z direction so circular(?) sections through the cylinder are in planes z = constant. Is the compression applied uniaxially and to which axis? 


#3
Jan1013, 08:36 PM

Mentor
P: 5,354

Poisson's ratio is a property of the material, and does not vary with spatial location.



#4
Jan1413, 03:28 AM

P: 4

Radial variation in Poisson's ratio
The cylinder axis is in the zdirection with applied uniaxial compression in the z also.
Poisson's ratio may be an intrinsic material property, however, during experiments and FE modelling, I find radial variation (ie, along the x axis) with the highest value occuring at the circumferential edge. This must be the result of the configuration  unconfined compression. I am guessing it may be due to the unconstrained nature of the circumerential edge that this experiences greatest lateral expansion? Regards 


#5
Jan1413, 04:18 AM

P: 5,462

OK we are getting somewhere, but detail is still in short supply.
You appear to be modelling the cylinder compression test (ie short cylinders so no buckling)? As Chestermiller pointed out, poissons ratio is a material constant, but depending upon your stress model the effect of the loading will produce a variable response due to the confining effect of the material in the cylinder. Which model are you using, plane stress or plane strain? If you do not know, just post the equations you are using. I am convinced what you are observing is not a variation of PR but inherent in you stressstrain relationship. 


#6
Jan1413, 11:55 AM

P: 4

There is no buckling in the sample at all due to near frictionless specimencompression platen interface.
As for modelling, I have modelled a cylindrical disk as a neohookean elastic material and applied a uniaxial uniform displacement in the z direction upon the superior surface of the disk. I am a complete novice in modelling and mechanics so not sure I can go into anymore detail regarding the equations employed by the FE software. Regards 


#7
Jan1413, 09:39 PM

Mentor
P: 5,354

You may be a novice, but you owe it to yourself to examine the problem analytically for a neohookean material. The kinematics of this deformation are very simple. Do not surrender to FE software without understanding what it is doing. It may very well be possible that, for a (nonlinear) neohookean material in this deformation, the quantity that you might define as the Poisson ratio would vary radially. Start out by examining the kinematics of the deformation. The principal directions will be axial, radial, and circumferential. Write out the equations for the three principal stretch ratios. Write out the components of the finite Green's tensor. Write out the equations for the deformational invariants. Plug these into the neohookean equation for the components of the stress tensor. Recognize also that the radial component of the stress tensor is zero at the edge of the cylinder. Write out the stress equilibrium equations, and substitute the stresses into these equations. See if you can solve these equations. 


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