Radial variation in Poisson's ratio

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Discussion Overview

The discussion revolves around the phenomenon of radial variation in Poisson's ratio observed in a compressed cylindrical specimen. Participants explore the implications of this variation in the context of material properties, modeling approaches, and experimental setups.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the existence of radial variation in Poisson's ratio when a cylinder is compressed, noting that values appear lower toward the center compared to the circumferential edge.
  • Another participant asks for clarification on the axes and loading conditions of the cylinder, suggesting a uniaxial compression along the z-axis.
  • It is asserted by one participant that Poisson's ratio is a material property that should not vary with spatial location.
  • A participant acknowledges that while Poisson's ratio is typically a material constant, their experimental and finite element (FE) modeling observations indicate a radial variation, with the highest values at the circumferential edge, potentially due to the unconfined nature of the edge.
  • Further discussion includes the modeling of the cylinder compression test, with one participant emphasizing the need to consider the stress model and its effects on the observed responses.
  • Another participant describes their modeling approach using a neo-hookean elastic material and expresses uncertainty about the equations used in the FE software.
  • A later reply encourages a deeper analytical examination of the problem, suggesting that the non-linear nature of neo-hookean materials could lead to a radial variation in the defined Poisson ratio.

Areas of Agreement / Disagreement

Participants express differing views on whether Poisson's ratio can vary radially under compression, with some asserting it is a constant property while others provide evidence of variation based on experimental and modeling results. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants note the importance of understanding the kinematics of deformation and the implications of the stress model used in the analysis, highlighting that assumptions about material behavior and loading conditions may influence the observed results.

Farrell1
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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
 
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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?
 
Poisson's ratio is a property of the material, and does not vary with spatial location.
 
The cylinder axis is in the z-direction 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 occurring 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
 
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 stress-strain relationship.
 
There is no buckling in the sample at all due to near frictionless specimen-compression platen interface.

As for modelling, I have modeled a cylindrical disk as a neo-hookean 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
 
Farrell1 said:
There is no buckling in the sample at all due to near frictionless specimen-compression platen interface.

As for modelling, I have modeled a cylindrical disk as a neo-hookean 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

Let me say this back to you so we are sure I understand. The upper and lower platen contacts with the specimen are taken to be frictionless. The cylindrical disk is being compressed by moving the upper platen downward.

You may be a novice, but you owe it to yourself to examine the problem analytically for a
neo-hookean 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 (non-linear) neo-hookean 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 neo-hookean 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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