converting strain tensor from Cartesian to cylindrical coordinates

[jisb007]

Hi,

This may not be directly related to Abaqus CAE or Abaqus. But I was hoping to generate the strain tensor in a cylindrical coordinate system, and need some help. I was able to use Python to read the 6 NE components from Abaqus odb file after Explicit run. I was also able to construct the strain tensor 3-by-3 matrix. I just need to convert the strain components from the default Cartesian coordinates into a cylindrical coordinates. I know I can do that in Abaqus CAE by creating a cylindrical coordinate system, but how can I do this by writing my own program? i.e., what is the formula? Thanks very much!!

 

[TGS4]

Start here:

http://en.wikipedia.org/wiki/Stress_(mechanics)#Transformation_rule_of_the_stress_tensor,

continue here:

http://en.wikipedia.org/wiki/Infinitesimal_strain_theory#Strain_tensor_in_cylindrical_coordinates.

Have fun.

 

[jisb007]

Appreciate your help! I have actually already came across the links. I know how to generate the strain tensor in a rotated coordinate system (also a Cartesian one), but just don't know how to apply the rules found in the second link to derive the strain components in the cylindrical coordinates, if I have strain tensor in the corresponding Cartesian coordinates. My memory on the calculus derivations are rusted and need to refresh myself.

If you got an existing derivation somewhere, that'll be much appreciated!

 

[TGS4]

Sorry - nope. I'd be doing it "from scratch" myself... Better brush up on that calculus.

 

[jisb007]

OK, I tried to use numerical method to evaluate all those partial derivatives. What I found out was interesting: the strain values are very close to (but not exact with) what Abaqus reported when at the beginning of deformation. The discrepancy became larger and larger when I calculated strain values at later of the simulation. I suspect that this is due to the fact that all my own computations were based on the undeformed configuration while Abaqus has taken into consideration the deformation. Therefore when the deformation got larger, the difference was also elevated.

Any idea exactly what is happening? Or how to rectify? Thanks.