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Stresses interpretation in ABAQUS


I am doing the beam tutorial in ABAQUS and I get the mises stress output as given in the tutorial document (ABAQUS manual appendix B).

I am trying to understand the S11, S22 and S33 outputs from this model. The document I am using for my steps are attached. Couldn't attach my .cae file here.

Principal compression and tension stress and strain plots


I have a question with regards to the various stress-strain plots that I see from FEM softwares.

They have plotted principal compression and tension stress plots  and strain plots for a 2d geomterical analysis from a FE software (MARC). They have used a finite strain theory. So does this mean that the principal compression and tension values for the various elements just correspond to the minimum and maximum values of a Cauchy green tensor or some other finite tensor like first or second piola kirchoff stress tensor??

Exponential model W (strain energy density function)- Zero stress zero strain condition



I am new here and have a very basic question on the Strain Energy Density (SED) function of exponential model.

 This is the exponential model SED form : W=a(e(b(I1-3))-1)

Now we have certain postulates such as that

1.W=0 when there is no deformation and

2. stress=0 when strain =0.

 When there is no deformation I1=3 and hence W=0, which is correct.

However, when we take the 1st derivative of W with respect to I1 to get our stress and then substitute I1=3 we don't get stress=0.

Stresses interpretation ABAQUS

Why do some strain energy density (SED) function have 1 invariant (like neo-Hookean) while some others have both 1st and 2nd invariant like mooney-rivlin? is there a specific reason behind using 1st invariant in SED vs all invariants in the SED?


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