Theory vs FE - Internal Energy of Solid Cylinder in Pure Axial Compression

[bsquared55848]

Hi there,

I am having a bit of a conundrum here with Abaqus.

As I understand it, when doing internal energy calculations, the energy of the FE solution should go higher as the number of elements in some geometry increases. As would be expected this continues to a point. Also, the energy as calculated using FE should be in theory lower than that calculated using analytical expressions for the same geometry, as we have discretized the domain and the stiffness of individual elements is higher than that of a solid continuum.

I am trying to find the internal energy stored in a solid cylinder loaded in axial compression. I have an analytical expression for this energy, but the analytical expression is calculating a LOWER energy than what I am finding using Abaqus (I would think it should be the opposite). The loading condition is purely axial.

I have double and triple checked that the material properties and geometry are the same between the FE simulation and the analytical calculations.

Do I have the comparison between the theory and FE simulations right? Or am I completely missing something here?

 

[IceBreakerSours]

"..when doing internal energy calculations, the energy of the FE solution should go higher as the number of elements in some geometry increases."

If the FE model is set-up correctly, not at all! Internal energy comes from the deformation (i.e., change in the kinematic state) of the domain (in a structural analysis). Indeed, beyond a certain number of elements, the energy must converge (unless singularities are present).

" energy as calculated using FE should be in theory lower than that calculated using analytical expressions for the same geometry, as we have discretized the domain and the stiffness of individual elements is higher than that of a solid continuum."

It depends on the element formulation.

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