Abaqus/Explicit energy growth issue with S4RS elements
Abaqus/Explicit energy growth issue with S4RS elements
(OP)
I am trying to compare different shell element formulations in Abaqus/Explicit and I stumbled upon an energy growth issue. Here are the specifics of my test case:
-2m x 2m rectangular plate with 5mm thickness
-Element size 0.1m x 0.1m (total of 400 elements)
-All edges fixed (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0)
-Elastic material (steel properties)
-Short duration pressure pulse
-Default hourglass formulations
-Section integration before analysis AND another case where section integrated using 3 Gauss points
-Time step calculated using global stable increment estimator AND another case using a very small time step (time scaling factor 0.15)
I know this is quite coarse mesh and simple test case, but I am using the student version of Abaqus which allows only a maximum of 1000 elements. Nevertheless, I believe it is good enough for comparison purposes.
I ran the test case using S4R (finite strain), S4RS (small strain) and S4RW (small strain, warping considered) elements. The displacement history of plate middle point is quite similar for each model during the first few oscillations (max. displacement approximately 80mm, max. discrepancy between models <2%), but strain contour plots show a slightly larger variance. This of course can be attributed to the different element formulations. What I can't understand is the energy balance. For finite strain elements (S4R) the total energy remains low and negative, as it is supposed to. But for small strain elements (S4RS and S4RW) the total energy is large and positive and continues to increase boundlessly, which is a clear sign of instability. And because of this, the displacement amplitude also continues to increase.
Any idea what might be causing this instability? I always thought that using the small strain elements might give slightly inaccurate results when used in relatively large deformation applications, but I never realized that they could result in fully unstable results.
-2m x 2m rectangular plate with 5mm thickness
-Element size 0.1m x 0.1m (total of 400 elements)
-All edges fixed (U1 = U2 = U3 = UR1 = UR2 = UR3 = 0)
-Elastic material (steel properties)
-Short duration pressure pulse
-Default hourglass formulations
-Section integration before analysis AND another case where section integrated using 3 Gauss points
-Time step calculated using global stable increment estimator AND another case using a very small time step (time scaling factor 0.15)
I know this is quite coarse mesh and simple test case, but I am using the student version of Abaqus which allows only a maximum of 1000 elements. Nevertheless, I believe it is good enough for comparison purposes.
I ran the test case using S4R (finite strain), S4RS (small strain) and S4RW (small strain, warping considered) elements. The displacement history of plate middle point is quite similar for each model during the first few oscillations (max. displacement approximately 80mm, max. discrepancy between models <2%), but strain contour plots show a slightly larger variance. This of course can be attributed to the different element formulations. What I can't understand is the energy balance. For finite strain elements (S4R) the total energy remains low and negative, as it is supposed to. But for small strain elements (S4RS and S4RW) the total energy is large and positive and continues to increase boundlessly, which is a clear sign of instability. And because of this, the displacement amplitude also continues to increase.
Any idea what might be causing this instability? I always thought that using the small strain elements might give slightly inaccurate results when used in relatively large deformation applications, but I never realized that they could result in fully unstable results.





RE: Abaqus/Explicit energy growth issue with S4RS elements
RE: Abaqus/Explicit energy growth issue with S4RS elements
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See FAQ569-1083: Asking questions the smart way on Eng-Tips fora for details on how to make best use of Eng-Tips.com
RE: Abaqus/Explicit energy growth issue with S4RS elements
-Kinetic energy
-Elastic strain energy
-Work done by external forces
-Hourglass energy
Hourglass energy is negligible and the mesh shows no signs of hourglassing. Kinetic energy and strain energy oscillate and their sum continues to increase. Therefore, the total energy continues to increase (as the work done by external forces remains constant after the pressure has gone to zero). The thing that wonders me, is that this happens even when I'm using small enough pressure load to excite only 20mm mid-point displacement, which in my opinion is quite small value compared to plate dimensions. Even using extremely low time increments does not remove this behavior even though the displacement increments during these time increments remain very small. Now, the second order accuracy setting removes this behavior, but also increases the cost of the analysis when using larger models. Otherwise I would suspect something wrong in my test case, but the fact that using second order accuracy OR using S4R elements removes the energy issue, is making me distrust the S4RS element (which apparently is the default shell element formulation in other software such as LS-DYNA and Radioss).
The reason I am inspecting this case is that I am trying to check my own FE-code and my implementation of Belytschko-Tsay shell element (which is named S4RS in Abaqus/Explicit). I am just wondering if this element is not appropriate for this kind of test case or if the energy issue is always present when using this element formulation.
RE: Abaqus/Explicit energy growth issue with S4RS elements
------------
See FAQ569-1083: Asking questions the smart way on Eng-Tips fora for details on how to make best use of Eng-Tips.com
RE: Abaqus/Explicit energy growth issue with S4RS elements
RE: Abaqus/Explicit energy growth issue with S4RS elements