Hourglass control & shear locking in ABAQUS

Aaquib Shakeel, Application Engineer Mar 18th, 2024

Selecting the right finite element type in ABAQUS is essential to producing precise and trustworthy forecasts. Nevertheless, using the right element type can occasionally be difficult due to Abaqus’ vast array of element formulations. Traditional hand calculations and FEA projections can sometimes contradict since many analysts are not aware of the restrictions of particular element types, such as solid brick elements (shear locking).

Shear Locking

When elements are subjected to pure bending Shear locking is an error that occurs in finite element analysis due to the linear nature of first order elements. The linear elements do not accurately capture curvature present in the element under bending, and a shear stress is introduced. The additional shear stress in the element (which does not occur in the actual beam) causes the element to reach equilibrium with smaller displacements, i.e., it makes the element appear to be stiffer than it actually is and gives bending displacements lower than they should be.

For visualization ,dotted lines that pass through the Integration points are plotted ,it can be visualise that the upper line gets increased (tension) while the lower got compressed (length decreases) due to the pure bending load. Indicating that the direct stress along direction X-X () is tensile in nature and the direct stress on lower side indicates compressive in nature

Though we have not seen any changes in vertical dotted lines along Y-Y()

Hence we can say there is no stress induced along Y-Y () This means stress is zero at all integration points. From the fig it is clearly visible that the angle between horizontal and vertical lines was 90 deg initially but after the application of pure bending load the angle has been changed to some extent, this signifies that there is some shearing stress, but in actual pure bending there is no shearing stress when any beam is subjected to pure bending. this problem will be seen with fully integrated elements having 4 integration points on each face (considering quad 4 ) .in order to minimise the shear locking effect we should use reduced integration element having one integration point on centre.

Though reduced integration elements are good to eliminate shear locking effect.

But they too face problems with hourglass effect (weird deformation that is not expected in physical scenario but comes in FEA only)

Hourglass effect

weird deformation that is not expected in physical scenario but comes in FEA only.in order to minimise the weird deformation or distortion we need to add some kind of artificial work to prevent the distortion. Abaqus CAE have different types of hourglass control that can be shown in fig below, we need to play with the length ratio that is deformed edge / actual edge length of hourglass element and specify the same in length ratio.
Distortion control=yes
Hourglass control =Enhanced
Geometric order =linear (first order)
Reduced integration =yes
All the above controls are only for element type C3D8R (8 nodded linear brick element with hourglass control)

Below is the image where hourglass control has not been implemented I have highlighted the elements that got effected by hourglass.

In order to control the hourglass effect in reduced integration elements we need to use hourglass control that are Available in Element type this is nothing but the distortion control based on the stiffness (increase element level stiffness ) .

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AUTHOR: Aaquib Shakeel, Application Engineer

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