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Hertz contact between a sphere and a rigid plane

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sparta92

Mechanical
Mar 11, 2015
1
Hey,

I'm modeling a Hertz contact between a sphere and a rigid plane. I'm using Abaqus/CAE 6.13-1. My goal is to get consistent results with the analytical solution.

Both parts are 3D deformable solids. My sphere radius is 1 and material steel (Property assigned is Density 8000 and Elasticity with Young's modulus 210E9 and Poisson's ratio 0.3). I'm using surface-to-surface contact. I've given contact properties Tangential behaviour (Frictionless) and Normal behaviour (Hard contact, default). Other surface-to-surface settings are default. I have one constraint, which is rigid body constraint between the plane and a reference point. In Load-module, I have set Body Force to the sphere by magnitude 1000. There is two BCs: first to not let the RP of the plane to move and second to allow the displacement of the sphere only in the direction of the force. The sphere is meshed with "Hex-dominated" element shape with global size of 0.22. Minimum size is 0.1 of the global size. I have 1 step defined with Nlgeom ON, Increment size Initial 0.1, Minimum 1E-6 and Maximum 1.

The problem comes after I submit the job and enter Visualization-module. I get for contact pressure (CPRESS) a maximum value of 4.799E4 (Pascals) even though my analytical solution gives a value of 1.37E8 for maximum Hertzian contact pressure. What did I do wrong? Any suggestions are greatly appreciated!

 
 http://files.engineering.com/getfile.aspx?folder=58b400cb-32fa-4363-8257-54f641eef0d2&file=HertzSpherePlaneContact.cae
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Hi,

In Abaqus documentation you can find benchmark for Hertz contact problem:
Abaqus Benchmarks Guide, 1.1.11 The Hertz contact problem

Maybe it will help you with your model.

Regards,
Bartosz

 
The mesh is way too coarse in the contact area for an investigation of the contact pressure. Make sure you have multiple nodes in contact.
You can use symmetry or even run the analysis axisymmetric.

I also recommend not to have boundary conditions in the contact area.

Keep an eye on the penetration of the parts. Maybe the default penalty stiffness is not high enough. Scale it up or switch to the direct method if necessary.

You may also activate the surface smoothing within the contact pair definition.
 
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