Hertz Contact

  • Last Post 10 December 2019
maxtran196 posted this 09 December 2019


So I'm simulating a contact problem with a rigid cylinder and a foundation base. Both materials have different Young's Modulus and Poisson Ratio. The contact between the two bodies is frictionless. 

The uniform distributed load is applied at the bottom of the foundation. The result I'm interested in is the force and the displacement at the top of the foundation. 

Force versus Displacement

As you can see, the results from both are quite different. I already know that the equation to compute the force from the displacement is correct. So there must be something wrong with my model.

Also when I try to change from PLANE 183 to PLANE 182, the results hardly change. And I'm having difficulty trying to refine the mesh.

I'm honestly at lost and I don't know how to check if I did anything wrong. I attached the zip file to my model. Any help would be very great. Thank you.

Attached Files

peteroznewman posted this 10 December 2019

Here are your loads and supports.

(1) Displacement [A] is redundant because the whole of the punch body has Fixed Support [D].

(2) Displacement 2 [B] has X = 0, which is redundant because this edge is on the axis of an axisymmetric model so it already can't move in the X direction.

Delete both displacements and the problem will solve the same without them.

A better mesh control method to capture the Hertz stress pattern at the edge of the punch is a set of three Body Sizing mesh controls using Sphere of Influence (which needs a Csys at the corner). There is a small radius with small elements, a medium radius with medium element size and a large radius with large elements then the global mesh size is huge.

You plot reaction force of the punch vs the displacement of the bottom of the foundation and compare that to an analytical force. The analytical force seems to be about 1/4 of the force in your model.  I don't know where you got this analytical force from, but if you want your model to put out force results closer to the analytical values, just make the foundation 4 times deeper (longer in the Y direction). You will then get to the same displacement as before with 1/4 of the force. Of course if the analytical force has an input for foundation depth, that may defeat the purpose of making a model with a deeper foundation.