I am working with cartilages that are in contact on the hip. In order to obtain a contour plot of the contact pressure I performed a mesh sensitivity test by selecting linear tetrahedral elements (C3D4). Nevertheless, I was advised to use a finer mesh for visualizing von Mises stress.
After doing some reading, I came across the term "reduction integration scheme" which states that strain and stress in FE uses an integration point in the center of the element. Thus, since Contact Pressure is measured in nodes of elements, it makes sense to me to increase the density of the mesh to obtain better results.
Am I correct? or Is there another explanation for this?
Thanks!
Dear Jose,
In your question there is two important points, the first one why should we use finer mesh in stress calculation. You know the FEM theory, when you have a mesh with finer density predict better stress distribution within the element as compared to coarser. This concept is very relevant and important for the mesh within the loading region and away from the loading even coarser mesh is sufficient. The second question i.e. contact pressure..in FEM the primary unknown is displacement that needs to calculate at various node points of the element. The displacement within the element is to be distributed with the use of shape function. The contact pressure shall be calculated at various integration points within the element. Now, when you go with smaller element size in case of finer mesh, stress distribution within the loading region is closer..so the distribution of stress and its magnitude is going to converge with exact solution. I suggest you to read any FEM text book for further understanding in this aspects..ok all the best..
This document may help you to solve the problem:
Preprint How to get meaningful and correct results from your finite e...
Nodal values of von Mises stress are obtained as a result of extrapolation and averaging of its centroidal (in your case) values while contact pressures are calculated in analisys immediately.
Dear Mr. Karthigeyan,
I understand what you mention, in fact, before I came to analyze my contact pressure in the region of interest (cartilage), I performed a mesh analysis test for convergence by setting up a 1% change of threshold in the results of my average contact pressure and contact area.
I understand from what you mention, and after reading the proposed document of Mr. Assogba, that strain and stress results are the result of the displacement differences between element nodes(first and second order derivatives of displacement). Hence, the smaller the element, the smaller the distance between displaced nodes and the more accurate the results.
Thanks for the advice
Dear Mr. Assogba Ogoubi Cyriaque ,
Thanks for the advice, the document has proven to be very useful!
Dear Victor J. Аdlucky ,
Thanks for the clarification. I've been doing more reading now and your comments make more sense now. Since I'm using C3D4 elements, I only have one integration point in the center which is extrapolated to the 4 nodes present to obtain von Mises stress at nodes.
In FE regardless of the types of loads - concentrated or distributed, have to be converted to nodal forces. Contact forces between two surface is in reality distributed; with coarse mesh, the distributed force will not be representative of actual loading condition, as the nodes will be further away from contact locations between contacting elements. On the other hand a smaller element with finer mesh will be closer to representing distributed loading type, as the nodes will be closer to the locations of the contact. In addition, as a general principle of any numerical method, the finer the discretization the closer it is to the exact solution.
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