Application of the Localised Lagrange Multiplier Method to a 3D Contact Patch Test

The ability to represent constant stress states is an important issue in finite element analysis. State of the art elements are able to perform flawlessly for such states as long as meshes are conforming. When two domains share a boundary, their meshes do not match at the common boundary when no special care is taken. Sometimes it can be even impossible to make such meshes conforming like for instance in contact analysis with sliding. Patch tests for testing the transfer of constant stress states at nonconforming shared boundaries have been formulated for the 2D case. Here we intent to introduce such a test for the 3D case and demonstrate that the localised Lagrange multiplier approach can be used successfully to pass the 3D Patch test for nonconforming grids.