Consistent mesh tying methods for topologically distinct discretized surfaces in non-linear solid mechanics

This work presents a new technique for joining dissimilar meshes in non-linear nite element analysis, with the novel result that the adjoining surfaces do not need to be spatially coincident for patch tests to be passed. The work builds in some sense on results previously presented by Dohrmann et al. (International Journal for Numerical Methods in Engineering 1991; 40:1205), but considerably generalizes upon the results presented there. Most importantly, it is shown that consistency of the tied nite element formulation may be achieved such that implementation of element formulations is not a ected, through the use of a three- eld variational principle applied over the contacting region. A key conclusion of the work is that although the approach advocated bears some resemblance to mortar element schemes for contact analysis (see, for example, McDevitt and Laursen, International Journal for Numerical Methods in Engineering 2000; 48:1525), a straightforward application of a mortaring scheme is not su cient to guarantee patch test passage when dissimilar meshing of curved surfaces leads to local open volumes (or overlaps) between tied surfaces in their reference con gurations. The proposed algorithm is demonstrated through a number of numerical examples performed within a matrix-free non-linear equation solving framework