In a multi-body part, a conformal mesh ensures that the nodes on both sides of the interface matches. With a non-conformal mesh, the nodes on one side of the interface does not match the nodes on the other side of the interface. The reason why conformal meshes is preferred over non-conformal meshes: with a conformal mesh there is no (or very little) interpolation at the interface which therefore reduces computational time and ensures higher accuracy of the solution. One way to review the results of a non-conformal mesh is to request a Directional Displacement scoped to the two parts. Zoom in on the surface that has the bonded contact. On the legend, grab the line that separates red from the color below and drag it down until red fills one of the parts with red and back off a little so there is a couple of colors leading up to the bonded surface. Now grab the line that separated blue from the color above and drag it up until blue fills one of the parts and back off a little so there is a couple of colors leading up to the bonded surface. You have just created a very sensitive colormap to see displacement discontinuities across the bonded interface. If you had a conformal mesh, the displacements must be continuous across the interface because there is a shared node. If the bonded contact allows some relative motion, you will see a step in the displacement contour. You can use the colormap to quantify the size of the step. In most cases, the first recommendation is to use Shared Topology instead of bonded contact (even) because depending on which formulation is used, there can be some shear flexibility added by the contact element. Two reasons a conformal mesh might not converge when a non-conformal mesh did converge is if the element size was larger on the conformal mesh, or if the element quality was worse on the conformal mesh. When I have two bodies of different materials that move together because they are bonded, I first choose shared topology, which creates a conformal mesh, and let the two bodies be connected to the same nodes shared on the common face. If I want to study the stress in the bonded interface, then I change to bonded contact where I have more options for that study. I say two bodies of different materials because if they are the same material, then I could unite them in CAD. Sometimes you can get a better quality mesh by splitting a single body into multiple bodies that are easier to mesh and use shared topology to connect them.