mesh bezier modifier curve
To bend a mesh, you need to add a bezier curve (or any other line I suppose). The mesh then follows the curve. The non obvious trick was to move the mesh along the common axis of the curve, like following a rail, until they both align, else you get crazy bendy results.
It seems that I had already figured out how to produce this bendy effect months ago, but then forgot and had to go through the learning process again.