You know the way you'll sometimes see someone with a rag tied over a jar? I tried to make this effect with a jar and a ring (torus) where the cloth falls over the top of the jar (this part works perfectly) and then the ring cinches around the cloth. The jar and ring are both set to collision. When the ring reaches the cloth it seems to cut right through it and distorts it beyond recognition. I'm certainly not getting the nice cord around a cloth effect I'm going for. I've also tried using a force field on the ring with similar outcome.
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$\begingroup$ Try subdividing the torus (or giving it a subdivision surface modifier, then applying it) - this gives Blender more geometry to work with and deform for the cloth simulation and in general increases realism. However, it's hard to not get glitches in the cloth (especially for non-planar cloth) when one side moves through the other, etc., without making it very stiff - but fiddle around with the cloth sim settings a bit and get back to us. $\endgroup$– CubitCommented Mar 8, 2016 at 8:35
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For starters, I'd say model the thing manually if its not necessary to use the cloth sim. Cloth sim is for interactivity, i.e. if you want the cloth to interact with something later in an animation.
However, if you want to use the cloth sim, try using Cloth Sewing (new since 2.70), here is a general tutorial: https://www.youtube.com/watch?v=ySyQsLD_7GM
In your case, i would use a similar approach as in the video with the cloak, wrap the cloth mesh around the jar lid, connect all open vertices with edges and mark them as seams to pull together.
I would model the string holding it together entirely manually.
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$\begingroup$ This doesn't really answer his question. He didn't specify if the cloth simulation is necessary for interactivity either, so he may well be planning to make an animation. $\endgroup$– CubitCommented Mar 8, 2016 at 8:36
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$\begingroup$ For one, i gave an answer with using the cloth sim, but suggested to do it without IN CASE its not needed. B. the straight answer to his question is that Blender isnt a simulation of reality. The approach to simulate tying a rope around a piece of cloth using collision objects is an approach for reality, not a 3D modeling software. The cloth sim is only a rough approximation of real cloth behavior for deformation. I would give the same answer if he asked me how to tie a knot using the cloth sim, its the wrong tool for the job. $\endgroup$– AdamTMCommented Mar 8, 2016 at 10:56
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$\begingroup$ In the same way, although Blender's cloth simulation is not an exact representation of reality, it has the potential to be with workarounds. One may simply need to increase the number or steps or the FPS to get more realistic results. $\endgroup$– CubitCommented Mar 10, 2016 at 12:47