Jim,
Thanks for the offer to ask your son.
Daryl
caveat: my adviser has no experience with cuben fiber material (HDPE/mylar laminate) … just lots with composites using kevlar, fiberglass and carbon fiber with epoxy resins.
The question I posed: "If I do a decent job of gluing a reinforcing patch to the corner of a tarp and then stress it with some load will a larger patch mean a lower concentration of stress at the boundary by virtue of the boundary being longer?"
His unequivocal answer: Yes
But he then qualified the answer with by saying that you can sometimes create a failure on the larger patch with less load than on the smaller by varying the circumstances … direction of the load, elasticity of the materials (cuben fiber is more elastic on the bias than parallel to the fibers) and other factors. But all other things being equal, the larger patch will produce a stronger corner.
Also, since there's failure modes other than just the fabric failure the best arrangement is one where all parts of the corner have about the same breaking load. SO, a very large patch might avoid fabric failure at the boundary of the patch because it is weaker and fails first at the stitch lines where the webbing is sewn on. So then you beef up the area where it is stitched enough and the failures happen elsewhere. The best solution is one that is balanced and "strong enough" with the lowest weight or cost.
Regarding multi-layer corner patches he advocates the "upside-down wedding cake" layup. Like this:
corner
_____________________
___________ tarp fabric ↓
===============================================
or for many layers, an interleaved layup:
corner
_______________________
______________
___________________
__________ tarp fabric ↓
===============================================
But he doesn't recall seeing that when using fewer than 5 layers