This question is related to a a question about self-tightening knots.
I am supervising a senior thesis and my student is interested in knots. My student is also a rock climber and has an interesting idea for a project, but I am not sure how reasonable it is. She wants to look at the mathematics of knot security. As a climber, she may tie a single rope to a closed loop or tie two pieces of rope together. There are some knots you should trust your life with and others you should avoid while hanging from a cliff. She wants to understand what properties of a knot make it secure. I like the idea, but I have no idea what kind of model we would use. The only articles I could find were about knot security for surgeons tying sutures and were based on experimental evidence only.
Does anyone know any mathematical references for studying physical knots and knot security?