In response to the second question (which I interpret as asking for math models of spider webs as they appear in Nature): There exist several <A HREF="https://en.wikipedia.org/wiki/Spider_web#Types">distinct types</A> of spider webs, one type that has been extensively studied is the *orb web*, see <A HREF="http://www.phys.ocha.ac.jp/okumuralab/h16/inside/papers/AoyanagiPRL.pdf">Simple Model for the Mechanics of Spider Webs</A>.    

A key property of the orb web model is that the web is free of stress concentrations even when a few spiral threads are broken. This is distinctly different from usual elastic materials in which a crack causes stress concentrations and weakens the material.

The model highlights the mechanical adaptability of the web: spiders can increase the number of spiral threads to make a dense web (to catch small insects) or they can adjust the number of radial threads (to adapt to environmental conditions or reduce the cost of making the web) – in both cases without reducing the damage tolerance of the web.

<IMG SRC="https://i.sstatic.net/WjDd6.png" WIDTH="400"/>

Construction of the orb web described in the cited paper.