The Weak Link Problem: an Asymptotic Approach.

Liya Zhornitskaya, University of Utah

Abstract:

We consider a semi-infinite chain of linear elastic springs connected
to each other. The structure is pulled with a constant velocity $V$.
Suppose that somewhere in the chain there is a weak link, i.e.
the link which breaks whenever its elongation reaches a certain critical
value. We use an asymptotic approach to address two questions:

(1) What is the critical value of velocity $V$ such that below this
value the chain does not break?

(2) If the chain does break, when does it happen?