# A simple model for the dynamics of adhesive failure

(under construction)

Original Entry: Ian Burgess Fall 2009

## Contents

## Keywords

## References

D. Vella, L. Mahadevan, "A simple model for the dynamics of adhesive failure" *Langmuir* **22**, 163 (2006).

## Summary

This paper describes a simple model of adhesive failure used to describe the physical processes that result in bimodal nature of stress/strain curves in experiments. They consider two parallel plates attached to each other by an array of <math> N(t)</math> nonlinear springs, which dissociate as the plates are pulled apart at a constant velocity. They describe the dissociation rate by the equation:

<math> k(t)=k_{0}\exp\left(\frac{\gamma vt}{bL(1-vt/L)}\right)</math>

where <math> \gamma</math> is a lengthscale associated with the adhesive's bond potential, <math> k_{0}</math> is the dissociation rate when no force is applied, *v* is the velocity at which the plates are being pulled apart, and *b* and *L* are lengths associated with the polymer chain in the adhesive. <math> N(t)</math> is then described by the equation,

<math> \frac{\mathrm{d}N}{\mathrm{d}t}=-k(t)N</math>