A Continuum Description of Failure Waves

TL;DR

This paper develops a thermodynamically consistent continuum theory for failure waves in brittle materials, modeling them as analogous to deflagration waves and unifying classical models within a new variational framework.

Contribution

It introduces a novel two-function thermodynamic approach and a new Lagrangian formulation for failure wave dynamics, extending classical models.

Findings

The theory is thermodynamically consistent.

It unifies classical failure wave models.

Linearized analysis reveals coupling mechanisms.

Abstract

Shattering of a brittle material such as glass occurs dynamically through a propagating failure wave, which however, can not be assigned to any of the classical waves of the elasto-plastic theories of materials. Such failure waves have been a topic of research for decades. In this paper, we build a thermodynamically consistent theory based on the idea that a failure wave is analogous to a deflagration wave. Our theory admits, as special cases, the classical models of Feng and Clifton. Two fundamental thermodynamic functions (the free energy and the entropy production rate) form the basis of our theory. Such a two-function approach allows for the construction of a new variational principle and a new Lagrangian formulation that produce the equations of motion. Finally, a linearization of this theory is examined to gain insight into the coupling between the diffusive and elastic wave phenomena.