The possibility to predict crack patterns on dynamic fracture

TL;DR

This paper extends Slepyan's Maximum Energy Dissipation Principle to include time delays and ruggedness, providing a theoretical framework to predict crack patterns in dynamic fracture and explaining experimental results in PMMA.

Contribution

The authors modify the MEDP to incorporate time delays and dissipation ruggedness, enabling prediction of crack patterns in dynamic fracture beyond previous models.

Findings

The modified MEDP describes instability and pattern formation in dynamic fracture.

The framework explains experimental results in PMMA crack propagation.

It predicts crack patterns in various experimental configurations.

Abstract

The Maximum Energy Dissipation Principle (MEDP) for dynamics fracture, far from equilibrium, proposed by Slepyan was modified. This modification includes a decoupling between the injected and dissipated energy by adding of a time delay and a description of the ruggedness produced by dissipation patterns. A time delayed energy conservation equation is deduced and dynamical equations that describe the dynamical system evolution were obtained in analogous way to the Slepyan's calculations. The conditions for the rising of the instability process were presented by a bifurcation map. These results shown that the theoretical framework proposed can describe the instability process along with dissipation patterns formation. This proposal was applied to dynamics fracture where it was possible to explain the results obtained by Fineberg-Gross for the fast crack propagation in PMMA. For unstable or dynamical crack propagation it is shown the possibility to predict crack patterns using this MEDP for other experimental configurations.