# Mathematical modelling and investigation of explosive pinch, friction and shear problems

Timms, Robert (2018) Mathematical modelling and investigation of explosive pinch, friction and shear problems. Doctoral thesis, University of East Anglia.

## Abstract

The mechanisms which lead to the accidental ignition of explosive materials in response to low energy stimuli are still not well understood. It is widely agreed that localised regions of increased temperature, so-called `hot spots', are responsible. Many mechanisms for hot spot generation have been suggested as a result of experimental studies, but the understanding of such processes remains incomplete. In this thesis, we use asymptotic and numerical techniques to investigate hot spot mechanisms, with a particular focus on those arising from impacts which pinch and shear explosives.

First, a model which accounts for the effect of friction as an explosive material is pinched between two at plates is developed. An analytical solution is found by exploiting the small aspect ratio of the explosive sample. Numerical solution of the thermal part of the problem demonstrates that our model is able to predict important features observed in experiments, such as additional heating near to the plates.

We then go on to study how the presence of a chemical reaction affects the development of shear bands as explosive materials are deformed. Through a boundary layer analysis, we are able to extract key non-dimensional parameters which control the development of shear bands in explosives, and discuss how this may inform the design of materials that are less susceptible to accidental ignitions due to mechanical insults.

Finally, we investigate how molten layers of explosive, which can form between sliding surfaces during shear deformation, may act as a site for hot spot generation. In particular, we consider how the inhomogeneous nature of explosive materials affects the propagation of the melt front. Through a lubrication-type analysis, we demonstrate that the melt front is unstable to perturbations in the presence of a chemical reaction, and that material non-uniformities lead to localised heating within the molten layer.

Item Type: Thesis (Doctoral) Faculty of Science > School of Mathematics Users 9280 not found. 24 Sep 2018 10:30 24 Apr 2021 00:38 https://ueaeprints.uea.ac.uk/id/eprint/68331