Safety is of paramount importance both in storage and deployment of explosives in both military and civilian applications. Explosives are typically surrounded by other inert materials which contain, protect or confine them. Under normal circumstances there is very little movement of the explosive relative to its surroundings and no significant hazard. However, unforeseen events can occur, typically where the explosive is hit by some projectile accidently, or possibly deliberately, when the resulting deformation of the explosive can cause motion of the explosive relative to its surroundings, sometimes with simultaneous compression.
It can occur that a resulting frictional interaction at the surface of the explosive results in sufficient heating to initiate it; that is, that the explosive starts to decompose. If conditions are adverse then the reaction can grow to thermal runaway and in extreme cases disastrous detonation. Attempts to model this physical process with a Lagrangian code such as DYNA struggle. This is because the onset of high shear in the explosive in the vicinity of the surface causes massive mesh distortion. It is believed that there is a layer where extreme shear deformation of the explosive is occurring. This may or may not coincide with a layer of melting and may or may not be a boundary layer depending on the loading.
High explosives have a crystalline structure, but it may be reasonable to suppose that the explosive may be modelled as an elastic-plastic material which melts to become a viscous fluid. Under those circumstances what insights can mathematical methods give? Could e.g. asymptotic methods have a useful role to play? An absolutely ideal outcome of the Study Group would be simple analytical formulae that allowed understanding of the physics and chemistry, but it is recognized that this is very unlikely. A much more realistic goal is the statement of some key boundary-value and initial-value problems, which if solved, would aid our understanding and the offering of some potential solution methods.
A possible approach is to investigate a series of ideal 2-D problems, starting with a steady-state incompressible formulation, ignoring heat effects and the reaction completely, then allow transient effects, moving on to an incompressible formulation with heating but no reaction, then to include compressibility, and the Arrhenius reaction of the explosive, etc. etc.
It is hoped that there should be sufficient scope here to engage the academics over the week and to lead to some fruitful academic research.
Problem presented by:
John Curtis (AWE)
Study Group contributors
Cameron Hall (University of Oxford)
Peter Hicks (University of East Anglia)
Richard Purvis (University of East Anglia)
Melanie Roberts (Universtiy of Western Australia)
David Binding (Aberystwyth University)
Russell Davies (Cardiff University)
Mazgorzata Fraszczak (CIAMSE & Poznan University)
Ikenna Ireka (Obafemi Awolowo University)
Mohit Dahradi (University of Oxford)
Michelle De Decker (Centre de Recerca Matematica)
Francesc Font (Centre de Recerca Matematica)
Cara Morgan (University of Oxford)
Ellen Murphy (University of Limerick)
Tom Shearer (Manchester University)
Emma Warneford (University of Oxford)
Zhiyan Wei (Harvard University)
John Ockendon (University of Oxford)
Andrew Lacey (Heriot-Watt University)
Matthew Crooks (Manchester University)
Other defense projects
Other materials projects
Other Study Group projects