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It is in general believed that explosive ignition is of thermal origin, with mechanical energy being converted into heat energy in localised regions, forming so-called “hot spots”. We investigate how an instability caused by thermal softening may give rise to localised plastic deformation which may lead to subsequent ignition. \u003cbr\u003eWe consider the homogenous deformation of a material which exhibits strain hardening, strain-rate hardening and thermal softening behaviour. As the strain is increased the material enters into the plastic regime and hardening behaviour is observed, exacerbated by any material inhomogeneity. If the deformation takes place at a high enough strain-rate, there is insufficient time for the heat generated by plastic work to be conducted away, and the material subsequently exhibits thermal softening. Where the local softening dominates over the hardening, the material strength decreases, leading to regions of highly localised deformation. \u003cbr\u003eWe exploit an idealised geometry, using asymptotic methods to obtain a reduced system of equations which govern the growth rate of the disturbances. Further, we discuss how the growth rate is affected by the constitutive properties of the material, and highlight how this instability may lead to localised reactions in a range of loading scenarios. \u003cbr\u003eThis work is British Crown Owned Copyright 2017/AWE.\u003cbr\u003e","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://dspace.lib.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