Fronts of weakly exothermal chemical reaction may propagate in solids at ve
ry low temperatures (4 K less than or equal to T less than or equal to 77 K
) thanks to a quite unusual mechanism, involving a feedback between the hea
t produced by the reaction and the disruption of the solid matrix. In this
class of phenomena, the reaction may be induced by mechanical constraints,
without a large elevation of temperature. On the basis of a simple phenomen
ological model, we investigate ignition of a propagating front by, initiall
y (i) disrupting a localized zone of the solid matrix, or by (ii) introduci
ng a temperature jump, leading to a thermal shock with strong temperature g
radients. In particular, we show that reaction can be initiated by disrupti
ng only a very small fraction of the sample. Applications to the problem of
initiation of solid explosives by friction or shocks is briefly discussed.