  Motivated by an increasing number of remarkable experimental observations on
the role of pressure and shear stress in solid reactions,explosions and
detonations,we present a simple toy model that embodies nonlinear elasticity
and dispersion as well as chemical or phase transformation.This generalization
of the Toda Lattice provides an effective model for the description of the
organization during an abrupt transformation in a solid.One of the challenges
is to capture both the equilibrium degrees of freedom as well as to quantify
the possible role of out-of-equilibrium perturbations.In the Toda Lattice,we
verify that the particle velocities converge in distribution towards the
Maxwell-Boltzmann distribution,thus allowing us to define a bona-fide
temperature.In addition,the balance between nonlinearity and wave dispersion
may create solitary waves that act as energy traps.In the presence of reactive
chemistry,we show that the trapping of the released chemical energy in solitary
waves that are excited by an initial perturbation provides a positive feedback
that enhances the reaction rate and leads to supersonic explosion front
propagation.These modes of rupture observed in our model may provide a
first-order description of ultrafast reactions of heterogeneous mixtures under
mechanical loading.
