  We explore local existence and properties of classical weak solutions to the
initial-boundary value problem of a one-dimensional quasilinear equation of
elastodynamics with non-convex stored-energy function, a model of phase
transitions in elastic bars proposed by Ericksen [19]. The instantaneous
formation of microstructures of local weak solutions is observed for all smooth
initial data with initial strain having its range overlapping with the phase
transition zone of the Piola-Kirchhoff stress. As byproducts, it is shown that
such a problem admits a local weak solution for all smooth initial data and
local weak solutions that are smooth for a short period of time and exhibit
microstructures thereafter for some smooth initial data. In a parallel way, we
also include some results concerning one-dimensional quasilinear
hyperbolic-elliptic equations.
