PERTURBED SCALE-INVARIANT INITIAL-VALUE PROBLEMS IN ONE-DIMENSIONAL DYNAMIC ELASTOPLASTICITY

The author considers an initial value problem for equations describing the longitudinal motion of an elastoplastic rod. Conditions on the st ress a determine whether the deformation of the rod is plastic or elas tic, both of which are described by wave equations with different wave speeds. Also, plastic deformation is quasi-linear while elastic defor mation is assumed to be linear. The initial conditions are continuous, piecewise C-1, and have a jump in the first derivative only at the or igin. This is a generalization of the scale-invariant problem solved b y D. Schaeffer and M. Shearer, in which plastic deformation is assumed to be linear and the initial conditions are piecewise linear. The ana lysis is divided into cases according to the structure of the correspo nding scale-invariant problem; the most interesting case reduces to a free boundary problem for the plastic equations on a wedge with two fr ee boundaries.