Dynamic growth of martensitic plates in an elastic material

The growth of martensitic plates under conditions of anti-plane shear is considered for a particular isotropic hyperelastic material. An asymptotic solution is presented for the displacement field near the tip of a plate growing at an arbitrary velocity up to the shear wave speed of the austenite. An energy balance shows that the rate of energy dissipation is essentially the same as for the quasi-static motion of a normal equilibrium shock. Numerical solutions illustrate how the martensitic plates develop in an initial boundary value problem.This work was supported by the National Science Foundation through grant MSM-8658107 and through a grant of supercomputer resources at the John von Neumann Center.