An analysis of propagation of elastic-plastic spherical waves in a thick-walled sphere

An analysis of dynamic behavior is carried out in the case when dynamic load with central symmetry is applied on the inner surface of the cavity with central symmetry of a thick-walled elastic-work hardening plastic sphere. The static stress-strain curve for the material in simple tension is assumed to be a smooth curve, concave toward the strain axis. Formulas are derived of the propagation speeds of spherical waves in an isotropic elastic-work hardening plastic body. Ordinary differential equations are derived among physical quantities along characteristic curves. Formulas of propagation speeds of the spherical waves in approximate bodies such as the elastic-linear hardening plastic, the elastic-perfectly plastic, the rigid-work hardening plastic, the rigid-linear hardening and the rigid-perfect plastic bodies are derived from those in the elastic-work hardening plastic body. Calculated results are also presented on the basis of the propagation theory of the spherical waves in the elastic-work hardening plastic body.