Analytical solution of the spherical cavity expansion process

The dynamic spherical cavity expansion is treated through a complete analytical solution of the equations of motion for an elasto-plastic solid obeying von-Mises yield criterion. The solutions for various metals, with different elastic and plastic properties, are fitted with a third order polynomial which relates the normalized pressure inside the cavity with the normalized velocity of the cavity wall. An extensive search for material similarities is conducted in order to highlight the roles of the elastic properties of the solid, as well as its strength and equation of state parameters. Using the simple terms we derive, for the coefficients in the third order polynomial, one can easily calculate the relation between pressures inside the cavity and their wall velocities for any solid to within 1%.