Self-similar solutions of shock propagation in particle composite materials: Scaling dependence on particle drag and percolation models

Self-similar solutions are solved for a shock propagation in a hydrodynamically coupled, two-phase media system using Lie group analysis. The composite media consists of a polymer matrix loaded with micron-sized spherical tungsten particles. Tuning both the particle diameter, Dp, and the particle volume fraction, ф0, we find that the self-similar solutions depend on the form of the particle drag law and the constitutive material behavior as the spherical particle percolation limit is approached. As a validation of the model we study the scaling behavior of the self-similar solutions for different values of the particle volume fraction and compare our analysis with experimental shock transit times for different tungsten loadings of the polymer matrix.