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, D_p, and the particle volume fraction, f₀, 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. We study the scaling behavior of the self-similar solutions for different drag and percolation scaling laws. We then compare our analysis with experimental velocity time histories for different tungsten loadings of the polymer matrix.