Towards a smoothed particle hydrodynamics algorithm for shocks through layered materials

Hypervelocity impacts (HVIs) are collisions at velocities greater than the target object’s speed of sound. Such impacts produce pressure waves that generate sharp and sudden changes in the density of the materials. These are propagated as shock waves. Previous computational research has given insight into this shock loading for the case of homogeneous materials. Shock-wave propagation through materials with discontinuous density distribution has not been considered in depth yet. Smoothed Particle Hydrodynamics (SPH) is a numerical technique, which has been extensively used for the simulation of HVIs. It is especially suitable for this purpose as it describes both the solid and fluid-like behavior effectively as well as the violent breakup of the material under impact. In previous studies on SPH, impact loading of composite materials was modeled by homogenization of the material, or under assumption of being a so-called functionally graded material (FGM). Both these models neglect the reflection-transmission effects on the interface between materials of different density. In this paper the shock loading of layered materials is studied. A modification to the standard SPH method is developed and tested, that incorporates materials with purely discontinuous density distribution. The developed method’s performance at simple shock loading cases is investigated; reflection-transmission patterns of shockwaves through layered materials are discussed, along with a parametric study of the governing parameters. NOMENCLATURE Symbol Definition αu, αρ Dissipative terms coefficients η Smoothing length factor Πij , Φij Artificial terms ρ, ρo, ?̅? Density, reference density, mean density σ, τ, p Total, deviatoric, normal stress element c, c̅ Speed of sound, mean speed of sound Ca Cauchy number h, h̅ Smoothing length, mean smoothing length i, j Particle indices K Bulk modulus m Particle mass N Total number of particles t, δt Time, time step u, uimpact Velocity, impact velocity V Particle volume W SPH interpolation kernel x, δx Position, spacing