Towards a Smoothed Particle Hydrodynamics Algorithm for Shocks Through Layered Materials

Abstract

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 shock-waves through layered materials are discussed, along with a parametric study of the governing parameters.

Modeling and Simulation Techniques Used in High Strain Rate Projectile Impact

“…The cubic spline kernel reduces the number of particles included in the calculations to those that are within twice the smoothing length of the particle of interest, while still maintaining C 2 continuity. The kernel function is generally chosen based on the type of problem being addressed, and a reduced interaction function, such as the cubic spline kernel, is often better suited for highly time dependent problems that occur over a short duration, such as impact events [49]. Regardless of kernel chosen, for numerical operations the field variables can be approximated though a kernel summation, which is presented in Equation (23).…”