Smoothed Particle Hydrodynamics (SPH) are often used to model solid bodies undergoing large deformation during hypervelocity impacts due to the ability of the method to handle distortion without the mesh entanglement issues posed by other Lagrangian discretizations such as the finite element method. Rather than using mesh connectivity, SPH uses a kernel function and performs smoothed integration over nearest neighbors to enforce the conservation laws of continuum dynamics. A number of improvements to the formulation have been proposed to increase stability and accuracy of the results. Despite such improvements, the performance of the SPH method is limited by the way in which boundary conditions are applied. Deficiency in the SPH field near solid boundaries is a shortcoming inherent to the formulation resulting in an inaccurate representation of contact mechanics during an impact event. To address this, the first part of this work focuses on improving SPH contact by treating the particles as if they were nodes in a finite element mesh. We investigate the effect of distributing contact loads across free surfaces using a Lagrange multiplier scheme. In addition, we propose a method for improving the initial distribution of Lagrangian particle mass and evaluate its effective on pressure waves traveling through a body. There is also potential to improve SPH modeling during non-uniform deformation resulting from impact. As deformation occurs, compressive forces cause SPH particle density to increase in the impact direction and decrease perpendicular to the impact. This can reduce accuracy in the perpendicular plane as the spatial resolution is coarsened. In the most extreme cases, numerical fracture can occur when the particles disperse to the degree that immediate neighbors are no longer recognized. We demonstrate the use of an ellipsoid kernel method, allowing the kernel to deform anisotropically with the particle field to maintain resolution and prevent numerical fracture. We discuss the implications of the method with respect to hypervelocity impacts, and compare results with baseline output obtained using a typical spherical kernel to evaluate its effectiveness.
Kupchella, R., Stowe, D., Weiss, M., Pan, H., & Cogar, J. (2015). SPH modeling improvements for hypervelocity impacts. In Procedia Engineering (Vol. 103, pp. 326–333). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2015.04.054