An Accurate SPH Scheme for Hypervelocity Impact Modeling

Abstract

We focus in this paper on the use of a meshless numerical method called Smooth Particle Hydrodynamics (SPH), to solve fragmentation issues as Hyper Velocity Impact (HVI). Contrary to classical grid-based methods, SPH does not need any opening criteria which makes it naturally well suited to handle material failure. Nevertheless, SPH schemes suffer from well-known instabilities questioning their accuracy and activating nonphysical processes as numerical fragmentation. Many stabilizing tools are available in the literature based for instance on dissipative terms, artificial repulsive forces, stress points or Particle Shifting Techniques (PST). However, they either raise conservation and consistency issues, or drastically increase the computation times. It limits then their effectiveness as well as their industrial application. To achieve robust and consistent stabilization, we propose an alternative scheme called γ -SPH-ALE. Firstly implemented to solve Monophasic Barotropic flows, it is secondly extended to the solid dynamics. Particularly, based on the ALE framework, its governing equations include advective terms allowing an arbitrary description of motion. Thus, in addition of accounting for a stabilizing low-Mach scheme, a PST is implemented through the arbitrary transport velocity field, the asset of ALE formulations. Through a nonlinear stability analysis, CFL-like conditions are formulated ensuring the scheme conservativity, robustness, stability and consistency. Besides, stability intervals are defined for the scheme parameters determining entirely the stability field. Its implementation on several test cases reveals particularly that the proposed scheme faithfully reproduces the strain localization in adiabatic shear bands, a precursor to failure. By preventing spurious oscillations in elastic waves and correcting the so-called tensile instability, it increases both stability and accuracy with respect to classical approaches.

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

“…If 𝛼 approaches zero, Equations ( 17)- (20) transforms into the fully Eulerian formalism expressed in Equations ( 12)- (15). By contrast, if 𝛼 approaches one, Equations ( 17)- (20) transforms into the fully Lagrangian formalism expressed in Equations ( 6)-(9).…”

“…Vila 13 expanded his research path, relying on the SPH-ALE combination and a finite volume-stabilizing low-Mach scheme, the so-called γ-SPH-ALE method. 14 The proposed scheme exhibited increased stability and accuracy in high-velocity impact (HVI) modeling 15 and on various hydrodynamics problems. 14 Oger et al 12 worked with SPH-ALE by using the approximate Riemann solver.…”

“…In recent SPH studies, many researchers have explored Arbitrary Lagrangian Eulerian (ALE) formulations to utilize both Eulerian and Lagrangian natures. [12][13][14][15][16][17][18] The ALE formalism was first proposed in the finite element (FE) framework to combine the advantages of the Eulerian and Lagrangian frameworks; subsequently, it was first introduced in the SPH context by Vila. 13 In the ALE-SPH scheme, motion of the reference frame is defined by an arbitrary transport velocity (u 0 ) that differs from the physical velocity (u) of the particle.…”