Larry D. Libersky

Smoothed Particle Hydrodynamics : Some recent improvements and applications

Abstract The Smoothed Particle Hydrodynamics (SPH) computing technique has features which make it highly attractive for simulating dynamic response of materials involving fracture and fragmentation. However, full exploitation of the methods potential has been hampered by some unresolved problems including stability and the lack of generalized boundary conditions. We address these difficulties and propose solutions. Continuum damage modeling of fracture is discussed at length with scalar and tensor formulations proposed and tested within SPH. Several recent applications involving fracture with predicted fragment patterns and mass distributions are compared with experiment.

Normalized SPH with stress points

Smoothed particle hydrodynamics is extended to a normalized, staggered particle formulation with boundary conditions. A companion set of interpolation points is introduced that carry the stress, velocity gradient, and other derived field variables. The method is stable, linearly consistent, and has an explicit treatment of boundary conditions. Also, a new method for finding neighbours is introduced which selects a minimal and robust set and is insensitive to anisotropy in the particle arrangement. Test problems show that these improvements lead to increased accuracy and stability. Published in 2000 by John Wiley & Sons, Ltd.

Recent improvements in SPH modeling of hypervelocity impact

Four improvements to Smoothed Particle Hydrodynamics which enhance its ability to simulate hypervelocity impact are discussed and applied to the impact fracture of a steel cube on an aluminum plate at 2.2 km/s.

A contact algorithm for smoothed particle hydrodynamics

Abstract This paper describes the development and testing of a contact algorithm for Smoothed Particle Hydrodynamics (SPH). The treatment of contact boundary conditions in SPH has not been adequately addressed, and the development of the normalised smoothing function approach has highlighted the need for correct treatment of boundary conditions. A particle to particle contact algorithm was developed for 2D. The penalty formulation was used to enforce the contact condition, and several equations for the penalty force calculation were considered. The contact algorithm was tested for 1- and 2D problems for the velocity range between 0.2 and 4.0 km/s to determine the best penalty force equation and the best approach for applying the contact force. The tests showed that the zero-energy mode problem in the SPH method had to be addressed, as contact excited a zero-energy mode that caused non-physical motion of particles. The test results were compared to the DYNA3D results for the same problems.

A treatment of zero-energy modes in the smoothed particle hydrodynamics method

Abstract This paper describes the development and testing of an approach for treatment of zero-energy modes in the Smoothed Particle Hydrodynamics (SPH) method. The zero-energy modes are a consequence of the fact that field variables and their derivatives are calculated at the same points, so that an alternating field variable has a zero gradient at the particles. An alternative discretisation method that uses two types of particles, “velocity particles” where the velocity is known and “stress particles” where the stress is known, is proposed as a solution to this problem. This approach prevents the zero-energy modes from occurring, and also is a probable solution to the tensile instability problem. 1D and 2D algorithms are presented and test results shown, demonstrating that it does solve the zero-energy mode problem. This approach also offered a method to satisfy the stress-free boundary condition with out the need to explicitly enforce it, as is required in conventional normalised SPH. This was achieved by placing only the velocity points (points where the velocity is known) at material boundaries. The proposed type of discretisation and boundary treatment significantly improves performance and simplifies penalty based contact algorithm for SPH.

The Development of Thermals from Rest

Abstract Conventional techniques for releasing a thermal in laboratory experiments induce enough initial motion to affect seriously the thermals subsequent evolution. We have invented a mechanism for releasing thermals from very close to a state of rest. This allows the examination of the transient behavior of thermals previous to the development of self-similarity. A thermal starting from rest exhibits a much smaller entrainment rate than a self-similar thermal for a distance from its starting point of at least six initial diameters. Since we find that thermals typically penetrate four initial diameters or less in a stably stratified environment, this has potentially great significance for atmospheric convection. Numerical simulations using an axisymmetric, two fluid model aid in the interpretation of these results.

Stability of DPD and SPH

It is shown that DPD (Dual Particle Dynamics) and SPH (Smoothed Particle Hydrodynamics) are conditionally stable for Eulerian kernels and linear fields. This result is important because it is highly desirable to move and change neighbors where the material deformation is large. For higher dimensions (than 1D), stability for general neighborhoods is shown to require a two-step update, such a predictor-corrector. Co-locational methods (all field variables calculated on every particle) benefit from the completeness property also. We show that SPH with corrected derivatives is conditionally stable. Linear completeness of interpolations is shown to assert itself as a powerful ally with respect to stability as well as accuracy.

A technique for the investigation of organic reactions driven by shock waves in liquids

A method has been developed for investigating the chemical reactions of organic compounds under the dynamic shock loading conditions of detonation. Sealed capsules are placed along the axis of a cylindrical charge which is initiated at one end. As the detonation wave progresses along the charge, a major part of the sample inside each capsule is subjected to a well‐balanced annular compression with peak pressure approximately equal to the Chapman–Jouguet pressure of the explosive used. The geometry of the system ensures both minimal structural deformation and low residual velocity of the capsules; consequently high survival rates have been obtained. The temperature and pressure distribution within the sample space has been calculated as a function of time by a computer simulation using MAGI, a three‐dimensional Smooth Particle Hydrodynamics code. The temperature has also been measured experimentally with a variety of organic reactions known to be insensitive to pressure, whose Arrhenius parameters are obtained from the literature and measurements in our laboratory.

MAGI, a smoothed particle hydrodynamics code for space impact analysis

Natural and man-made debris in space pose significant hazards towards space systems vulnerability and survivability. Unfortunately, the problem continues to grow because of mans continued access to space and our tendency, albeit accidental, to leave trash behind. The problem is made worse as systems breakup due to impact or other accidents, which further adds to the debris burden. Interaction with debris is a virtual certainty for long-lifetime systems. Consequently, a clear understanding of the hazards posed by debris is necessary for the implementation of damage minimization and mitigation strategies. The response of a spacecraft to impact is characterized as occurring in two stages. The first involves the prompt interaction between the spacecraft components and the primary projectile and debris cloud. Second is the late time structural response effects which can occur on a time scale significantly longer than the prompt interaction. It is the prompt interaction phase that is the major focus of this paper.