8 research outputs found
Shock loading of layered materials with SPH
Hypervelocity impacts into structures produce shock waves propagating through the colliding bodies. SPH has given insight into shock loading of homogeneous materials; nevertheless, shock wave propagation through solids with discontinuous density distribution, has not been considered in depth, yet. In previous studies using SPH, impact loading of laminated or composite materials was modeled by homogenization of the structure or under the assumption of being functionally graded materials. Both models neglect the reflection-transmission effects on the interface of different density materials. To capture these reflection-transmission effects, a holistic treatment for the multi-phase material is proposed, with kernel interaction over all parts of the structure. The algorithm employs a variable smoothing length formulation. A dissipative mass flux term is also introduced in order to remove spurious post-shock oscillations on the interface of different materials. In this paper, the SPH solution is presented, along with a relevant benchmark case. The algorithm’s performance is studied and the necessity of a variable smoothing length formulation is investigated
Shock loading of layered materials with SPH
Hypervelocity impacts into structures produce shock waves propagating through the colliding bodies. SPH has given insight into shock loading of homogeneous materials; nevertheless, shock wave propagation through solids with discontinuous density distribution, has not been considered in depth, yet. In previous studies using SPH, impact loading of laminated or composite materials was modeled by homogenization of the structure or under the assumption of being functionally graded materials. Both models neglect the reflection-transmission effects on the interface of different density materials. To capture these reflection-transmission effects, a holistic treatment for the multi-phase material is proposed, with kernel interaction over all parts of the structure. The algorithm employs a variable smoothing length formulation. A dissipative mass flux term is also introduced in order to remove spurious post-shock oscillations on the interface of different materials. In this paper, the SPH solution is presented, along with a relevant benchmark case. The algorithm’s performance is studied and the necessity of a variable smoothing length formulation is investigated
From continuum mechanics to SPH particle systems and back : systematic derivation and convergence
In this paper, we employ measure theory to derive from the principle of least action the equation of motion for a continuum with regularized density field. The eventual equation of motion depends on the order in which regularization and the principle of least action are applied. We obtain two different equations, whose discrete counterparts coincide with the scheme used traditionally in the Smoothed Particle Hydrodynamics (SPH) numerical method, and with the equation treated by Di Lisio et al. in 1998, respectively. Additionally, we prove the convergence in the Wasserstein distance of the corresponding measure-valued evolutions, moreover providing the order of convergence of the SPH method. The convergence holds for a general class of force fields, including external and internal conservative forces, friction and non-local interactions. The proof of convergence is illustrated numerically by means of one and two-dimensional examples. Keywords: Smoothed Particle Hydrodynamics, principle of least action, Wasserstein distance, measure-valued equations, convergence rat
Identification of a response amplitude operator for ships
At the European Study Group Mathematics with Industry 2012 in Eindhoven, the Maritime Research Institute Netherlands (MARIN) presented the problem of identifying the response amplitude operator (RAO) for a ship, given input information on the amplitudes of the sea waves and output information on the movement of the ship. We approach the problem from a threefold perspective: a direct least-squares approach, an approach based on truncated Fourier series, and an approach using low-dimensional measures of the RAO. We give a few recommendations for possible further investigations
Identification of a Response Amplitude Operator for Ships
At the European Study Group Mathematics with Industry 2012 in Eindhoven, the Maritime Research Institute Netherlands (MARIN) presented the problem of identifying the response amplitude operator (RAO) for a ship, given input information on the amplitudes of the sea waves and output information on the movement of the ship. We approach the problem from a threefold perspective: a direct least-squares approach, an approach based on truncated Fourier series, and an approach using low-dimensional measures of the RAO. We give a few recommendations for possible further investigations
Shock loading of layered materials with SPH
Hypervelocity impacts into structures produce shock waves propagating through the colliding bodies. SPH has given insight into shock loading of homogeneous materials; nevertheless, shock wave propagation through solids with discontinuous density distribution, has not been considered in depth, yet. In previous studies using SPH, impact loading of laminated or composite materials was modeled by homogenization of the structure or under the assumption of being functionally graded materials. Both models neglect the reflection-transmission effects on the interface of different density materials. To capture these reflection-transmission effects, a holistic treatment for the multi-phase material is proposed, with kernel interaction over all parts of the structure. The algorithm employs a variable smoothing length formulation. A dissipative mass flux term is also introduced in order to remove spurious post-shock oscillations on the interface of different materials. In this paper, the SPH solution is presented, along with a relevant benchmark case. The algorithm’s performance is studied and the necessity of a variable smoothing length formulation is investigated
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 shock-waves through layered materials are discussed, along with a parametric study of the governing parameters
Smoothed Particle Hydrodynamics for Hypervelocity Impacts Into Inhomogeneous Materials
Smoothed Particle Hydrodynamics numerical method is extensively used in the study of hypervelocity impacts and subsequent shock propagation into solids. During impacts into inhomogeneous materials, effects produced on the interface of adjacent materials by shock waves need to be resolved. The present study discusses an SPH multiphase scheme for compressible processes, that is based on the number density estimate and exhibits the scheme’s performance at shock propagation through inhomogeneous materials. In specific, a one-dimensional Riemann problem with known solution validates the scheme and results of two-dimensional hypervelocity impact scenarios into materials with (large-scale and small-scale) inhomogeneities are studied