Modeling shockwaves and impact phenomena with Eulerian peridynamics

Silling, Stewart A.; Parks, Michael L.; Kamm, James R.; Weckner, Olaf; Rassaian, Mostafa

doi:10.1016/j.ijimpeng.2017.04.022

Modeling shockwaves and impact phenomena with Eulerian peridynamics

Journal Article · Tue May 09 00:00:00 EDT 2017 · International Journal of Impact Engineering

DOI:https://doi.org/10.1016/j.ijimpeng.2017.04.022· OSTI ID:1360930

Silling, Stewart A. ^[1]; Parks, Michael L. ^[1]; Kamm, James R. ^[1]; Weckner, Olaf ^[2]; Rassaian, Mostafa ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
The Boeing Company, Seattle, WA (United States)

Most previous development of the peridynamic theory has assumed a Lagrangian formulation, in which the material model refers to an undeformed reference configuration. Here, an Eulerian form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformations make the Lagrangian form unsuitable. The Eulerian capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The Eulerian and Lagrangian contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1360930

Alternate ID(s):: OSTI ID: 1398102

Report Number(s):: SAND--2017-5347J; PII: S0734743X16308934

Journal Information:: International Journal of Impact Engineering, Journal Name: International Journal of Impact Engineering Journal Issue: C Vol. 107; ISSN 0734-743X

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (22)

A finite element method for crack growth without remeshing Mo�s, Nicolas; Dolbow, John; Belytschko, Ted International Journal for Numerical Methods in Engineering, Vol. 46, Issue 1 https://doi.org/10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J	journal	September 1999
Dual-horizon peridynamics: Dual-horizon peridynamics Ren, Huilong; Zhuang, Xiaoying; Cai, Yongchang International Journal for Numerical Methods in Engineering, Vol. 108, Issue 12 https://doi.org/10.1002/nme.5257	journal	July 2016
Formulations of Artificial Viscosity for Multi-dimensional Shock Wave Computations Caramana, E. J.; Shashkov, M. J.; Whalen, P. P. Journal of Computational Physics, Vol. 144, Issue 1 https://doi.org/10.1006/jcph.1998.5989	journal	July 1998
A meshfree unification: reproducing kernel peridynamics Bessa, M. A.; Foster, J. T.; Belytschko, T. Computational Mechanics, Vol. 53, Issue 6 https://doi.org/10.1007/s00466-013-0969-x	journal	January 2014
Peridynamic States and Constitutive Modeling Silling, S. A.; Epton, M.; Weckner, O. Journal of Elasticity, Vol. 88, Issue 2 https://doi.org/10.1007/s10659-007-9125-1	journal	July 2007
Studies of dynamic crack propagation and crack branching with peridynamics Ha, Youn Doh; Bobaru, Florin International Journal of Fracture, Vol. 162, Issue 1-2 https://doi.org/10.1007/s10704-010-9442-4	journal	January 2010
Predicting crack propagation with peridynamics: a comparative study Agwai, Abigail; Guven, Ibrahim; Madenci, Erdogan International Journal of Fracture, Vol. 171, Issue 1 https://doi.org/10.1007/s10704-011-9628-4	journal	September 2011
Modeling jet flows caused by the incidence of a shock wave on a profiled free surface Ogorodnikov, V. A.; Mikhailov, A. L.; Romanov, A. V. Journal of Applied Mechanics and Technical Physics, Vol. 48, Issue 1 https://doi.org/10.1007/s10808-007-0003-1	journal	January 2007
Reformulation of elasticity theory for discontinuities and long-range forces Silling, S. A. Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 1 https://doi.org/10.1016/S0022-5096(99)00029-0	journal	January 2000
Peridynamic Theory of Solid Mechanics Silling, S. A.; Lehoucq, R. B. Advances in Applied Mechanics https://doi.org/10.1016/S0065-2156(10)44002-8	book	September 2010
Cluster dynamics method for simulation of dynamic processes of continuum mechanics Davydov, I. A.; Piskunov, V. N.; Veselov, R. A. Computational Materials Science, Vol. 49, Issue 1 https://doi.org/10.1016/j.commatsci.2010.02.043	journal	July 2010
A meshfree method based on the peridynamic model of solid mechanics Silling, S. A.; Askari, E. Computers & Structures, Vol. 83, Issue 17-18 https://doi.org/10.1016/j.compstruc.2004.11.026	journal	June 2005
Computational methods for bird strike simulations: A review Heimbs, Sebastian Computers & Structures, Vol. 89, Issue 23-24 https://doi.org/10.1016/j.compstruc.2011.08.007	journal	December 2011
On the similarity of meshless discretizations of Peridynamics and Smooth-Particle Hydrodynamics Ganzenmüller, G. C.; Hiermaier, S.; May, M. Computers & Structures, Vol. 150 https://doi.org/10.1016/j.compstruc.2014.12.011	journal	April 2015
Implementing peridynamics within a molecular dynamics code Parks, Michael L.; Lehoucq, Richard B.; Plimpton, Steven J. Computer Physics Communications, Vol. 179, Issue 11 https://doi.org/10.1016/j.cpc.2008.06.011	journal	December 2008
Peridynamics via finite element analysis Macek, Richard W.; Silling, Stewart A. Finite Elements in Analysis and Design, Vol. 43, Issue 15 https://doi.org/10.1016/j.finel.2007.08.012	journal	November 2007
Force flux and the peridynamic stress tensor Lehoucq, R.; Silling, S. Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 4 https://doi.org/10.1016/j.jmps.2007.08.004	journal	April 2008
Peridynamic Analysis of Impact Damage in Composite Laminates Xu, Jifeng; Askari, Abe; Weckner, Olaf Journal of Aerospace Engineering, Vol. 21, Issue 3 https://doi.org/10.1061/(ASCE)0893-1321(2008)21:3(187)	journal	July 2008
A Method for the Numerical Calculation of Hydrodynamic Shocks VonNeumann, J.; Richtmyer, R. D. Journal of Applied Physics, Vol. 21, Issue 3 https://doi.org/10.1063/1.1699639	journal	March 1950
Large-scale molecular dynamics study of jet breakup and ejecta production from shock-loaded copper with a hybrid method Durand, O.; Soulard, L. Journal of Applied Physics, Vol. 111, Issue 4 https://doi.org/10.1063/1.3684978	journal	February 2012
Quantification of ejecta from shock loaded metal surfaces Kullback, Brendan A.; Terrones, Guillermo; Carrara, Mark D. AIP Conference Proceedings https://doi.org/10.1063/1.3686445	conference	January 2012
Peridynamics as an Upscaling of Molecular Dynamics Seleson, Pablo; Parks, Michael L.; Gunzburger, Max Multiscale Modeling & Simulation, Vol. 8, Issue 1 https://doi.org/10.1137/09074807X	journal	January 2009

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Spallation Analysis of Concrete Under Pulse Load Based on Peridynamic Theory Wang, Jianfeng; Qian, Songrong Wireless Personal Communications, Vol. 112, Issue 2 https://doi.org/10.1007/s11277-020-07085-9	journal	January 2020
A non-ordinary state-based Godunov-peridynamics formulation for strong shocks in solids Zhou, Guohua; Hillman, Michael Computational Particle Mechanics, Vol. 7, Issue 2 https://doi.org/10.1007/s40571-019-00254-z	journal	June 2019
Modeling and simulation of ice–water interactions by coupling peridynamics with updated Lagrangian particle hydrodynamics Liu, Renwei; Yan, Jiale; Li, Shaofan Computational Particle Mechanics, Vol. 7, Issue 2 https://doi.org/10.1007/s40571-019-00268-7	journal	July 2019
Peridynamics review Javili, Ali; Morasata, Rico; Oterkus, Erkan Mathematics and Mechanics of Solids, Vol. 24, Issue 11 https://doi.org/10.1177/1081286518803411	journal	October 2018
Attenuation of waves in a viscoelastic peridynamic medium Silling, S. A. Mathematics and Mechanics of Solids, Vol. 24, Issue 11 https://doi.org/10.1177/1081286519847241	journal	May 2019

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