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Title: Modeling shockwaves and impact phenomena with Eulerian peridynamics

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.
Authors:
 [1] ;  [1] ;  [1] ;  [2] ;  [2]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. The Boeing Company, Seattle, WA (United States)
Publication Date:
Report Number(s):
SAND-2017-5347J
Journal ID: ISSN 0734-743X; PII: S0734743X16308934
Grant/Contract Number:
AC04-94AL85000
Type:
Accepted Manuscript
Journal Name:
International Journal of Impact Engineering
Additional Journal Information:
Journal Volume: 107; Journal Issue: C; Journal ID: ISSN 0734-743X
Publisher:
Elsevier
Research Org:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING
OSTI Identifier:
1360930
Alternate Identifier(s):
OSTI ID: 1398102

Silling, Stewart A., Parks, Michael L., Kamm, James R., Weckner, Olaf, and Rassaian, Mostafa. Modeling shockwaves and impact phenomena with Eulerian peridynamics. United States: N. p., Web. doi:10.1016/j.ijimpeng.2017.04.022.
Silling, Stewart A., Parks, Michael L., Kamm, James R., Weckner, Olaf, & Rassaian, Mostafa. Modeling shockwaves and impact phenomena with Eulerian peridynamics. United States. doi:10.1016/j.ijimpeng.2017.04.022.
Silling, Stewart A., Parks, Michael L., Kamm, James R., Weckner, Olaf, and Rassaian, Mostafa. 2017. "Modeling shockwaves and impact phenomena with Eulerian peridynamics". United States. doi:10.1016/j.ijimpeng.2017.04.022. https://www.osti.gov/servlets/purl/1360930.
@article{osti_1360930,
title = {Modeling shockwaves and impact phenomena with Eulerian peridynamics},
author = {Silling, Stewart A. and Parks, Michael L. and Kamm, James R. and Weckner, Olaf and Rassaian, Mostafa},
abstractNote = {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.},
doi = {10.1016/j.ijimpeng.2017.04.022},
journal = {International Journal of Impact Engineering},
number = C,
volume = 107,
place = {United States},
year = {2017},
month = {5}
}