A higherorder Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics
Abstract
We present a new multidimensional highorder Lagrangian discontinuous Galerkin (DG) hydrodynamic method that supports hypoelastic and hyperelastic strength models for simulating solid dynamics with higherorder elements. We also present new onedimensional test problems that have an analytic solution corresponding to a hyperelastic–plastic wave. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated highorder Taylor series polynomials. The stress fields are represented using nodal quantities. The constitutive models used to calculate the deviatoric stress are either a hypoelastic–plastic, infinitesimal strain hyperelastic–plastic, or finite strain hyperelastic–plastic model. These constitutive models require new methods for calculating highorder polynomials for the velocity gradient and deformation gradient in an element. The plasticity associated with the strength model is determined using a radial return method to with a J_{2} yield criterion and perfect plasticity. The temporal evolution of the governing equations is achieved with the total variation diminishing Runge–Kutta (TVD RK) time integration method. A diverse suite of 1D and 2D test problems are calculated. Here, the new 1D piston test problems, which have analytic solutions for each elastic–plastic model, are presented and calculated to demonstrate the stability and formal accuracy of the various models with the newmore »
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1523239
 Alternate Identifier(s):
 OSTI ID: 1547188
 Report Number(s):
 LAUR1827653
Journal ID: ISSN 00457825
 Grant/Contract Number:
 89233218CNA000001; LAUR1827653
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Computer Methods in Applied Mechanics and Engineering
 Additional Journal Information:
 Journal Volume: 353; Journal Issue: C; Journal ID: ISSN 00457825
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 42 ENGINEERING; Lagrangian; Hydrodynamics; Discontinuous Galerkin; Solid dynamics; Analytic solutions; Shocks
Citation Formats
Lieberman, Evan J., Liu, Xiaodong, Morgan, Nathaniel Ray, Luscher, Darby Jon, and Burton, Donald E.. A higherorder Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics. United States: N. p., 2019.
Web. https://doi.org/10.1016/j.cma.2019.05.006.
Lieberman, Evan J., Liu, Xiaodong, Morgan, Nathaniel Ray, Luscher, Darby Jon, & Burton, Donald E.. A higherorder Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics. United States. https://doi.org/10.1016/j.cma.2019.05.006
Lieberman, Evan J., Liu, Xiaodong, Morgan, Nathaniel Ray, Luscher, Darby Jon, and Burton, Donald E.. Wed .
"A higherorder Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics". United States. https://doi.org/10.1016/j.cma.2019.05.006. https://www.osti.gov/servlets/purl/1523239.
@article{osti_1523239,
title = {A higherorder Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics},
author = {Lieberman, Evan J. and Liu, Xiaodong and Morgan, Nathaniel Ray and Luscher, Darby Jon and Burton, Donald E.},
abstractNote = {We present a new multidimensional highorder Lagrangian discontinuous Galerkin (DG) hydrodynamic method that supports hypoelastic and hyperelastic strength models for simulating solid dynamics with higherorder elements. We also present new onedimensional test problems that have an analytic solution corresponding to a hyperelastic–plastic wave. A modal DG approach is used to evolve fields relevant to conservation laws. These fields are approximated highorder Taylor series polynomials. The stress fields are represented using nodal quantities. The constitutive models used to calculate the deviatoric stress are either a hypoelastic–plastic, infinitesimal strain hyperelastic–plastic, or finite strain hyperelastic–plastic model. These constitutive models require new methods for calculating highorder polynomials for the velocity gradient and deformation gradient in an element. The plasticity associated with the strength model is determined using a radial return method to with a J2 yield criterion and perfect plasticity. The temporal evolution of the governing equations is achieved with the total variation diminishing Runge–Kutta (TVD RK) time integration method. A diverse suite of 1D and 2D test problems are calculated. Here, the new 1D piston test problems, which have analytic solutions for each elastic–plastic model, are presented and calculated to demonstrate the stability and formal accuracy of the various models with the new Lagrangian DG method. 2D test problems are calculated to demonstrate the stability and robustness of the new Lagrangian DG method on multidimensional problems with highorder elements, which have faces that can bend.},
doi = {10.1016/j.cma.2019.05.006},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 353,
place = {United States},
year = {2019},
month = {5}
}
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