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Title: A higher-order Lagrangian discontinuous Galerkin hydrodynamic method for solid dynamics

Abstract

We present a new multidimensional high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method that supports hypoelastic and hyperelastic strength models for simulating solid dynamics with higher-order elements. We also present new one-dimensional 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 high-order 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 high-order 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 newmore » Lagrangian DG method. 2D test problems are calculated to demonstrate the stability and robustness of the new Lagrangian DG method on multidimensional problems with high-order elements, which have faces that can bend.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]
  1. 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):
LA-UR-18-27653
Journal ID: ISSN 0045-7825
Grant/Contract Number:  
89233218CNA000001; LA-UR-18-27653
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 0045-7825
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 higher-order 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 higher-order 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 higher-order 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 higher-order 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 high-order Lagrangian discontinuous Galerkin (DG) hydrodynamic method that supports hypoelastic and hyperelastic strength models for simulating solid dynamics with higher-order elements. We also present new one-dimensional 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 high-order 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 high-order 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 high-order 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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