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

Journal Article · Wed May 15 00:00:00 EDT 2019 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2019.05.006· OSTI ID:1523239

Lieberman, Evan J.  ^[1]; Liu, Xiaodong  ^[1]; Morgan, Nathaniel Ray  ^[1]; Luscher, Darby Jon  ^[1]; Burton, Donald E.  ^[1]

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1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: 89233218CNA000001; LA-UR-18-27653
• OSTI ID: 1523239
• Alternate ID(s): OSTI ID: 1547188
• Report Number(s): LA-UR-18-27653
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Vol. 353, Issue C; ISSN 0045-7825
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
Lagrangian
Hydrodynamics
Discontinuous Galerkin
Solid dynamics
Analytic solutions
Shocks