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Title: High order curvilinear finite elements for elastic–plastic Lagrangian dynamics

Journal Article · · Journal of Computational Physics
 [1];  [1];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
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This paper presents a high-order finite element method for calculating elastic-plastic flow on moving curvilinear meshes and is an extension of our general high-order curvilinear finite element approach for solving the Euler equations of gas dynamics in a Lagrangian frame. We consider elastic-plastic materials with a constant shear modulus and constant plastic yield stress. In order to handle transition to plastic flow, we formulate the stressstrain relation in rate (or incremental) form and augment our semi-discrete equations for Lagrangian hydrodynamics with an additional evolution equation for the deviatoric stress which is valid for arbitrary order spatial discretizations of the kinematic and thermodynamic variables. The semi-discrete equation for the deviatoric stress rate is developed for 2D planar, 2D axisymmetric and full 3D geometries. For each case, the strain rate is approximated via a collocation method at zone quadrature points while the deviatoric stress is approximated using an L2 projection onto the thermodynamic basis. We apply high order, energy conserving, explicit time stepping methods to the semi-discrete equations to develop the fully discrete method. We conclude with numerical results from an extensive series of verification tests that demonstrate several practical advantages of using high-order finite elements for elastic-plastic flow.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
1634893
Report Number(s):
LLNL-JRNL-567119; 632992; TRN: US2201398
Journal Information:
Journal of Computational Physics, Vol. 257, Issue PB; ISSN 0021-9991
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science

References (11)

The Construction of Compatible Hydrodynamics Algorithms Utilizing Conservation of Total Energy journal October 1998
A cell-centered Lagrangian Godunov-like method for solid dynamics journal August 2013
Computational methods in Lagrangian and Eulerian hydrocodes journal September 1992
A Free-Lagrange Augmented Godunov Method for the Simulation of Elastic–Plastic Solids journal January 2002
On the analysis of rotation and stress rate in deforming bodies journal December 1979
A nominally second-order accurate finite volume cell-centered scheme for anisotropic diffusion on two-dimensional unstructured grids journal March 2012
High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics journal January 2012
Adaptive Lagrangian modelling of ballistic penetration of metallic targets journal March 1997
An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces journal March 2003
Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme journal December 2010
Two-Dimensional Stress-Induced Adiabatic Flow report January 1970

Cited By (1)

High Order ADER Schemes for Continuum Mechanics journal March 2020

Figures / Tables (19)

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Related Subjects

97 MATHEMATICS AND COMPUTING