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

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 [1,2]. In order to handle transition to plastic flow, we formulate the stress–strain 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 L{sub 2} 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.
Authors:
 [1] ;  [1] ;  [2]
  1. Center for Applied Scientific Computing, Lawrence Livermore National Laboratory (United States)
  2. Weapons and Complex Integration, B-Division, Lawrence Livermore National Laboratory (United States)
Publication Date:
OSTI Identifier:
22230855
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 257; Journal Issue: Part B; Other Information: Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; APPROXIMATIONS; AXIAL SYMMETRY; EQUATIONS; FINITE ELEMENT METHOD; GEOMETRY; HYDRODYNAMICS; LAGRANGIAN FUNCTION; STRAIN RATE; STRESSES