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Three‐dimensional adaptive meshing by subdivision and edge‐collapse in finite‐deformation dynamic–plasticity problems with application to adiabatic shear banding
Author(s) -
Molinari J. F.,
Ortiz M.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.325
Subject(s) - finite element method , adiabatic process , adaptive mesh refinement , subdivision , robustness (evolution) , spurious relationship , computer science , algorithm , mathematics , geometry , structural engineering , physics , engineering , computational science , biochemistry , machine learning , gene , thermodynamics , chemistry , civil engineering
This paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three‐dimensional finite‐deformation dynamic–plasticity problems. Mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem. The particular mesh‐refinement strategy adopted is based on Rivara's longest‐edge propagation path (LEPP) bisection algorithm. Our strategy for mesh coarsening, or unrefinement, is based on the elimination of elements by edge‐collapse. The convergence characteristics of the method in the presence of strong elastic singularities are tested numerically. An application to the three‐dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method. Copyright © 2001 John Wiley & Sons, Ltd.