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An energy‐consistent material‐point method for dynamic finite deformation plasticity
Author(s) -
Love E.,
Sulsky D. L.
Publication year - 2005
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.1512
Subject(s) - hyperelastic material , finite element method , material point method , dissipative system , mathematics , plasticity , consistency (knowledge bases) , conservation of energy , energy–momentum relation , point (geometry) , matrix (chemical analysis) , mass matrix , numerical analysis , mathematical analysis , classical mechanics , physics , structural engineering , engineering , geometry , materials science , quantum mechanics , neutrino , nuclear physics , composite material , thermodynamics
Abstract Energy consistency for the material‐point method (MPM) is examined for thermodynamically consistent hyperelastic‐plastic materials. It is shown that MPM can be formulated with implicit, three‐ field variational, finite element algorithms which dissipate energy and conserve momentum for that class of material models. With a consistent mass matrix the resulting overall numerical method inherits the energy‐dissipative and momentum‐conserving properties of the mesh solution. Thus, the proposed MPM algorithm satisfies by construction a time‐discrete form of the second law of thermo‐ dynamics. Properties of the method are illustrated in numerical examples. Copyright © 2005 John Wiley & Sons, Ltd.