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Explicit forms for the tangent modulus tensor in viscoplastic stress analysis
Author(s) -
Brockman R. A.
Publication year - 1984
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.1620200210
Subject(s) - viscoplasticity , finite element method , constitutive equation , tangent , tensor (intrinsic definition) , tangent modulus , stress (linguistics) , cauchy elastic material , matrix (chemical analysis) , displacement (psychology) , tangent stiffness matrix , mathematics , infinitesimal strain theory , cauchy stress tensor , modulus , mathematical analysis , computer science , structural engineering , geometry , materials science , engineering , stiffness matrix , composite material , psychology , linguistics , philosophy , psychotherapist
Viscoplastic constitutive models typically lead to compliance (strain–stress) relationships, which must be inverted for use in the finite element displacement method. Computational requirements can be increased significantly for models of practical size due to the large number of matrix inversions which are necessary. This paper describes a method of obtaining the required stress–strain relations analytically, thus eliminating the need for numerous matrix inversions in the solution. The technique is applicable to a number of commonly‐used viscoplastic models, as demonstrated in the examples.