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An updated reference configuration formulation for large‐deformation problems
Author(s) -
Stolle D. F. E.,
Schad H.
Publication year - 1992
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.1610160405
Subject(s) - infinitesimal , stress (linguistics) , lagrangian , deformation (meteorology) , simple (philosophy) , mathematics , constitutive equation , shear (geology) , shear rate , classical mechanics , mathematical analysis , physics , rheology , materials science , thermodynamics , finite element method , philosophy , linguistics , epistemology , meteorology , composite material
This paper examines difficulties encountered when using the Green‐Nagdi rate and presents an updated configuration formulation for problems dealing with large deformations. It is shown that a natural link can be established between the updated reference configuration and linearized updated Lagrangian formulations, if Truesdell's objective stress rate is used. Owing to this connection, any limitations associated with the described formulation would be expected to also apply to an updated Lagrangian formulation and vice versa. It is pointed out that, if second‐order effects are induced, the Truesdell rate appears in the rate equation for equilibrium even when strains are infinitesimal. By examining a simple‐shear problem, where hypoelastic material behaviour with ‘Hooke's law’ is assumed, it is shown that the spherical state of stress is coupled with the shear stress when using the Truesdell or Green‐Nagdi stress rate. It is suggested that objective stress rates, introduced in large‐deformation formulations, may contribute to erroneous predictions if a constitutive law is developed independent of the adopted stress rate.