Automatic substepping integration of the subloading tij model with stress path dependent hardening

Farias, Marcio M., Pedroso, Dorival M. and Nakai, Teruo (2009) Automatic substepping integration of the subloading tij model with stress path dependent hardening. Computers and Geotechnics, 36 4: 537-548. doi:10.1016/j.compgeo.2008.11.003

Author Farias, Marcio M.
Pedroso, Dorival M.
Nakai, Teruo
Title Automatic substepping integration of the subloading tij model with stress path dependent hardening
Journal name Computers and Geotechnics   Check publisher's open access policy
ISSN 0266-352X
Publication date 2009-05-01
Year available 2008
Sub-type Article (original research)
DOI 10.1016/j.compgeo.2008.11.003
Open Access Status Not Open Access
Volume 36
Issue 4
Start page 537
End page 548
Total pages 12
Place of publication Kidlington, Oxford, United Kingdom
Publisher Pergamon
Language eng
Formatted abstract
This paper discusses the numerical integration of the subloading tij model. This is an elastoplastic model with stress path dependent hardening, which can predict the behaviour of normally consolidated clays or loose sands, as well as of over-consolidated clays or dense sands, with a small number of material parameters. Three features distinguish the subloading tij model from the conventional ones: (a) the use of a modified stress space given by tensor tij; (b) the split of the plastic strain increments in two components leading to a stress path dependent hardening; and (c) the use of two yield surfaces (subloading yield surface and normal yield surface). This last feature is based on the concept of sub-yielding stress states and adds an extra internal strain-like hardening variable, related to the relative density state, which demands its own evolution law. The three characteristics above greatly improve the prediction capabilities of the model, with respect to those of the well-known Cam clay model, at the cost of only two additional parameters. Nonetheless, the numerical integration of the constitutive equations of subloading tij model is a bit challenging, mainly due to the stress path dependent hardening. In order to integrate the equations of subloading tij model in the same way as for any conventional model, the authors reformulated its equations in a simpler and direct manner. Here, these equations are integrated using multi-step explicit schemes, such as modified-Euler and Runge-Kutta-Dormand-Price, with automatic error control. Simple forward-Euler scheme is also used for the sake of comparison. The results show that the modified-Euler scheme is more accurate as well as faster than the other schemes analysed over a wide range of error tolerance. Besides, the automatic feature of these schemes is a great convenience for the users of numerical codes.
© 2008 Elsevier Ltd. All rights reserved.
Keyword Constitutive models
Stress path dependent hardening
Numerical integration
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Unknown
Additional Notes Available online 31 December 2008

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Civil Engineering Publications
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Created: Fri, 18 Mar 2011, 01:21:57 EST by Jeannette Watson on behalf of School of Civil Engineering