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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 739068, 10 pages
Research Article

A Mathematical Approach to Establishing Constitutive Models for Geomaterials

1Guangdong Provincial Research Institute of Water Conservancy and Hydropower, Guangzhou 510610, China
2State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China

Received 1 March 2013; Accepted 25 May 2013

Academic Editor: Pengcheng Fu

Copyright © 2013 Guang-hua Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The mathematical foundation of the traditional elastoplastic constitutive theory for geomaterials is presented from the mathematical point of view, that is, the expression of stress-strain relationship in principal stress/strain space being transformed to the expression in six-dimensional space. A new framework is then established according to the mathematical theory of vectors and tensors, which is applicable to establishing elastoplastic models both in strain space and in stress space. Traditional constitutive theories can be considered as its special cases. The framework also enables modification of traditional constitutive models.