Abstract
Based on Ilyushin’s postulate, this paper deals with the necessity and features of researching the geotechnical elasto-plastic theory in strain space. In the paper, we established the relations between stress in variants and elastic strain invariants, brought about the transformation from the stress yield surfaces into the strain yield surfaces, derived and discussed the strain expressions from 12 yield criteria expressed by stress. By normality rule, we also derived 12 constitutive relations for ideal plastic materials associated with the above expressions. The results presented here can be applied to practice and are helpful to the study of the plastic theory in strain space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- ε = [ε 11 ε 22 ε 33 ε 13 ε 31 ε 12]T σ = [σ 11 σ 22 σ 33 σ 13 σ 31 σ 12]T D:
-
elastic matrix
- I 1, I 3 :
-
the first and third invariant of stress tensor
- J 2 :
-
the second invariant of deviatoric stress
- θ σ, θ 691-3:
-
the Lode angle in the stress space and elastic strain space
- Kα :
-
non-reversible internal variable
- I 691-4:
-
the first invariant of elastic strain tensor
- J 691-5, J 691-6:
-
the second and third invariant of elastic strain deviatoric tensor c cohesion
- γc= 2(1 + μ)c/E e 691-7:
-
component of elastic strain deviator
- C=D−1 εp :
-
plastic strain
- εc = ε − εp :
-
elastic strain
References
Y. Dafulls, Elasto-plastic coupling with a thermodynamic space formulation of plasticity. Int. J. Nonlinear Mech., 12 (1977), 327–337.
Qu Sheng-nian and Yin You-quan, ‘Drucker’s and Ilyushin’s postulate of plasticity’, Mechanics Journal, 5, (1981), 465–473.
Yin You-quan and Qu Sheng-nian, Elasto-plastic coupling and generalized normality rule, Mech. Journal, 1 (1982), 63–70.
Wang Ren and Yin You-quan, On the elasto-plastic constitutive equation of engineering rocklike materials, Mech. Journal, 4 (1981), 317–325.
Yin You-quan and Qu Sheng-nian, Constitutive Relations Used in Finite Element Analysis for Structures Made up of Rocklike Materials, Peking Univ. Journal, 1. (1981), 37–46.
Zienkiewicz, O. C., G. N., Pande, Finite Elements in Geomechanics, ed. by Gudehus, G., ASME, (1978), 179–190.
Zienkiewicz, O. C., C. Humpheson, Viscoplasticity: A Generalized Model for Description of soil Behavior, in Numerical Methods in Geotechnical Engineering, Ed. by C. S. Desai and J. T. Christian, (1977), 116–147.
Author information
Authors and Affiliations
Additional information
Communicated by Xue Da-wei and Pan Li-zhou.
Rights and permissions
About this article
Cite this article
Chang-an, C., Ying-ren, Z. Geotechnical yield criteria and constitutive relations in strain space. Applied Mathematics and Mechanics 6, 691–699 (1985). https://doi.org/10.1007/BF03250490
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF03250490