Applied Mathematics and Mechanics

, Volume 6, Issue 7, pp 691–699

# Geotechnical yield criteria and constitutive relations in strain space

• Chen Chang-an
• Zheng Ying-ren
Article

## 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.

## Keywords

Constitutive Relation Yield Surface Yield Curve Plastic Theory Stress Space
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Notation

ε = [ε11ε22ε33ε13ε31ε12]T σ = [σ11σ22σ33σ13σ31σ12]T D

elastic matrix

I1, I3

the first and third invariant of stress tensor

J2

the second invariant of deviatoric stress

θσ, 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/Ee 691-7

component of elastic strain deviator

C=D−1 εp

plastic strain

εc = ε − εp

elastic strain

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