A polynomial expression for the Mohr-Coulomb criterion for failure of brittle or frictional materials in terms of stress invariants is derived. The form of the polynomial expression corresponds to the pyramidal shape of the failure surface in principal stress space. The pressure-sensitive character of the failure of a Mohr-Coulomb material is indicated by a linear influence of the first stress invariant I1 in the polynomial expression.

Issue Section:
Brief Notes
Topics:
Coulombs, Failure, Stress, Polynomials, Brittleness, Friction materials, Pressure, Shapes
1.
Chen, W. F., and Han, D. J., 1988, Plasticity for Structural Engineers, Springer-Verlag, New York.
2.
Gurtin, M. E., 1981, Introduction to Continuum Mechanics, Academic, New York.
3.
Novozhilov
V. V.
,
1952
, “
On the Physical Interpretation of the Stress Invariants used in the Theory of Plasticity
,”
Prikladnaya Mathematika i Mekhanika, (Applied Mathematics and Mechanics)
, Vol.
16
, No.
5
, pp.
617
–
619
(in Russian).
4.
Prager, W., and Hodge, P. G., 1963, Theory of Perfectly Plastic Solids, John Wiley and Sons, New York.
5.
Schajer
G. S.
,
1994
, “
A Teaching Note on failure criteria and failure surfaces for ductile and brittle materials
,”
International Journal of Mechanical Engineering Education
, Vol.
22
, No.
1
, pp.
1
–
13
.
This content is only available via PDF.
Copyright © 1998
 by The American Society of Mechanical Engineers
You do not currently have access to this content.