The Mohr-Coulomb criterion (1773), used for civil engineering applications,
assumed that the critical shearing stress depends on the cohesion and the
internal friction which depends on the normal stress. Rankine proposed the
maximum principal stress theory, where assuming tensile stresses to be positive,
yielding occurs if the algebraically maximum principal stress, exceeds the
tensile yield stress or the minimum stress exceeds the compressive stress. While
not followed in general, the criterion is convenient for uniaxial design.
Corresponding to this, St. Venant proposed the maximum principal strain theory.
Based on the results for metals, Tresca (1864), following Coulomb, proposed
that yielding occurs when the maximum shear stress at a point reaches a critical
value. To simplify the resulting surfaces, von Mises (1913) independently
reintroduced the maximum octahedral shear stress criterion of Huber, by which
yielding occurs when the maximum octahedral shearing stress at a point reaches a
critical value. This criterion was interpreted by Hencky (1924) as being
equivalent to the criterion that predicts yielding when the distortion energy at
a point reaches critical value, although this may not be the case for
anisotropic materials (Hill, 1950).
For
geologic materials, where the mean pressure significantly affects yield
behavior, models developed included the Drucker-Prager criterion, the CAP model
and the Cam Clay model developed at Cambridge for clay.
A unified yield function, HiSS, was developed by
Desai (2001) for simulating continuous
yield. It contains most prior yield functions as special cases and has been
applied to several types of materials including metals and solder alloys,
ceramics, sands, rocks, soil and concrete. Several
issues were detected
with HiSS (Dube, 2004), and although
simple
schemes were provided to mitigate
the effects of individual issues with the prior function, a
new yield function was developed to
resolve all issues in a comprehensive manner.