The Mohr-Coulomb yield criterion is used widely in elastoplastic geote
chnical analysis. There are computational difficulties with this model
, however, due to the gradient discontinuities which occur at both the
edges and the tip of the hexagonal yield surface pyramid. It is well
known that these singularities often cause stress integration schemes
to perform inefficiently or fail. This paper describes a simple hyperb
olic yield surface that eliminates the singular tip from the Mohr-Coul
omb surface. The hyperbolic surface can be generalized to a family of
Mohr-Coulomb yield criteria which are also rounded in the octahedral p
lane, thus eliminating the singularities that occur at the edge inters
ections as well. This type of yield surface is both continuous and dif
ferentiable at all stress states, and can be made to approximate the M
ohr-Coulomb yield function as closely as required by adjusting two par
ameters. The yield surface and its gradients are presented in a form w
hich is suitable for finite element programming with either explicit o
r implicit stress integration schemes. Two efficient FORTRAN 77 subrou
tines are given to illustrate how the new yield surface can be impleme
nted in practice.