A new yield function for geomaterials. - Ingegneria - Università degli ...

On a yield function 273
Table 1. Yield criteria obtained as special cases of (6)-(9), r = fc/ft and fc and ft are the
uniaxial strengths in compression and tension, respectively.
Criterion Meridian function f(p) Deviatoric function g(θ)
von Mises
Drucker-Prager
Tresca
mod. Tresca
Coulomb-Mohr
α =1, m =2,
M = 2ft
, c = pc −→ ∞
pc
α =0, M =
3(r − 1)
√ 2(r +1) ,
c = 2fc
, pc = fc m −→ ∞
3(r − 1)
as for von Mises,
√
except that
3ft
M =
pc
as for Drucker-Prager, except that
M = 3√3(r − 1)
2 √ 2(r +1)
as for Drucker-Prager, except that
M = 3 r cos β π
π
π
− − cos β 6 3
6
√
2(r +1)
c = fc
π π
π
cos β − +cosβ 6 3
6
π
− 3cosβ
3r cos β π
6
− π
3
6
β =1, γ =0
as for von Mises
β =1, γ −→ 1
as for Tresca
β = 6
π tan−1
√
3
2r +1 ,
γ −→ 1
mod. Cam-clay m =2,α=1,c=0 as for von Mises
The Mohr-Coulomb limit merits a special mention. In fact, if the following values
of the parameters are selected
α =0, c = fc
π π
π
cos β 6 − 3 +cosβ6 3r cos β π
π
π ,
6 − 3 − 3cosβ6 M = 3 r cos β π
(14)
π
π
6 − 3 − cos β 6
√ ,
2(r +1)