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

On a yield function 277
q/f C
4
3.5
3
2.5
2
1.5
1
0.5
(a) =
(b) =
0.5 1 1.5 2
p/f C
q/f C
4
3.5
3
2.5
2
1.5
1
0.5
0.5 1 1.5 2
Figure 8. Comparison with experiments for rocks. Chert (a) and dolomite (b), data taken from
Hoek and Brown (1980).
q (MPa)
250
200
150
100
50
p (MPa)
q (MPa)
p/f C
(a) =
(b) =
100 200 300 400
250
200
150
100
50
100 200 300 400
p (MPa)
Figure 9. Comparison with experimental results for polymers. Methacrylate (a) and an epoxy
binder (b), data taken from Ol’khovik (1983).
of the yield surface proposed by Deshpande and Fleck [2000, their eqns. (2)-(3)] is
obtained setting
β =1, γ =0, m =2, α =1,
and assuming the correlations given in Tab. 3.
The proposed function (6)-(9) is also expected to model correctly yielding of
porous ductile metals. As a demonstration of this, we present in Fig. 10 a comparison
with the Gurson (1977) model. The Gurson yield function has a circular deviatoric
section so that β =1and γ =0in our model, in addition, we select
α =1, m =2,
2
pc = c = σM
3q2
2
M = σM 1+q3f 2 − 2fq1,
pc
cosh −1 1+q3f 2
2fq1
,
(17)