Issue 53

Z. Li et alii, Frattura ed Integrità Strutturale, 53 (2020) 446-456; DOI: 10.3221/IGF-ESIS.53.35 453 ( , , ) : : 0 p p p P p p p F F F F       = + + =    σ D σ D σ D (33) ( , ) : : 0 D D D F F F   = =   Y D Y + D Y D (34) By drawing the constitutive equations, the plastic hardening law, and damage criterion (33)~(34), into one system, the plastic and damage multiplier can be determined [37-39]: 3 4 1 6 2 6 3 5 1 5 2 4 2 6 3 5 p D R R R R R R R R R R R R R R R R   −  =  −   −  =  −  (35) where 1 : p F R  =  σ σ , 2 2 6 p ij ij p s s F R J   =  , 3 : p D F R Y    =      Y D , 2 4 : : e e D R Y     = −   Y D , 2 5 2 : 6 ij ij D p s s R Y J    = −   Y D , 2 6 : : D D D F R Y Y        = −            Y Y D D D . N UMERICAL SIMULATIONS or limestone, the below parameters are obtained in triaxial compression tests: 0 88.198 E GPa = , 0 0.255 v = , 0.004 r m  = , 1.5 k = , 1 133  = , 2 1800  = , 11.5 m = , 7.5 n = , 0.13  = , 0 0.00012  = , 0.00014 m  = , 0.25 B = − , 3 1.33  = , 5 0 4.9795 10 Y =  Pa. The dilute scheme, which is used for an elastic solid that has been weakened by an isotropic distribution of non-interacting closed microcracks[40-42], yields the following theoretical initial values of damage variable: 11 0.02 D = , 22 0.02 D = . Figure 2: Simulation of stress-strain curve under triaxial compressive test with confining pressure 10MPa 0 20 40 60 80 100 120 140 160 -2000 -1500 -1000 -500 0 500 1000 1500 2000 2500 3000 3500 Present model Experimental data ε 1 x10 -6 ε 2 x10 -6 (σ 1 -σ 2 )/MPa F