Abstract:Strain localization of rock sample in uniaxial compression is the result of self-organization of deformation during loading. Based on the objective existence of localization strain,a constitutive model of rock is proposed. The principle of establishing the constitutive model is that the mechanical behavior of localization strain band is used to describe the complete loading;and the parametric equation is used to describe the constitutive relations of rock. A quasi-static balance equation of energy increment is established based on the energy conservation principle,and a parametric equation of stress-strain curve is deduced. A criterion of instability and a criterion of class II behavior are put forward. Based on the critical condition of instability,an equation of system stress dropping is deduced. The research work shows if the strain softening of the constitutive relations has an inflection point,the system stress dropping happens,else if brittle failure happens. It is proven that the class II behavior of rock is instable or it is self-sustained deformation. And it is proven that the servo-controlled testing machines can not obtain the complete stress-strain curve of class II during loading with increasing constant strain rate. The mechanical parameters of the constitutive model are studied and compared,which show there are effects of the sample size not only on the softening stage of complete stress-strain curve,but also on the hardening stage. The longer the sample length is,the more brittle the material becomes;and the thicker the localization strain band thickness is,the less brittle the material becomes.