Abstract：Influences of constitutive parameters，such as elastic modulus，softening modulus and internal length parameter，on localized damage are investigated analytically. In the strain-softening stage beyond the peak strength，both damage variable and damage variable rate are concentrated into the narrow localized band whose width depends on internal length parameter of rock material. Local damage variable increases as flow tensile stress acting on the band decreases. Higher softening modulus leads to lower local damage variable. The larger the elastic modulus is，the larger the local damage variable is. The relationship between maximum local damage variable at the center of the band and flow tensile stress becomes flat as softening modulus increases or the elastic modulus decreases. The influences of softening modulus and elastic modulus on local damage variable rate depend on the flow stress level. At higher stress level approaching peak strength，local damage variable rate increases with decreasing softening modulus. However，at lower stress level，it increases with softening modulus. Lower internal length parameter causes higher gradients of local damage variable and local damage variable rate. Whether internal length parameter is large or not，maximum local damage variable and maximum local damage variable rate remain constants，which is different from previous numerical predictions. As elastic modulus increases or softening modulus decreases，maximum local damage rate-flow stress curve approximately becomes linear.
