Analysis of localization of Mohr-Coulomb strength law with damage effect

The damage critical curved surface is derived by considering the related effect of isotropic damage and degradation of cohesion and internal friction angle of Mohr-Coulomb strength law. The characteristics of stress-displacement curve and networks of shear bands with the change of degree of damage, confining pressure and Poisson??s ratio are investigated numerically by monitoring the stress-displacement values in the process of deformation of samples under plane strain and different initial conditions. The dependence of elastic-plastic response of localization is discussed. The non-uniqueness of the solution of equation is given. The orientation angle of shear band is derived by considering the related effect of isotropic damage and degradation of cohesion and internal friction angle. The orientation angle of shear band obtained by numerical simulation is contrasted to the orientation angle by measuring Mohr circle. It is shown that peak strength and residual strength depend on confining pressure. The networks of shear bands begin to appear in phase II of elasticity and develop in soften phase, and the shear band is formed in the phase of residual strength. As the degree of damage increases, axial displacement at the points of bifurcation and shear band decreases. The orientation angle of shear band increases with the increase of the damage degree. The orientation angle of shear band obtained by numerical simulation and measuring Mohr circle is not much difference when the damage degree is equivalent. The Mohr-Coulomb theory may predict the localized instability of sample by considering the degradation of cohesion and internal friction angle.