Analytical solution of complete stress–strain curve in uniaxial compression based on gradient-dependent plasticity

Complete stress-strain curve of rock specimen in uniaxial compression was derived analytically using displacement method and energy conservation method, respectively. Phenomenon of shear strain localization initiated just at peak stress was considered in the form of a single shear band intersecting two lateral edges of specimen. Consistent with experimental observations at least qualitatively, the size of shear band and the distributed plastic shear strain in the band were described by gradient-dependent plasticity where an internal length parameter reflects the heterogeneity of rock. For displacement method, the total axial deformation of specimen was decomposed into elastic and plastic parts. The latter was concerned with shear band thickness, softening modulus and shear band inclination. For energy conservation method, the adopted assumption was that energy consumed by shear band was equal to the work done by axial stress. It is found that the resulting analytical expressions for complete stress-strain curve according to two kinds of methods are identical; however, the former is even more concise. Comparisons of previous experimental results regarding length effects and the present analytical solutions were presented to check the validation of the present model. Parametric studies show that geometrical size of specimen and constitutive parameters as well as shear band inclination influence the post-peak response.