Unified analytical stress — strain curve for quasibrittle geomaterial in uniaxial tension, direct shear and uniaxial compression

Abstract

Considering strain localization in the form of a narrow band initiated just at peak stress, three analytical expressions for stress — strain curves of quasibrittle geomaterial (such as rock and concrete) in uniaxial tension, direct shear and uniaxial compression were presented, respectively. The three derived stress — strain curves were generalized as a unified formula. Beyond the onset of strain localization, a linear strain-softening constitutive relation for localized band was assigned. The size of the band was controlled by internal or characteristic length according to gradient-dependent plasticity. Elastic strain within the entire specimen was assumed to be uniform and decreased with the increase of plastic strain in localized band. Total strain of the specimen was decomposed into elastic and plastic parts. Plastic strain of the specimen was the average value of plastic strains in localized band over the entire specimen. For different heights, the predicted softening branches of the relative stress — strain curves in uniaxial compression are consistent with the previously experimental results for normal concrete specimens. The present expressions for the post-peak stress — deformation curves in uniaxial tension and direct shear agree with the previously numerical results based on gradient-dependent plasticity.