Three-dimensional elastoplastic constitutive model for cement stone based on fractional flow rule

The strain paths of cement stone in the deviatoric and meridian planes under the constant Lode angle loading path (true triaxial stress state) are analyzed. The amount of volumetric and shear strains first increases and then decreases with the intermediate principal stress coefficient. Owing to the generation of plastic volumetric strain and plastic shear strain in the direction of deviatoric stress, the strain path exhibits nonlinearity in the meridian planes. The deviation of the strain path from the constant Lode angle arises from the accumulation of plastic shear strain along the Lode angle direction. In the framework of fractional plasticity, a three-dimensional elastoplastic constitutive model incorporating Lode angle is proposed, including yield function, potential function, and fractional flow rule. The yield surface evolves in both meridian and deviatoric planes, allowing the yield function to precisely characterize the stress state. Since the plus-minus sign in the flow direction of the yield surface is opposite to that in the flow direction of cement stone, a simple elliptic function incorporating Lode angle serves as the potential function. The procedure for the determination of fractional order based on the entirety of the deformation process is proposed, including variable and constant fractional order. The comparison between the experimental result and the analytical solution of constitutive model confirms its accuracy and validity. Furthermore, the difference between variable and constant fractional order on deformation is analyzed. The comparison results indicate that the variable fractional order can provide a more accurate description of deformation than the constant fractional order.