Fractional plasticity and its application in constitutive model for sands

It has been recognized that the stress-dilatancy and stress-strain relationship of sand depend on the material state. The plastic flow direction does not usually coincide with the corresponding loading direction but evolves with the material state. To consider such non-associativity, an additional plastic potential surface that is independent of the yielding surface is usually assumed. A state parameter is then incorporated into the material constants of the plastic potential surface, which brings more model parameters where some of them even have no physical meanings. Unlike the traditional plasticity theory, the fractional plasticity is established on non-local fractional operators and gradients where the derivatives of a stress point are determined not only by the state of the stress point of interest but also by the loading history before reaching this point. Therefore, without the necessity of assuming an additional plastic potential (yielding) surface, a state-dependent non-associated fractional plasticity model for sands can be easily developed by conducting fractional order derivatives on the yielding (plastic potential) surface. To validate the proposed model, a series of drained and undrained triaxial compression test results of different sands are simulated and then compared. A good agreement between the model simulations and the corresponding test results can be observed.