A pressure-sensitive kinematic hardening model incorporating Masing’s law

A model is proposed to simulate the stress–strain behavior of sands subjected to cyclic loads in general three-dimensional stress space. A novel formulation is developed using Prager’s kinematic hardening rule and extending the one-dimensional Masing’s rule to general three-dimensional stress space. The hysteretic stress–strain curves are constructed based on skeleton curves. In order to do this, the Masing’s rule is generalized to the proportional rule, which consists of two sets of rules: the internal and external rule. Subsequently, a drag rule is introduced to simulate cyclic stress–strain behavior in which the stress amplitude increases at a decreasing rate during cyclic loading with a constant strain amplitude. The dimensionless kinematic hardening rate is assumed to depend on the current stress value along the stress path. When the direction of loading is reversed, the initial rate of hardening is restored. The rate of variation of hardening is scaled according to an extended Masing’s law. As a result, a closed hysteretic stress–strain loop is obtained during cyclic loading.