Constitutive Modeling for Nonlinear Response of Materials

It has been a long standing problem to solve the cyclic loading phenomena by a reasonably accurate cyclic model. Most of the existing cyclic models are unable to reproduce the memory effect i.e., material’s memory about its last load reversal point in the shear stress-strain plane, which produces a closed hysteretic loop. A novel formulation of kinematic hardening rule is developed by extending the one dimensional Masing’s rule to general three dimensional stress-space. The cyclic behaviour is simulated by introducing a new framework in which the dimensionless kinematic hardening rate is varied according to the instantaneous stress value at that point along the stress path. When the direction of the loading is reversed, the initial rate of hardening is restored and the rate of variation of hardening is scaled according to extended Masing’s law. As a result, a closed hysteretic stress-strain loop is obtained due to cyclic loading.