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The von-Mises plasticity model, in the small strain regime, along with a class of multicomponent nonlinear kinematic hardening rules is considered. The material is assumed to be stabilized after several load cycles and therefore, isotropic hardening will not be accounted for. Application of exponential-based methods in integrating plasticity equations is provided, which is based on defining an augmented stress vector and using exponential maps to solve a system of quasi-linear differentialdoi:10.1061/(asce)em.1943-7889.0000192 fatcat:vv2wvsz765bdddoxck2woae63m