Angles based integration for generalized non-linear plasticity model

•A new formulation for integration of generalized non-linear plasticity is proposed.•This scheme reduces the system of constitutive equations into a set of fewer scalar ones.•The Exponential Map integration is also advanced for the cyclic plasticity.•The results demonstrate the superiority of the suggested technique.

An effective integration method is proposed for a generalized nonlinear plasticity. The core of this study is to reduce the system of constitutive equations into a set of fewer scalar ones, which could be solved with a great many numerical integrations. The Optimal Implicit Strong Stability Runge–Kutta methods are suggested for this purpose due to their substantial features, such as precision, stability, and robustness. The qualities of the new approach are clearly discussed in a wide range of numerical tests comprising accuracy, efficiency, stability, and convergence rate assessments. Moreover, an initial boundary value problem is solved utilizing the proposed approach in practice. In addition to the implementation of the Optimal Implicit SSP Runge–Kutta methods, the Exponential Map integration is also advanced for the cyclic plasticity as a measure for the numerical tests, likewise, the Euler׳s integrations to conclude the study. The results demonstrate the superiority of the suggested technique.