A Comprehensive Implicit Substepping Integration Scheme For Multisurface Plasticity

A complex elastoplastic model requires a robust integration procedure of the evolution equations. The performance of the finite element solution is directly affected by the convergence characteristics of the state-update procedure. Thereby, this study proposes a comprehensive numerical integration scheme to deal with generic multisurface plasticity models. This algorithm is based on the backward Euler method aiming at accuracy and stability, and on the Newton-Raphson method to solve the unconstrained optimization problem. In this scenario, a line search strategy is adopted to improve the convergence characteristics of the algorithm. The golden section method, an exact line search, is considered. Also, a substepping scheme is implemented to provide additional robustness to the state-update procedure. Therefore, this work contributes to computational plasticity presenting an adaptive substep size scheme and a consistent tangent modulus according to the substepping technique. Finally, some numerical problems are evaluated using the proposed algorithm. Single-surface and novel multisurface plasticity models are employed in these analyses. The results testify how the line search and substepping strategies can improve the robustness of the nonlinear analysis.