A comprehensive implicit substepping integration scheme for multisurface plasticity

Abstract

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.

A robust computational strategy for failure prediction of masonry structures using an improved multi‐surface damage‐plastic based interface model

“…As shown in Figure 9, the time step size $$$ \Delta t $$$ at global level is sub‐divided into a number of sub‐steps, which are denoted by $$$ {t}^m\in \left[0,1\right] $$$ and the corresponding stresses are denoted as $$$ {\sigma}^m $$$. The size of a sub‐step $$$ \Delta {t}^m $$$ is adaptively adjusted based on the performance of the NR iteration in the previous sub‐step using a multiplier $$$ {\delta}^m $$$ based on the concept of Reference 41, which is defined as: $$$$ {\delta}^m=\max \left(\sqrt{\frac{k_d}{k}},\zeta \right), $$$$ where $$$ {k}_d $$$ is a predefined value which is the desirable number of maximum iterations to achieve convergence and k is the number of iterations utilized in the previous sub‐step. If $$$ k<{k}_d $$$, the step size adjustment multiplier $$$ {\delta}_m $$$ will be larger than 1, which indicates that the size of next sub‐step will be larger than previous step and vice versa.…”

“…[34][35][36] Furthermore, multi-surface models with corners introduce additional difficulties in achieving convergence since the active yield surfaces need to be updated during iterations and an improper strategy adopted in subsequent steps can led to an incorrect stress update. 37 To address these numerical issues, researchers have adopted different strategies such as the line search method [38][39][40] to improve convergence stability and accuracy for larger step size and exact/optimized/brute force 38,41,42 for detecting the correct active surfaces near corners of multi-surface plasticity models. Similar to line search method, the sub-stepping technique was adopted by some researchers 43,44 because this technique has a generic character and it is more powerful than the line search method.…”