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.

中文翻译：

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多表面塑性综合隐式子步积分方案

复杂的弹塑性模型需要对演化方程进行稳健的积分过程。有限元求解的性能直接受状态更新过程的收敛特性影响。因此，本研究提出了一种综合的数值积分方案来处理通用的多表面塑性模型。该算法基于以精度和稳定性为目标的后向欧拉方法，以及解决无约束优化问题的牛顿-拉夫森方法。在该场景下，采用线搜索策略来改善算法的收敛特性。黄金分割法，一种精确的线搜索，被考虑在内。此外，还实施了一个子步进方案来为状态更新过程提供额外的鲁棒性。所以，这项工作有助于计算可塑性，根据子步进技术呈现自适应子步长方案和一致的切线模量。最后，使用所提出的算法评估了一些数值问题。在这些分析中采用了单表面和新型多表面塑性模型。结果证明了线搜索和子步进策略如何提高非线性分析的鲁棒性。