Abstract This paper deals with problems emerging in a non-linear analysis of systems modelled by the strain softening material. Apart from sharp turns on the load-displacement diagram that characterize such numerical models, snap-back, artificial unloading and possibility of bifurcation occurrence are often encountered. These aspects challenge a non-linear system solver, in a sense of finding the appropriate equilibrium path. In this paper the CDPM2 concrete material model based on damage-plasticity is employed on notched geometry models in order to analyse convergence. A number of techniques for the solution of non-linear systems are tested and special emphasis is given to the snap-back occurrence and its influence on the convergence of the solution. A relatively simple new technique is developed for achieving better convergence throughout iterations to serve as an aid to conventional methods such as arc-length and line search.

中文翻译：

---

弧长法计算应变软化固体的收敛性改进

摘要 本文讨论了由应变软化材料建模的系统的非线性分析中出现的问题。除了表征此类数值模型的载荷-位移图上的急转弯外，还经常遇到回弹、人工卸载和发生分叉的可能性。在寻找合适的平衡路径的意义上，这些方面对非线性系统求解器提出了挑战。在本文中，基于损伤塑性的 CDPM2 混凝土材料模型被用于缺口几何模型，以分析收敛性。测试了许多用于解决非线性系统的技术，并特别强调了回弹的发生及其对解决方案收敛的影响。