In this work, we extend and generalize our solving strategy, first introduced in [1], based on a greedy optimization algorithm and the alternating direction method (ADM) for nonlinear systems computed with multiple load steps. In particular, we combine the greedy optimization algorithm with the direct data-driven solver based on ADM which is firstly introduced in [2] and combined with the Newton-Raphson method for nonlinear elasticity in [3]. We numerically illustrate via one- and two-dimensional bar and truss structures exhibiting nonlinear strain measures and different constitutive datasets that our solving strategy generally achieves a better approximation of the globally optimal solution. This, however, comes at the expense of higher computational cost which is scaled by the number of "greedy" searches. Using this solving strategy, we reproduce the first cycle of the cyclic testing for a nylon rope that was performed at industrial testing facilities for mooring lines manufacturers. We also numerically illustrate for a truss structure that our solving strategy generally improves the accuracy and robustness in cases of an unsymmetrical data distribution and noisy data.

翻译：本文扩展并推广了我们在文献[1]中首次提出的基于贪婪优化算法与交替方向法(ADM)的求解策略，该方法适用于多加载步非线性系统的计算。具体而言，我们将贪婪优化算法与文献[2]中首次提出、后经文献[3]与牛顿-拉夫逊方法结合用于非线性弹性问题的直接数据驱动求解器相结合。通过采用一维和二维的杆系及桁架结构（展示非线性应变度量及不同本构数据集）的数值实验表明：本文提出的求解策略通常能更精确地逼近全局最优解，但这一优势以更高的计算开销为代价，其计算成本随"贪婪"搜索次数呈比例增长。我们应用该求解策略，复现了工业系泊缆制造商测试设施中尼龙绳循环加载试验的首个周期。此外，针对桁架结构的数值算例表明，在处理非对称数据分布和含噪声数据时，该求解策略通常能提升解的精度与鲁棒性。