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：在本文中，我们扩展并推广了最初在文献[1]中提出的求解策略，该策略基于一种贪心优化算法和用于多载荷步非线性系统的交替方向法（ADM）。具体而言，我们将该贪心优化算法与基于交替方向法的直接数据驱动求解器相结合——后者首次在文献[2]中提出，并已在文献[3]中与牛顿-拉夫逊法结合用于非线性弹性问题。通过一维和二维杆件与桁架结构的数值算例（这些结构具有非线性应变度量及不同的本构数据集），我们证明所提出的求解策略通常能实现对全局最优解的更好逼近。然而，这是以更高的计算成本为代价的，其成本随“贪心”搜索次数成比例增长。利用该求解策略，我们再现了工业系泊缆制造商测试设施中对尼龙绳进行的循环测试的第一个周期。此外，针对桁架结构的数值算例表明，在非对称数据分布及含噪声数据的情况下，我们的求解策略通常能提高解的精度与鲁棒性。