In this paper, several Newton-type methods of convergence order 2 or higher were tested on various nonlinear systems of equations and on an advanced material law implemented in a finite-element code. The computational speed, numerical efficiency, and robustness of each method were evaluated for each studied case. The effect of numerical damping was also studied. The results were then compared to put in light the strengths and weaknesses of each method. The most efficient and robust method for the material law in the finite-element code was identified as the Newton method with a selective numerical damping.

中文翻译：

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高阶牛顿型方法和数值阻尼对高级耦合勒梅特损伤模型求解的影响

在本文中，在各种非线性方程组和在有限元代码中实现的高级材料定律上测试了几种收敛阶数为 2 或更高阶的牛顿型方法。针对每个研究案例评估了每种方法的计算速度、数值效率和鲁棒性。还研究了数值阻尼的影响。然后将结果进行比较，以阐明每种方法的优缺点。有限元代码中材料定律的最有效和最稳健的方法被确定为具有选择性数值阻尼的牛顿法。