A review of higher order Newton type methods and the effect of numerical damping for the solution of an advanced coupled Lemaitre damage model - Morch, Hélène; Yuan, Sibo; Duchêne, Laurent; Harzallah, Ridha; Habraken, Anne Marie (Finite elements in analysis and design, 2022)
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. •Several Newton-type methods were evaluated for solving various numerical problems.•The methods were compared based on computational speed, efficiency, and robustness.•Classic numerical damping can improve the robustness of some, but not all, methods.•Newton method with selective numerical damping is the most efficient and robust.