Fracture angle search with Puck's 3D interfiber fracture criterion using the damped Newton's method

Developing a fast search algorithm to predict the fracture angle in the case of interfiber fracture represents a major challenge for the implementation of the 3D Puck's criterion into finite element codes. Since there is no analytical solution available, it is necessary to apply numerical methods. The algorithm devised here uses the damped Newton's method as a gradient based method for predicting the fracture angle in the interfiber fracture criterion of Puck. The paper describes how to apply Newton's method to this problem with regard to the mechanical background of this issue as well. Hence, the paper shows how to choose the initial guesses and how to simplify the search algorithm in the case of specific stress states. Furthermore, it also describes an optimization of the algorithm in the case of explicit analysis. Finally, a comparison of the wall-clock time in a finite element analysis shows that the algorithm devised here is veritably faster compared to the existing methods.