Overcoming the Convergence Difficulty of Cohesive Zone Models through a Newton-Raphson Modification Technique

TL;DR

This paper introduces a simple and robust Newton-Raphson modification technique to improve the convergence of cohesive zone models in static analysis, ensuring faster and more reliable computations without sacrificing accuracy.

Contribution

It proposes a novel, easy-to-implement modification to the Newton-Raphson method that overcomes convergence issues in cohesive zone models, outperforming existing solutions.

Findings

The method ensures fast convergence in benchmark tests.

It is robust and easy to implement in finite element analysis.

The approach maintains analysis accuracy while improving efficiency.

Abstract

This paper studies the convergence difficulty of cohesive zone models in static analysis. It is shown that an inappropriate starting point of iterations in the Newton-Raphson method is responsible for the convergence difficulty. A simple, innovative approach is then proposed to overcome the convergence issue. The technique is robust, simple to implement in a finite element framework, does not compromise the accuracy of analysis, and provides fast convergence. The paper explains the implementation algorithm in detail and presents three benchmark examples. It is concluded that the method is computationally efficient, has a general application, and outperforms the existing methods.