On the use of non-iterative methods in cohesive fracture

Localisation of initially diffused cracking in softening materials is a numerically challenging task, which is difficult to accomplish with conventional iterative methods. The sequentially linear approach has been used to overcome convergence problems. However, the use of such a total approach raises some difficulties, namely can not be treated in a straightforward way and significant load decays may occur. In this manuscript, new non-iterative numerical methods are proposed to overcome the difficulties mentioned above: (i) an improved total non-proportional analysis and (ii) a purely incremental approach. Similar to the Sequentially Linear Approach, the evolution of the material response is based on the control of the damage state. A mixed-mode discrete damage model is used to exemplify the implementation of these methods. Finally, examples are presented to illustrate the improvements obtained with these new techniques.