A novel, total-iterative approach to model quasi-brittle materials

In quasi-brittle materials, such as reinforced concrete, localisation of initially diffuse cracking evolving in localised cracking patterns consists of a numerically challenging task. With conventional iterative methods, convergence of the numerical solution scheme to model crack localisation is often difficult to obtain. On the other hand, conventional total approaches, such as the Sequentially Linear Approach, although robust, fail to approximate properly the underlying material law. In the present work, a new model is introduced, designated the Total Iterative Approach, in which the internal damage variables are updated iteratively. It is found that this approach is robust, allows for the correct approximation of the material law and is a powerful tool for the analysis of softening behaviour. Some examples are presented to illustrate the performance of the model.

Automated summary

Localisation of cracking in quasi-brittle materials is a challenging task, and conventional iterative methods often fail to provide convergence of the numerical solution. On the other hand, traditional total approaches cannot properly approximate the underlying material law. This study introduces the Total Iterative Approach, which updates internal damage variables iteratively, and demonstrates its robustness and ability to accurately approximate the material law in analyzing softening behavior through examples.