A mesh objective continuum damage model for quasi-brittle crack modelling and finite element implementation

In the framework of continuum damage mechanics, a computational model for quasi-brittle crack modelling is proposed. The proposed model has significant mesh-objectivity and accuracy advantages over existing methods for modeling quasi-brittle crack. These stem from the combination of the local crack tracking algorithm, the new calculation of crack bandwidth and the non-local treatment regarding strain field. Resorting to the implementation of local crack tracking algorithm, it is desirable that the spurious dependence of conventional continuum damage mechanics-based model on mesh bias can be effectively addressed. The new estimation of the real-time crack bandwidth can be not only depending on the element size and pattern, but also on the physical crack path within each consolidate cracked element. Thus, the energy dissipation during crack propagation can be characterized in a more accurate, physically based manner. The non-local averaging regarding the strain field in the course of failure evolution is carried out within an elliptical domain, the configuration of which is related to finite element and crack trajectory obtained by the local crack track algorithm. With this combined technique, it is expected that a more accurate crack evolution course can be achieved numerically, which allows engineers to adopt relatively coarse unstructured discretizations without sacrificing solution accuracy. By numerical examples, the proposed model, empowered by the combined techniques, demonstrates significant improvements in the prediction of crack propagating of quasi-brittle materials. This model may provide engineers a more reliable tool in practical application of computational material failure.