A discrete framework for fracture simulation based on the embedment of strong discontinuities with minimum degrees of freedom

Abstract

There are many situations where the ability to predict the premature failure of structures requires fracture models with high level of detail. For example, this is the case of concrete structures strengthened with CFRP where the knowledge of the occurrence of highly localised cracks is critical for its failure predictions. These crack patterns can be simulated using different finite element techniques within the scope of the discrete crack approach. Many techniques are typically based on enrichment strategies—which can be implemented at the element or nodal levels—or on remeshing strategies. Both have drawbacks, in particular, when dealing with numerous cracks. Regardless of particular implementa- tion issues, the significant increase on the number of degrees of freedom found with enrichment strategies, and the highly discretised and distorted elements found with remeshing algorithms, have a computational cost that precludes its efficient application in general structural problems. In this paper, a new approach is introduced that overcomes these limitations by embedding discontinuities within any regular finite ele- ment mesh with minimum additional degrees of freedom. The new formulation is exclusively based on the rigid body movement of the cracked subdomains and is applicable to brittle and quasi-brittle materials. The new formulation was validated against other existing approaches, including the DSDA and XFEM. It is concluded that the new approach requires significantly less degrees of freedom to handle discrete cracks for the similar accuracy.