ABSTRACT
The failure of quasi-brittle composite materials usually involves micro-cracking, debonding and other processes of progressive internal damage, such that the material can still transfer stresses across the fractured zone. As damage progresses, microcracking starts to localise. The local stresses gradually decrease, leading to the ‘softening’ of the material and, eventually, to the formation of dominant cracks. Two major approaches can be found regarding the way this process has been dealt with numerically. The smeared crack models assume the cracked solid to be continuum, as cracks are smeared inside bands of a weaker material that is modelled using classic stress-strain relations (Bazant & Oh, 1983, Rots, 1991, Chong et al., 2008, Khomwan et al., 2010). This approach is extremely suitable for computational implementation and this is the reason why different versions can be found disseminated in commercial software. There are practical limitations due to the conflict between the displacement continuity and the material separation associated with the opening of cracks. This is reflected in the pathological dependency of results on the mesh and on the
Duarte & Oden, 1996, Belytschko et al., 2009). The drawback of such approach is the difficulty with multiple cracks and the high number of additional degrees of freedom necessary. Other techniques based on enrichment have been developed such that the elements rather than the nodes are enhanced with additional degrees of freedom related with the discontinuities (Linder & Zhang, 2013, Simo & Rifai, 1990, Oliver et al., 1999, Jirásek, 2000). Most embedded formulations cannot assure continuity of stresses and crack openings across the edges of neighbouring elements, which can be a source of stress lock issues and other pathological behaviour.
