A size independent enriched finite element for the modeling of bimaterial interface cracks

A novel size independent symplectic analytical singular element for inclined crack terminating at bimaterial interface

“…However, only finite numbers of export nodes can be used in practice and the overlapping area cannot be avoided. Nevertheless, in the previous studies for the crack problems it was proven that the resulted numerical error can be limited when sufficient numbers of the export nodes of the SASE are used [40,46,47]. It was shown that the numerical error of the predicted SIFs, with respect to the analytical solution, was -1.2% and -0.5% when 13 and 25 export nodes were used respectively [40].…”

“…The rich information of displacement and stress fields around crack tip expressed in terms of analytical solution could lead to better solving accuracy and efficiency. Based on the existing analytical eigen solutions, a series of analytical singular elements were developed for the numerical study of cracks [46] , bimaterial interface crack [40,47] , fatigue crack growth [48] and Dugdale model based cracks [49,50] . These elements were termed as "singular element" or "enriched element" in the early publications [40,46,48,49,50].…”

“…These elements were termed as "singular element" or "enriched element" in the early publications [40,46,48,49,50]. However, considering the methodology used for construction of the element and its applications, the new developed elements in the recent publications [47,51,52,53] were termed as Symplectic Analytical Singular Element (SASE). In the future, SASE will be consistently used.…”

A crack-tip element for modelling arbitrary crack propagations

“…Due to the fact that the eigen solutions are solved by using a symplectic analytical approach, this type of element is termed as "symplectic analytical singular element (SASE)". The SASE has been applied for many basic crack problems such as, general cracks [60], fatigue crack growth [61,62], bimaterial crack [63,64], viscoelastic cracks [65], thermal conduction for crack [66,67], dynamic crack problem [68] and cohesive cracks [69]. The solving accuracy and stability of the SASEs have been shown to be highly satisfactory.…”

Floating node method with domain-based interaction integral for generic 2D crack growths

“…In XFEM/GFEM, a level set technique with enrichment functions is used to represent the crack in the domain, hence avoiding the requirement of remeshing during the crack propagation. This method has since been extended for interfacial crack (Sukumar et al, 2004;Pathak et al, 2013a;Kumar et al, 2015b;Hu et al, 2016), fatigue crack growth (Combescure et al, 2005;Singh et al, 2012;Pathak et al, 2015b;Hara et al, 2016a;Pant and Bhattacharya, 2017), elasto-plastic crack growth (Elguedj et al, 2006;Kumar et al, 2014;Kumar et al, 2015c;Kumar et al, 2016), three dimensional crack growth (Areias and Belytschko, 2005;Rabczuk et al, 2010;Pathak et al, 2013b, Pathak et al, 2013c, dynamic crack growth (Zi et al, 2005;Réthoré et al, 2005;Kumar et al, 2015d) fatigue crack growth in functionally graded materials (Singh et al, 2011;Bhattacharya and Sharma, 2014) and interaction of multiple cracks (Hara et al, 2016b). Despite its success in many types of problems, there exist some limitations: (1) it introduces an error during the mapping of discontinuities from the physical space to the natural space (Fries and Belytschko, 2010); (2) the implementation in FEM can be complicated as blending elements are generally required for connecting the enriched elements to standard elements; (3) the numerical solution is sensitive to the numerical integration scheme used for the enriched elements (Rabczuk, 2013); and (4) different enrichment functions are usually required to tackle different material problems.…”