ABSTRACT
Research on computational mechanics has been increasingly focusing on adaptive numerical analysis strategies such as meshfree methods e.g. Belytschko et al. (1996), Generalized-FEM e.g. Strouboulis et al. (2001) and Multi-scale methods Liu et al. (2000), which allow improvements in the accuracy of the numerical results by refining the model only where required without changing the global model of the whole structure. Common to these next generation numerical methods is that, the partition of unity concept is exploited to allow overlapping decomposition of the analysis domain so that a local enrichment can be incorporated seamlessly. In various types of problem which naturally give rise to multiple scales in the deformation fields, such as crack propagation and localized damage problems, e.g. Haidar et al. (2003), multiscale numerical analysis techniques were effectively used. In particular the Bridging multiscale method, originally developed by Liu et al. (1997) to enrich the nodal values of the FEM solution with meshfree solution, provides a basis to couple problems based on different physical assumptions, e.g. to incorporate nanomechanics and atomistic behaviour into the local model (Wagner and Liu 2003) and strain localization problems considering micropolar continuum model with different levels of resolution (Kadowaki and Liu 2004). The appealing feature of the Bridging multiscale method is that it can split the global analysis, which is based on simplified assumptions, from the local analysis which requires more sophisticated modelling approaches.
