ABSTRACT
Two-way coupling of scales, enabled in the concurrent methods, has been discussed in Chapter 13. This coupling is necessary for problems involving localization, damage and failure. “Bottom-up” coupling is needed for homogenization-based constitutive models that can be used for efficient macroscopic analysis in subdomains of relatively benign deformation. As discussed in Chapter 14, it would be impossible to analyze large structural regions without the advantage of continuum constitutive model-based macroscopic analysis. Methods that invoke simultaneous computations at the macro-and microscales, e.g. the FE2 method for hierarchical multi-scale modeling [120, 119] can suffer from prohibitively high computational overhead for problems with evolving plasticity and damage. “Top-down” coupling, on the other hand, is
a necessary feature for accurately predicting the damage and plasticity localization processes and failure evolution. The computational domains cascade down to the microstructural or even lower scales, and embed critical regions of localization or damage for detailed microscopic analysis. Microscopic computations, accounting for morphology and capturing important microstructural mechanisms, are often complex and computationally intense. This necessitates concurrent multi-scale analyses. However, such analyses are only plausible provided that the embedded micro-domains are optimally kept to a minimum. There is a paucity of multi-scale models in the literature that involve material nonlinearity and evolving microstructural damage. Discussions on evolving damage in composites have been provided in Talreja [403, 405, 404]. Ghosh and coworkers have proposed an adaptive multi-level analysis scheme using the Voronoi cell FEM model for micromechanical analysis. Their multi-level models encompass elastic-plastic composites with particle cracking and void evolution in [145, 139, 140] and elastic composites with matrix-fiber interface decohesion in [138].
