Clustering Analysis for the Micromechanics-Based Reduced Homogenization in the Mechanics of Composite Materials

The homogenized mechanical response of heterogeneous, elasto-plastic composite materials was investigated by the use of clustering analysis based homogenization (CAH) approaches, relying on two-scale coupling algorithms and on piecewise uniform microscopic fields of internal variables. Clustering algorithms fed by several micromechanical fields can be implemented for the spatial decomposition into the domains with uniform fields of variables. In cases of history-dependent responses of the materials however, the selection of the underlying deformation fields for the clustering procedure is crucial. Not optimized spatial subdomain decompositions of the microscopic domain, meaning that localized effects and evolving deformation patterns are not well represented, can cause overstiff inelastic composite material responses modeled by the CAH approaches. To improve homogenized predictions for the responses of heterogeneous materials, more accurate representations of inelastic localizations were targeted by new spatial decompositions. The numerical estimation of the interaction functions between the subdomains allows the use of the CAH approaches for the numerical modeling of general composite materials with arbitrary microstructures. The CAH methods based on clustering analyses were tested for materials with isotropic and anisotropic microstructures, various material systems with a particular emphasis on the complex case of perfectly plastic material phases, under both proportional and non-proportional loading conditions and histories. The assessment of the predictions by the CAH methods were based on comparisons to reference full-field homogenization results. After the extensive investigation, comparisons could be drawn between the CAH approaches based on different algorithms, and the effect of the underlying spatial decomposition based on elastic and inelastic fields was evaluated. It could be proven that more accurate predictions for the mechanical responses of composite materials can be found when inelastic fields are considered as the foundation of the spatial division into subdomains. Subsequently, a novel approach for the three-scale bridging of woven composite materials based on the CAH approaches was employed. Very good predictions under various complex loading conditions prove the suitability for woven materials, and offer a promising technique for the homogenization of materials with underlying heterogeneous meso and microstructures. Finally, a novel multi-step homogenization scheme as an extension of the transformation field analysis was proposed and employed for the consideration of two scale levels.