Thick MMC Rings: Asymptotically Correct Homogenization

Abstract

Composite materials show heterogeneity at different length scales. Hence, concurrent multi-scale analysis is the only reliable method to analyze them. Most of the micro-mechanical models in the literature extract the Representative Volume Element (RVE) from the continuum for analysis, which results in loss of information and accuracy. In the proposed approach also, the RVE will be extracted from continuum but with the major difference that all asymptotically relevant macro/mesoscopic parameters will appear in the model as drivers. Based on the success of the variational asymptotic approach for regular composite structures, we propose to develop an efficient high-fidelity micro-mechanical model for SiC-coated C-fiber reinforced Ti-MMC composite. A uniform stress σ33, representing uniform pressurization or suction on the RVE due to the presence of the continuum is identified as a natural fallout of the asymptotically accurate modeling of the RVE. This new variable will then supplement the four macro/meso-scopic one-dimensional parameters, which asymptotically accurately define any highly-curved beam-like self-connected structure: for one-dimensional stretch γ11, for torsion κ1, and for bending κ2 , κ3. The asymptotically accurate variations in the above macro/meso-scopic parameters will be determined in all spatial directions. Hence, the analysis would be valid for any location and not restricted to any local domain. A micro-mechanical model, in conjunction with damage mechanics, for a highly-curved beam-like self-connected structure is developed in variational asymptotic method framework for two separate RVEs: Healthy RVE without any defects and Unhealthy RVE with matrix crack as the damage.