Semi-analytical MAC/GMC versus RUC-based finite element homogenization: A comparative study for a 4D composite

Multidirectional composite architectures are advanced material systems that use fibers in multiple orientations, unlike conventional unidirectional or bidirectional composites, to achieve superior performance. They improve structural integrity under multiple loading scenarios, making them suitable for aerospace, defense, automotive, and biomedical applications. Among these, the four-directional (4D) architecture is a commonly employed design in carbon-carbon (C/C) composite systems. A gap exists in applying micromechanical analysis codes, particularly the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC), for predicting effective properties of multidirectional composites. This study employs MAC/GMC to determine the elastic properties of 4D composites and validates them through finite element (FE) homogenization using a Repeating Unit Cell (RUC). While MAC/GMC, as a semi-analytical method, ensures computational efficiency, FE analysis provides a more detailed assessment of localized stress distributions. To further investigate 4D composite behavior, static and dynamic FE simulations are performed in ABAQUS/CAE on a slender composite member modeled using two approaches: (1) explicit 4D architecture, where fiber bundles are embedded within the matrix and (2) homogenized solid model, where the composite is treated as a continuum with effective properties derived from MAC/GMC and FE homogenization. Comparative analysis shows that the homogenized model has higher flexural rigidity but lower torsional rigidity than the explicit 4D structure. However, wave propagation characteristics remain unchanged, indicating homogenization does not significantly affect dynamic response. These findings highlight the effectiveness of MAC/GMC-based homogenization for multidirectional composites and underline the trade-off between computational efficiency and accuracy in structural analysis.