Comparative assessment of material homogenisation techniques

Abstract

This study evaluates the accuracy and computational demands of Mean Field Homogenisation (MFH) and Finite Element Method-Based Homogenisation (FEMBH) for composites. FEMBH requires generating a Representative Volume Element (RVE) to capture the essential microstructural characteristics. The focus is on nanoparticle-reinforced composites, considering the distinct mechanical properties of matrix and inclusion phases, as well as the influence of inclusion geometry, such as aspect ratio and reinforcement orientation. A comparative numerical analysis of various homogenisation techniques is conducted, assuming linear and elastic behaviour for both phases. Also, different FEMBH implementations are examined, including voxel and tetrahedral meshes, to assess their precision and computational efficiency. To represent the effect of the RVE size choice on the accuracy of the results, different RVE sizes are evaluated during the homogenisation process. The Mori-Tanaka method, representing MFH, demonstrates good accuracy in predicting macroscopic behaviour, while FEMBH, particularly with detailed meshing, yields precise results. However, FEMBH requires significant computational resources, especially with increasing aspect ratios and volume fractions of reinforcing particles, which demand higher mesh densities for accurate analysis.