How far can mean field theory take you? A nondimensional benchmarking of homogenisation strategies for nanoparticle-reinforced polymers

The present paper sets out a non-dimensional parametric sensitivity study of homogenisation approaches applied to nanoparticle-reinforced polymer composites. The effective elastic modulus and shear modulus are expressed as ratios normalised to their respective matrix values and the representative volume element (RVE) length is expressed as a ratio to inclusion diameter. This systematic quantification enables the influence of three governing parameters – inclusion aspect ratio, mass fraction, and RVE size – to be systematically quantified. A reinforcement efficiency metric, defined as the normalised stiffness gain per unit mass fraction, is introduced to evaluate the effectiveness of particle addition across the parameter space. Isotropy deviation heatmaps are a valuable tool for analysing the conditions under which numerical models preserve or violate material symmetry assumptions. A cost-accuracy trade-off analysis, employing normalised wall-clock time (the elapsed real-world solution time on identical hardware), provides actionable guidance on method selection. The findings indicate that both tetrahedral-mesh and voxel-mesh finite element method-based homogenisation (FEMBH) approaches converge towards the Mori-Tanaka mean field solution as the normalised RVE size increases. However, these approaches differ significantly in terms of the computational resources required to achieve this convergence. A method-recommendation map is proposed that classifies each parameter combination into regions where the mean field approach alone is adequate and regions where FEMBH is needed. This provides engineers with a practical decision tool for multiscale modelling workflows.