Particle size effect on the thermoelastic behavior of composites—A comparative study between heterogeneous and homogenized beams

The particle size effect on the overall thermoelastic behavior of a composite containing many identical spherical particles reduces with the specimen-particle size ratio (SPR). When SPR is large enough, the effective stiffness converges, and the homogenized properties can represent the composite. This paper addresses two challenging questions: How large of an SPR is enough to reach the convergent results for different loading conditions, and whether is the critical SPR obtained from a uniform loading condition applicable to a nonuniform loading condition? When a uniform load is applied to a composite beam, the elastic moduli and thermal expansion coefficients can be calculated from the material’s response. When the beam is subjected to pure or thermal bending, the deflection can be predicted by the heterogeneous or homogenized beams. The inclusion-based boundary element method (iBEM) is developed for high-fidelity simulation of many-particle systems. Given a volume fraction of particles, particle and beam size, and beam geometry, the local fields and the effective deformation are calculated for uniform and nonuniform loading conditions. The comparative study between a homogenized beam by the micromechanical approach and the numerical simulation of the heterogeneous particle system shows that a much larger SPR is required for thermal bending to reach a convergent result between the heterogeneous and homogenized beam. When the SPR is moderate, a cross-scale modeling method shall replace the micromechanical modeling to achieve accurate results.