Computational study of the elastic modulus of single size pebble beds for fusion applications

Highlights: • The universal distribution for the moduli of diverse granular materials is found. • The stability of granular system is observed to be stronger under external excitation. • The subtle difference in grain sizes is observed to soften the system. - Abstract: In this paper, the discrete element method (DEM) was used to report the mechanical behaviors and elastic moduli of single size pebble beds. The effect of cyclic pressure p and the subtle difference in particle sizes within the granular system were considered. In this study, we re-confirmed the nonlinear elastic stress-strain relation, the much lower elastic moduli of a granular system than that of solid materials and the faster growth of moduli than the p^1/3 law predicted by the effective medium theory (EMT). We also observed that cyclic pressure (mechanical excitation) would stiffen the granular system, but this effect will become smaller as the cycle number increases. This indicates that the stability of system will become stronger under this effect. Besides, the subtle difference in grain sizes was observed to soften the system although it caused a little higher packing density. Furthermore, although the effective moduli of different granular materials E_s are diverse, they were found to nearly collapse to the same distribution when both E_s and p are non-dimensionalized by particle moduli E_p. This can actually also be derived from the EMT theory.