Efficient prediction of the packing density of inorganic fillers in dental resin composites for excellent properties

•A modified 3-parameter model was developed and applied to dental resin composites.•Packing density of inorganic fillers in dental resin composites was predicted.•Compared with experiments and simulations, the prediction error is within 1.40%.•Higher packing density is beneficial to improving the performance of composites.•The optimization of filler compositions can obtain a high packing density. The purpose of this study is to develop a mathematical model for efficient prediction of the packing density of different filler formulations in dental resin composites (DRCs), and to study properties of DRCs at the maximum filler loading (MFL), thereby providing an effective guidance for the design of filler formulations in DRCs to obtain excellent properties. The packing density data generated by discrete element model (DEM) simulation were used to re-derive the parameters of 3-parameter model. The modifier effect was also induced to modify the 3-parameter model. DRCs with 10 filler formulations were selected to test properties at the MFL. The packing densities of binary and ternary mixes in DRCs were calculated by 3-parameter model to explore the regularity of composite packing. The predicted packing density was validated by simulation and experimental results, and the prediction error is within 1.40 vol%. The optimization of filler compositions to obtain a higher packing density is beneficial to enhancing the mechanical properties and reducing the polymerization shrinkage of DRCs. In binary mixes, the maximum packing density occurs when the volume fraction of small fillers is 0.35−0.45, and becomes higher with the reduction of particle size ratio. In ternary mixes, the packing density can reach the maximum value when the volume fractions of large and small fillers are in the 0.5−0.75 and 0.15−0.4 ranges, respectively. The modified 3-parameter model can provide an effective method to design the multi-level filler formulations of DRCs, thereby improving the performance of the materials.