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Introduction

Inorganic fillers provide dental resin composites with desirable properties such as high stiffness and hardness, and low coefficient of thermal expansion and polymerization shrinkage . However, not all material properties of dental composites can benefit from the addition of filler particles. For example, the viscosity of uncured composites increases dramatically with increasing filler fraction , leading to poor adaptation in the prepared cavities for dental restorations and a lower ability to relieve shrinkage stress. The development of shrinkage stress is considered to be a main cause for post-operative sensitivity and marginal leakage associated with composite restorations. A recent mathematical analysis showed the relative importance of the different material properties of dental composites in the build-up of shrinkage stress, with polymerization shrinkage being the most important, followed by Young’s modulus and viscosity . Thus, despite reduced polymerization shrinkage, increased filler content in dental composites may actually increase the shrinkage stress because of increased Young’s modulus and viscosity . Therefore, understanding the effect of filler particles on the above material parameters of dental composites is essential in selecting an appropriate filler volume to minimize shrinkage stress in composite restorations.

The dependence of the material properties of dental composites on the filler volume may be studied directly by testing a series of these materials with various filler fractions . However, available commercial materials have different compositions, the properties of which are not always known. Even if composites with known compositions are employed, it will still be difficult to control the degree of conversion in the resin matrix among samples with different filler fractions because of irradiation shielding by the fillers. The resulting uncertainties in the matrix condition will prevent the correct relationships between the filler fraction and bulk material properties of the composite from being determined. Furthermore, preparing the samples and performing the various tests to determine the material properties are very time-consuming.

Alternatively, analytical or numerical methods can be used to predict the material properties free of experimental errors and uncertainties. For example, Lingois and Berglund compared predictions from existing micromechanical models with data for experimental dental composites of different filler volume fractions. They observed that, for shrinkage, predictions given by the Rosen–Hashin model agreed well with experiments. For the elastic constants, semi-empirical models, such as Halpin–Tsai and that of Chantler et al. , provided good predictions. However, most analytical models require simplifications with regard to the filler particle shape, size and spatial distribution, which often lead to disagreement between predictions and experimental data. For example, at very high filler volumes, some of the analytical models under-predict the elastic constants, possibly because of contact interactions between the filler particles that are not accounted for.

These shortcomings of analytical models can be overcome by using geometrically realistic micromechanical models such as those based on the finite element method (FEM). A few applications of FEM to determine the elastic properties of composites with different volumetric fractions of randomly distributed fillers (short fibers and spherical particles) have been reported in the literature . For example, the finite element model used by Sun et al. contains spherical fillers of a uniform size randomly distributed within a BISGMA/TEGDMA resin matrix.

Of course, most dental composites do not contain fillers of a regular shape and size. The aim of this study is therefore to use FEM to explore the effects of the filler volume, as well as the material properties of the resin matrix, on the bulk properties of composites that contain randomly distributed fillers of irregular shapes and sizes. Geometrically realistic, 3D micromechanical FE models based on micro-CT images of a macro composite with a similar 2-phase construct were employed to predict the mechanical properties of such dental composites. The numerical results were compared with predictions from several analytical models.