Shrinkage stress development in dental composites - An analytical treatment

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Objectives The aim of this paper is to develop a comprehensive mathematical model for shrinkage stress development in dental composites that can account for the combined effect of material properties, specimen geometry and external constraints. Methods A viscoelastic model that includes the composite's elastic, creep and shrinkage strains, and their interaction with the sample's dimensions and the external constraint is developed. The model contains two dimensionless parameters. The first one represents the compliance of the external constraint relative to that of the composite sample, and the second controls the rate of shrinkage stress decay through creep. The resulting differential equation is solved for two special cases: zero compliance and zero creep. Predictions for shrinkage stress measurements are then made using the analytical solutions for instruments with different compliances, samples with different thicknesses and composites with different filler fractions. Results The model correctly predicts how shrinkage stress increases with time, its dependence on the interaction between the entire system's compliance and the material properties, and the effect of the filler fraction on its maximum value. Comparisons with reported shrinkage stress measurements have provided very good agreement between theory and experiments. Significance The results provided by the model can help to resolve most, if not all, of the seemingly conflicting experimental observations reported in the literature. They can also provide some useful guidelines for optimizing the mechanical performance of dental composite restorations. The compliance ratio, a new parameter derived from the model, represents a fuller description of the constraints of the system.

Original languageEnglish (US)
Pages (from-to)1108-1115
Number of pages8
JournalDental Materials
Issue number11
StatePublished - Nov 2013

Bibliographical note

Funding Information:
The author would like to thank Drs. Jianying Li and Haiyan Li for some useful discussion. This study was supported in part by the National Institute of Health through Grant 1R01DE021366-01 .


  • Compliance
  • Dental composites
  • Filler fraction
  • Mathematical model
  • Shrinkage stress


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