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The two sides of the C-factor.

Alex S L Fok1, Wondwosen A Aregawi1

  • 1Minnesota Dental Research Center for Biomaterials and Biomechanics, School of Dentistry, University of Minnesota, United States.

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Summary

Lateral constraints significantly impact resin composite shrinkage stress and strain. A new 3D model accurately predicts these effects, offering a correction factor for more precise bonded-disc method measurements.

Keywords:
C-factorComplianceDental compositesPoisson’s ratioShrinkage stress

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Area of Science:

  • Materials Science
  • Mechanical Engineering
  • Polymer Science

Background:

  • Resin composites are widely used in dental and industrial applications.
  • Shrinkage during polymerization can induce significant stress and strain, affecting material performance.
  • Laboratory measurements of shrinkage effects are influenced by specimen geometry and boundary conditions.

Purpose of the Study:

  • To investigate the influence of lateral constraints on shrinkage strain and stress development in resin composites.
  • To extend existing shrinkage stress theory into three dimensions, incorporating Poisson's ratio effects.
  • To develop a model that predicts shrinkage stress and provides a correction factor for strain measurements.

Main Methods:

  • Extended a 3D Hooke's law-based shrinkage stress theory to account for lateral constraints.
  • Incorporated a parameter for boundary layer thickness under multiaxial stress.
  • Solved the resulting differential equation for shrinkage stress under various boundary conditions.
  • Validated the model by comparing numerical solutions with experimental shrinkage strain and stress data.

Main Results:

  • Demonstrated good agreement between the theoretical model and experimental results.
  • Showed that the model accurately predicts instrument-dependent effects of the configuration factor (C-factor) on shrinkage stress.
  • Found that shrinkage stress increases with C-factor for noncompliant instruments and decreases for compliant instruments.
  • Provided a correction factor for bonded-disc method shrinkage strain measurements, dependent on C-factor, Poisson's ratio, and boundary layer thickness.

Conclusions:

  • The developed theory provides a robust engineering mechanics basis for understanding the C-factor's role in shrinkage stress.
  • The derived correction factor enhances the accuracy of linear shrinkage strain determination using the bonded-disc method for resin composites.