Effect of delayed modulus formation on shrinkage stress development in dental resin composites: A theoretical treatment

Objective: Shrinkage stress induced by polymerization remains a clinical concern in restoring teeth using resin-based dental composites. While many studies have investigated the buildup of shrinkage stress, the effect of differences in rate of development between the different material properties during curing has not been fully elucidated. Building on an existing theoretical model, this study examines the effect of delayed modulus formation, i.e., Young's modulus lagging behind shrinkage strain in their buildup during polymerization, on the development of shrinkage stress. Methods: A previously established and validated theoretical model was extended to incorporate a delay in Young's modulus development relative to shrinkage strain. The temporal increase of modulus was modeled as a power function of the shrinkage strain development, with a dimensionless exponent n (>1) quantifying the degree of delay. Analytical solutions for the shrinkage stress evolution were derived for n = 1 and n = 2. For general cases, shrinkage stress developments were computed by numerically integrating the governing equation. Results: For n = 1 and n = 2, the numerical solutions reproduced the analytical solutions, validating the numerical scheme. In general, as the delay in modulus formation increased (with higher n), shrinkage stress developed more gradually and reached a lower final value. Significance: The extended model can help explain the observed discrepancies in shrinkage stress between resin composites with similar mechanical properties after cure, i.e., final shrinkage strain and Young's modulus. It can also inform the development of novel composite formulations for reduced shrinkage stress in resin-composite restorations.