Analytical model of shrinkage stress development during polymerization processes

Behaviour of a cured polymer layer is described in terms of simplified analytical formulae. As macroscopic measure of the conversion degree at the time t, temporary volumetric shrinkage s(t) is taken [1]. To simulate the volumetric changes of the material, a temporary elastic behaviour of the polymer mixture is assumed, and the thermal expansion analogy is used. An appropriate Airy stress function [2] enables to express the shrinkage stresses in terms of polynomials those satisfy averaged equilibrium equations and required boundary conditions. As a result, for every time t and coordinates of the polymer particle x, the stresses, strains and displacements are given explicitly as functions of s(t, x), Young’s modulus E(t, x) and Poisson’s coefficient ν(t, x). Calculations performed for a flat layer of dental resin indicate a strong influence of the distribution of intensity of irradiation on the shrinkage stress level. The result indicates that one can diminish the shrinkage stresses by suitable mask procedures.