Numerical integration of the hereditary integrals in a viscoelastic model for glass

In this paper, numerical schemes are developed to evaluate the integrals produced by the temporal discretization of the hereditary constitutive equations for a viscoelastic model of glass. Such schemes can be implemented in a material module of a finite element code to provide a general capability for analyzing residual stresses in complicated glass components subjected to nonuniform cooling histories. The robustness of the integration strategy increases the accuracy of a finite element stress analysis, lessens the need for discriminating time step controls, and can reduce the number of time steps required to generate accurate transient solutions incrementally