A piecewise recursive semi-analytical method for effective evaluation of heterogeneous aging viscoelastic materials. (November 2022) - Qiang, Fu; Linlin, Zhang; Xinglin, Guo; Haitian, Yang
Abstract: A novel semi-analytical method in the time domain is proposed to predict the effective properties of heterogeneous aging viscoelastic materials. By virtue of a series expansion in a discretized time interval, variables and time varying constitutive coefficients can temporally be described more precisely, and a piecewise variable separation is realized. Consequently, a set of recursive constitutive equations are derived from a second-order differential constitutive equation with time-varying coefficients, and a spatially and temporally coupled effective evaluation is decoupled into a series of recursive spatial effective evaluations which can be tackled with Mori–Tanaka method (M–T), self-consistent method (SC), or other well developed skills, providing time-varying effective strain/stress. A recursive adaptive algorithm is stressed, so as to ensure stable temporal solution accuracy for different step sizes, and avoid the temporal inaccuracy caused either by the relatively lower truncation order or improper step size. Four numerical examples are provided to verify the effectiveness of the proposed approach by comparing the prediction results with reference solutions. Highlights: The time-varying constitutive coefficients can be described more precisely. Decouple the effective evaluations into a series of recursive effective evaluations. The evaluations can be tackled with M–T, SC methods, or other well developed skills. An adaptive algorithm is stressed in computing of the time-varying effective strain.