An approximate algorithm for solving the problems of linear viscoelasticity

This study is devoted to the development of approximate methods for solving the problems of linear elasticity theory. Based on the timeeffective moduli of Lagrangian and Castilian types obtained in early works, two pairs of unique effective characteristics of isotropic bodies are determined. In accordance with the known approach of mechanics of composite materials, the viscoelastic body is assumed to be a twocomponent composite, one component of which has the properties defined by the pair of effective moduli of Lagrangian type, and the characteristics of the second component are set by the pair of Castilian-type moduli. By averaging these characteristics according to Voigt Reyscu, expressions are written for two-component effective moduli. The mass fraction of one of the components is given as a function of time. A comparison of the approximate solutions obtained using the proposed effective moduli with the analytical solutions demonstrates their coincidence within 5% for two problems.