Generalization of the variable separation method for solving boundary value problems of linear viscoelasticity of kinds I and III.

At present, structural analysis of polymer composite materials is a highly relevant issue. The complexity of taking into account the viscoelastic stress–strain dependence and the time-dependent distribution of stress–strain state parameters over the volume occupied by a solid is a limiting factor. The relevance and demand for new efficient methods of mathematical modeling of creep and relaxation processes in viscoelastic structures are obvious. The aim of this work is to verify and validate the method for solving boundary value problems of a linear viscoelastic solid. The proposed approach is based on the formulation of the generalized principle of correspondence between elastic and viscoelastic problems, according to which a viscoelastic solution can be obtained by replacing elastic constants by some time functions, which are hereinafter called time-effective moduli. The results derived from the theoretical validation and the solution of several problems suggest that the proposed method can be used for solving problems on the stress–strain state of viscoelastic structures. [ABSTRACT FROM AUTHOR]