Approximate analytical solution for the problem of an inclusion in a viscoelastic solid under finite strains

The approximate analytical solution of a quasi-static plane problem of the theory of viscoelasticity is obtained under finite strains. This is the problem of the stress–strain state in an infinite body with circular viscoelastic inclusion. The perturbation technique, Laplace transform, and complex Kolosov–Muskhelishvili’s potentials are used for the solution. The numerical results are presented. The nonlinear effects and the effects of viscosity are estimated.