Account for incompressibility in the stress analysis near viscoelastic inclusion in a viscoelastic solid under finite strains

Approximate analytical solution for a specific plane quasistatic problem of the theory of viscoelasticity is found. This is the problem of the stress-strain state in infinitely extended body with circular incompressible viscoelastic inclusion (area with other material parameters) when the stresses at infinity are fixed at finite strains. Materials of body and inclusion are considered incompressible. Solution uses perturbation technique, complex Kolosov-Muskhelishvili potentials and Laplace transform. Some calculated results are shown and estimation of nonlinear effects is given.