This paper is concerned with the problem of an isotropic, linear viscoelastic
half-plane containing multiple, isotropic, circular elastic inhomogeneities. Three types
of loading conditions are allowed at the boundary of the half-plane: a point force, a
force uniformly distributed over a segment, and a force uniformly distributed over the
whole boundary of the half-plane. The half-plane is subjected to far-field stress
that acts parallel to its boundary. The inhomogeneities are perfectly bonded
to the material matrix. An inhomogeneity with zero elastic properties is
treated as a hole; its boundary can be either traction free or subjected to
uniform pressure. The analysis is based on the use of the elastic-viscoelastic
correspondence principle. The problem in the Laplace space is reduced to the
complementary problems for the bulk material of the perforated half-plane and
the bulk material of each circular disc. Each problem is described by the
transformed complex Somigliana’s traction identity. The transformed complex
boundary parameters at each circular boundary are approximated by a truncated
complex Fourier series. Numerical inversion of the Laplace transform is used to
obtain the time domain solutions everywhere in the half-plane and inside the
inhomogeneities. The method allows one to adopt a variety of viscoelastic models. A
number of numerical examples demonstrate the accuracy and efficiency of the
method.
Keywords
viscoelastic half-plane, multiple circular elastic
inhomogeneities, correspondence principle, direct boundary
integral method, numerical Laplace inversion
