Generalized self-consistent scheme for the effective behavior of viscoelastic heterogeneous media: A simple approximate solution

Abstract This paper gives a simple approximate solution for obtaining the effective behavior of linear viscoelastic heterogeneous media for the case of elastic inclusions immersed within a viscoelastic matrix. The solution in the Laplace–Carson space is obtained by the Generalized self-consistent model and the simplification is in an explicit expression of the inverse Laplace transform. It is shown that the solution in Laplace–Carson space can be approximated by a convenient rational fraction which is given explicitly as a function of viscoelastic parameters. This provides an easy way to perform the inverse Laplace transform. Examples of typical composites, including possibly void and rigid inclusions, are provided and show that the procedure provides reasonably accurate results. In addition, a complete rheological representation can be provided in some cases for describing the behavior of the effective medium.