Effective properties of viscoelastic heterogeneous periodic media: An approximate solution accounting for the distribution of heterogeneities

This paper describes a simple approximate method for obtaining the viscoelastic properties of particle–matrix viscoelastic heterogeneous materials. This method accounts for the spatial distribution of heterogeneities. It rests on a formulation used for elastic media which allows, at the cost of evaluating parameters accounting for the distribution of heterogeneities, to compute the effective properties. Using the Laplace-Carson transform, the solution is shown as being a rational fraction of the Laplace variable, which allows for simple expressions of inverse Laplace transform. Some examples are shown for various viscoelastic behaviors in the case of viscoelastic media of different types, including a comparison with results coming from other methods.

► We provide a new method for computing in a closed form the effective properties of viscoelastic heterogeneous materials.
► The method can accommodate any distribution of heterogeneities.
► The method can accommodate any kind of viscoelastic behavior of constituents.