Many materials, such as plastics, wood, concrete and metals at high temperatures, exhibit a mechanical behaviour that is intermediate between the elastic and the viscous one. Consequently, these materials cannot be adequately described using the well-known classical theories of elasticity and viscosity and it is therefore necessary to consider a more general theory that is capable of modelling the behaviour of these materials, also known as viscoelastic materials. 

In the first part of the talk, we will provide a brief overview of the theory of linear viscoelasticity, with a particular focus on the so-called Kelvin-Voigt rheology. Then, we will discuss the problem of viscoelastic wave propagation phenomena in a Kelvin-Voigt heterogeneous material and show numerical results obtained by means of a Galerkin spectral approach.