Effective behaviour of ageing linear viscoelastic composites: Homogenization approach

The correspondence principle is widely used to estimate the effective behaviour of non ageing linear viscoelastic composites, as it allows to take advantage of homogenization approaches originally developed in the elastic framework. However, this principle is no longer valid when the phases exhibit ageing. The approach proposed in this paper overcomes this limitation. Operating in the time domain, it allows to use homogenization of random media on composites made up of isotropic ageing linear viscoelastic phases. Several homogenization schemes are revisited to take into account information on morphology, namely the dilute, Mori Tanaka and self-consistent schemes with spherical shapes. This approach is validated against results obtained from either analytical or numerical computations. It is found to be efficient on nowadays computers: the effective relaxation tensor of a matrix-inclusions composite can be obtained in less than one second, whereas numerical FEM homogenization takes more than twelve minutes on a very coarse mesh.