Improved affine estimates for nonlinear viscoelastic composites

Motivated by recent results obtained in the context of variational approaches, new estimates are proposed for the homogenised behaviour of nonlinear viscoelastic materials. The key point relies in the introduction of field fluctuations in the context of hereditary behaviours. This is accomplished by incorporating the intraphase second moment of the mechanical fields of a reference linear viscoelastic material in an hereditary linearisation procedure. Analytical results for the evolution of field fluctuations within a linear viscoelastic composite are derived. Some illustrative results are presented for the creep response of a nonlinear viscoelastic matrix containing elastic inclusions with different morphologies. Compared with a classical approach, the proposed procedure leads to a softer overall response for both transient and steady-state regimes, and predicts a faster stress field redistribution.