Modelling of length scale effects in viscoelastic materials

A length scale dependent linear viscoelastic constitutive model is developed. First, a generalized Maxwell model that can describe standard linear viscoelasticity is considered. The model is then generalized to include effects of viscous strain gradients. The formulation of additional boundary conditions resulting from the strain gradient terms is discussed. It is shown that the boundary conditions can be formulated in terms of a surface energy. As an example, the thermal expansion of a thin polymeric film on an elastic substrate is analyzed. It is shown that the relative thermal expansion in the thickness direction of the film decreases for sufficiently small film thicknesses, in accordance with experimental observations. This effect cannot be captured by a standard thermo-viscoelastic theory, which gives a constant thermal expansion independent of film thickness.