On modelling strain gradient viscoelasticity of polymer nanocomposites

Theories of generalized continuum mechanics have found great success in the analysis of nanostructures. However, there exists no work on analysing composites whose constituents are generalized continua. The present work fills this gap and studies the strain gradient viscoelasticity of polymeric nanocomposites. The key problem is to assign the nonclassical boundary condition of the representative volume element (RVE). To resolve it, a perturbation field is superposed on the homogeneous displacement boundary condition. The wavelength of perturbation is comparable to the strain gradient characteristic length. Simulations to obtain the macroscopic effective mechanical properties are performed, which agree well with the experimental data. The frequency dependence of the perturbation field is revealed, and it has a clear physical interpretation in terms of the segmental motions of polymer chains.