Nanoindentations and theory of strain gradient viscoelasticity

Nanoindentations on polymeric viscoelastic materials indicated plastic deformation is size dependent when the indentation is small. The deformation behaviors were successfully modeled using strain gradient plasticity. In this investigation, dynamic nanoindentations on polymeric viscoelastic materials indicated that the storage and loss moduli are size dependent when indent size is small. This suggests that higher order strain gradient contributions to deformation need to be included in deformation of small scaled structures. In this paper, we extended the strain gradient theory to treat viscoelastic materials. A strain gradient viscoelastic bending theory for plane-strain beams is then developed based on this strain gradient viscoelastic theory. In classical bending theory, the normalized bending rigidity is independent of the length and the thickness of the beam. The theory predicts that the normalized creep compliance and the normalized bending relaxation modulus (related to the regular bending rigidity) depends on a higher-order bending parameter, bh and the thickness of the beam