Time-dependent interfacial sliding in nano-fibrous composites under longitudinal shear

• Time-dependent deformations of an elastic nano-fiber in an elastic matrix.
• Nano-fiber and matrix have separate and distinct surface elasticities.
• Sliding interface via a diffusion-controlled mechanism.
• Relaxation time and stress distribution controlled by three size-dependent parameters.
• Internal stress field is spatially uniform yet size-dependent and time-dependent.

We use complex variable methods to analyze time-dependent deformations of an isolated elastic nano-fiber embedded in an infinite elastic matrix under longitudinal shear subjected to uniform stress at infinity. In order to incorporate nanoscale size-effects into our continuum-based model, the nano-fiber and the matrix are each endowed with separate and distinct surface elasticities described by the Gurtin–Murdoch model. The fiber/matrix interface is allowed to slide via a diffusion-controlled mechanism. We show that the characteristic relaxation time and time-dependent stress distribution in the composite can be described completely by three size-dependent parameters and a size-independent mismatch parameter. Further, we note that the internal stress field is spatially uniform yet size- and time-dependent. Finally, we obtain the effective anelastic and size-dependent shear modulus of the fibrous composite using the mean-field method of Mori–Tanaka.