Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis (J. Mech. Phys. Solids, 2004) concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in t...

The scattering of guided waves through a coupling region is crucial information when studying waveguides. In this paper, the second strain gradient theory (SSG) used to describe wave transmission and reflection in three-dimensional micro-sized medium. First, constitutive relation 3D SSG model derived while six quintic Hermite polynomial shape functions are for displacement field. Then Hamilton’...

This work focuses on the dynamical behavior of carbon nanotubes, including vibration, wave propagation and fluid-structure interaction. In the present research, transverse vibration of nano fluid conveying carbon nanotubes is investigated. To this end, based on the nonlocal and strain-inertia gradient continuum elasticity theories and by using rod and Euler-Bernoulli beam models, the system’s d...