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’...

1. Abdelrahman A.A., Esen I., Özarpa C., Eltaher M.A., 2021, Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory, Applied Mathematical Modelling, 96, 215-235. CrossRef Google Scholar

The present work aims to primarily provide a general representation of the solution simplified elastostatics version Mindlin’s Form II first-strain gradient elastic theory, which converges corresponding classical boundary value problem as intrinsic parameters become zero. Through functional theory considerations, one-intrinsic-parameter strain elastostatic equation that comprises is rigorously ...

In this study, the free vibration analysis of smart vibration control (SVC) systems based on Reddy – Levinson model and modified strain gradient theory is developed. This system consist of a micro beam at middle and two magneto-electro-elastic (MEE) composite micro beams at top and bottom which connected by enclosing elastic medium and simulated by Winkler and Pasternak foundation. The effects ...