M. Shaat's blog

Natural nonlinear materials, e.g., biological materials and polymers, are mechanically weak. It has been amajor challenge to develop a nonlinear material with potentialmechanical applications. Here, we develop a nonlinear elastic metamaterial with giant and tailorable-nonreciprocal elastic moduli. The metamaterial is designed with a microstructural axial asymmetry, which activated nonlinear microstructural deformations in the axial direction and microstructural residual moments.

The classical continuum mechanics assumes that a material is a composition of an infinite number of particles each of which is a point that can only move and interact with its nearest neighbors. This classical mechanics has limited applications where it fails to describe the discrete structure of the material or to reveal many of the microscopic phenomena, e.g., micro-deformation and micro-dislocation.

A novel micromorphic beam theory that considers the exact shape and size of the beam’s microstructure is developed. The new theory complements the beam theories that are based on the classical mechanics by modeling the shape and size of the beam’s microstructure. This theory models the beam with a microstructure that has shape and size and exhibits microstrains that are independent of the beam’s macroscopic strains.

In this paper, we investigate the surface roughness-dependence of buckling of beam-nanostructures. A new variational formulation of buckling of Euler-Bernoulli rough beams is developed based on the Hamil- ton’s principle. The equation of motion of the beam is obtained with a coupling term that depends on the beam surface roughness. Exact solutions are derived for the buckling configurations and the pre-buckling and postbuckling vibrations of simply supported structures.

Current designs of artificial metamaterials with giant Poisson’s ratios proposed microlattices that secrete the transverse displacement nonlinearly varies with the longitudinal displacement, and the Poisson’s ratio depends on the applied strain (i.e., tailorable Poisson’s ratio). Whereas metamaterials with tailorable Poisson’s ratios would find many important applications, the design of a metamaterial with a giant Poisson’s ratio that is constant over all the material deformation range has been a major challenge.

In this paper, we put water flow under scrutiny to report radial distributions of water viscosity within hydrophobic and hydrophilic nanotubes as functions of the water-nanotube interactions, surface wettability, and nanotube size using a proposed hybrid continuum-molecular mechanics. Based on the computed viscosity data, phase diagram of the phase transitions of confined water in nanotubes is developed.

The modeling and performance of mechanical resonators used for mass detection of bio-cells, nanocrystalline materials characterization, and disease diagnosis of human immune-viruses (HIVs) are investigated. To simulate the real behavior of these mechanical resonators, a novel distributed-parameter model based on Euler-Bernoulli beam theory is developed. This model is equipped with a micromechanical model and an atomic lattice model to capture the inhomogeneity nature of the material microstructure.

Due to the intensive decrease in grain sizes of nanocrystalline materials (NcMs), a large volume fraction of atoms reside in the interface regions between crystals forming an atom-cloud phase with a distinct atomic structure. Moreover, the surface to volume ratio of the grain increases, thus its surface energy will significantly affect the mechanical properties of NcMs.

Recently, the nonlocal elasticity theories have been used in studying the different behaviors of micro/nanostructures. However, there is a complicity in applying the natural boundary conditions in the context of the nonlocal differential elasticity models. Also, the nonlocal integral elasticity could provide a suitable remedy for this type of problems but with paying highly computational efforts.

In the present paper, for linear elastic materials, effects of couple stresses on micro/nanosolids are physically discussed and mathematically represented in the context of the classical, the modified and the consistent couple–stress theories. Then, an evaluation is provided showing the validity and the limit of applicability of each one of these theories. At first, the possible couple stress effects on mechanics of particles and on continuum mechanics are represented.

This paper is now in Press and available on line at the Intenational Journal of Mechanical Sciences.

This paper is now in press at Finite Element Analysis and Design International Journal.

Many researchers have studied the effect of surface energy on the
elastic behavior of nano-structural elements based on Gurtin and Murdoch surface
model. Many of them, however, assumed that the surface energy depends only on
the 2D symmetric infinitesimal surface strains and neglects the second-order
products of surface strains/displacement gradients. Moreover, there are some
researchers assumed that the surface energy is independent on infinitesimal
rotation tensor and neglected all rotation

Extremely small size of nano-structures such as beams, sheets and
plates, which are commonly used as components in Nanoelectromechanical Systems
(NEMS), presents a significant challenge to the researchers of nano-mechanics.
Several studies have been developed on the mechanical behavior of nano-sized
bars, tubes, sheets and plates. The results of these studies show that the
elastic modulii of such nano-structural elements depend on their size.
Unfortunately, classical elasticity lacks an intrinsic length scale and thus