Introduction to Eringens Nonlocal

The nonlocal surface piezoelectricity theory based on Gurtin-Murdoch surface elasticity and Eringen’s nonlocal theory are incorporated to take the small-scale effects into account.

The dilemma with the deficiencies of the nonlocal kernel functions as the building blocks of the Eringen’s nonlocal theory has been of concern.

Eringen’s nonlocal elastic model has been widely applied to address the size-dependent response of micro-/nanostructures, which is observed in experimental tests and molecular dynamics simulation.

This study develops a comprehensive vibrational analysis of rotating nanobeams on visco-elastic foundations with thermal effects based on the modified couple stress and Eringen’s nonlocal elasticit.

The proposed model is based on Eringen’s nonlocal elasticity theory, Euler–Bernoulli's assumptions, and generalized thermoelasticity with two different phase lags.

In order to capture the small size effect, Eringen’s nonlocal elasticity theory is incorporated.

For the analysis, surface and size effects have been incorporated by employing the Gurtin-Murdoch surface theory and Eringen’s nonlocal theory, respectively.

This approach is based on models of generalized continuum mechanics and Eringen’s nonlocal medium.

Of the available theories, researchers utilize Eringen’s nonlocal theory most frequently because of its ease of implementation and seemingly accurate results for specific loading conditions and boundary conditions.

In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects.

Effects of nonlocal scale parameter and an initial axial tension force on fundamental frequencies are examined and compared with those obtained by Eringen’s nonlocal model.

In this work, to better describe the transient responses of nanostructures, a size-dependent thermoelastic model is established based on nonlocal dual-phase-lag (N-DPL) heat conduction and Eringen’s nonlocal elasticity, which is applied to the one-dimensional analysis of a finite bi-layered nanoscale plate under a sudden thermal shock.

Motivated by the existing complications of finding solutions of Eringen’s nonlocal model, an alternative model is developed here.

We use the four-unknown high-order shear deformation theory based on Eringen’s nonlocal theory and Hamilton’s principle to obtain the system of the governing differential equations.

They are a lattice elasticity model called the Hencky bar-grid model (eHBM), the continualised nonlocal plane model (CNM) and Eringen’s nonlocal plane model (ENM).

The Eringen’s nonlocal elasticity theory is employed to take account of the size-dependent effect of nanoplates.

For this purpose, the strain gradient theory of Mindlin is combined with the integral (original) form of Eringen’s nonlocal theory.

While the material behavior corresponds to the Eringen’s nonlocal theory of elasticity it is assumed that the cracks produce additional local compliance, which can be evaluated with the aid of the stress intensity factor at the crack tip.

It is well-acknowledged by the scientific community that Eringen’s nonlocal integral theory is not applicable to nanostructures of engineering interest due to conflict between equilibrium and constitutive requirements.