Higher order gradient elasticity theories are widely applied to determine the wave propagation characteristics of micro-sized structures. The novelty this paper, firstly, is using Second Strain Gradient (SSG) theory explore mechanism a 2D beam grid. strong formulas continuum model including governing equations and boundary conditions derived by Hamilton principle. Then, valuable long-range Latt...

Indentation tests at scales on the order of one micron have shown that measured hardness increases signi_cantly with decreasing indent size\ a trend at odds with the size!independence implied by conventional plasticity theory[ In this paper\ strain gradient plasticity theory is used to model materials undergoing small!scale indentations[ Finite element implementation of the theory as it pertain...

A simplified second strain gradient Euler–Bernoulli beam theory with two non-classical elastic coefficients in addition to the classical constants is presented. The governing equation and associated boundary conditions are derived aid of variational principles. governed by an eighth-order differential displacement, slope, curvature triple derivative displacement as degrees freedom. This can be ...

Nanotechnology is one of the pillars of human life in the future. This technology is growing fast and many scientists work in this field. The behavior of materials in nano size varies with that in macro dimension. Therefore scientists have presented various theories for examining the behavior of materials in nano-scale. Accordingly, mechanical behavior of nano-plates, nanotubes nano-beams and n...

Microtubules are used as targets for anticancer drugs due to their crucial role in the process of mitosis. Recent studies show that carbon nanotubes (CNTs) can be classified as microtubule-stabilizing agents as they interact with protein microtubules (MTs), leading to interference in the mitosis process. CNTs hold a substantial promising application in cancer therapy in conjunction with other c...

In this article, the Second Strain Gradient (SSG) theory proposed by Mindlin is used within a Wave Finite Element Method (WFEM) framework for dynamic analysis of one-dimensional Euler–Bernoulli bending beam and torsional bar. Firstly, strong forms continuum models including governing equations boundary conditions torsion cases, respectively, are derived using Hamilton’s principle. New “non-loca...

It has not been a simple matter to obtain a sound extension of the classical J2 flow theory of plasticity that incorporates a dependence on plastic strain gradients and that is capable of capturing size-dependent behaviour of metals at the micron scale. Two classes of basic extensions of classical J2 theory have been proposed: one with increments in higher order stresses related to increments o...