We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the solid along with boundary conditions various orders are derived from variational principle using integration by parts on surface. objectivity energy functional is achieved carefully selecting invariants under rigid-body transformation. third-order theory includes more than 10.000 mate...

This paper investigates the natural frequency, steady-state resonance and stability for the transverse vibrations of a nanobeam subjected to a variable initial axial force, including axial tension and axial compression, based on nonlocal elasticity theory. It is reported that the nonlocal nanoscale has significant effects on vibration behavior, which results in a new effective nonlocal bending ...

To improve the structural stiffness, strength and reduce weight of nanoplate structure, functionally graded (FG) graphene-reinforced nanocomposite (GRNC) laminated plates are exploited in this paper. The bending buckling behaviors FG-GRNC nanoplates investigated by using novel quasi-3D hyperbolic higher order shear deformation plate theory conjunction with modified continuum nonlocal strain gra...

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...

A mode III crack problem in a functionally graded material (FGM) modeled by anisotropic strain gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ` and `′, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived ass...

Phase-field modelling has been shown to be a powerful tool for simulating fracture processes and predicting the crack path under complex loading conditions. Note that total energy of in classical phase-field formulations includes strain density from linear elasticity theory resulting singular stresses at tip. Recently, we have demonstrated integrating gradient into conventional may improve fina...

in this study, to determine poisson’s ratio and modulus of elasticity of white seedless grapes during maturation, the fresh fruit samples were harvested from a vineyard at seven sequential weeks from 6th september to 18th october. in each run, six grape berries were randomly selected and the static loading test and digital photography were done together. considering true shape of the fruit and ...