In this paper, the flexural free vibrations of three dimensional micro beams are investigated based on strain gradient theory. The most general form of the strain gradient theory which contains five higher-order material constants has been applied to the micro beam to take the small-scale effects into account. Having considered the Euler-Bernoulli beam model, governing equations of motion are w...

Abstract We call nonlinear dilatational strain gradient elasticity the theory in which specific class of second continua is considered: those whose deformation energy depends, an objective way, on placement and determinant placement. It interesting particular case complete Toupin–Mindlin elasticity: indeed, it, only effects are due to inhomogeneous dilatation state considered deformable body. T...

present paper is devoted to stress and deformation analyses of heated variable thickness functionally graded (fg) circular plate with clamped supported, embedded on a gradient elastic foundation and subjected to non-uniform transverse load. the plate is coupled by an elastic medium which is simulated as a winkler- pasternak foundation with gradient coefficients in the radial and circumferential...

-Dislocation theory is used to invoke a strain gradient theory of rate independent plasticity. Hardening is assumed to result from the accumulation of both randomly stored and geometrically necessary dislocations. The density of the geometrically necessary dislocations scales with the gradient of plastic strain. A deformation theory of plasticity is introduced to represent in a phenomenological...

The size and viscosity effects are noticeable at the micro-/nano scale. In present work, strain gradient viscoelastic solution of mode-III crack in an infinite quasi-brittle advanced material is proposed based on viscoelasticity theory using Wiener–Hopf method. solutions to gradient-dependent problem obtained directly by correspondence principle between elasticity Maxwell’s standard linear soli...

Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material. The theory possesses two material characteristic lengths, , and ,8, which describe the size scale effect resulting from the underlining microstructure, and are associated to volumetric and surface strain energy, respectively. The governing differential equation of the ...

Several beam and plate models have been recently developed in the literature to accommodate for size-dependence. These are usually obtained starting from a generalized continuum theory (such as couple-stress, strain-gradient or non-local their modifications) then deducing governing equations through Hamilton’s principle ingenuous kinematical assumptions. This approach, originated by Kirchhoff, ...