Linear dynamic response of simply supported nanobeams subjected to a variable axial force is assessed by Galerkin numerical approach. Constitutive behavior is described by three functional forms of elastic energy densities enclosing nonlocal and strain gradient effects and their combination. Linear stationary dynamics of nanobeams is modulated by an axial force which controls the global stiffne...

Abstract.The paper focuses on the modelling of the quasi-brittle failure of materials with a heterogeneous microstructure. Failure induced anisotropy is incorporated in terms of the microplane theory. This theory is based on scalar damage laws formulated on several individual material planes. Anisotropy of the overall constitutive law is introduced in a natural fashion by transforming the scala...

Coated functionally graded materials (FGMs) are used in several industrial structures such as turbine blades, cutting tools, and aircraft engines. Given the need for analytical numerical analysis of these complex structures, a mathematical model tricoated FG is presented first time this paper. The objective work was to analyze analytically buckling problem unidirectional (1D), bidirectional (2D...

Torsional dynamic analysis of carbon nanotubes under the effect of longitudinal magnetic field is carried out in the present study. Torque effect of an axial magnetic field on a carbon nanotube has been defined using Maxwell’s relation. Nonlocal governing equation and boundary conditions for carbon nanotubes are obtained by using Hamilton’s minimum energy principle. Eringen’s nonlocal stress gr...

In this paper, the buckling of carbon nanotubes, modeled as nonlocal one dimensional continua within the framework of Euler–Bernoulli beams, is considered. Both a stress gradient and a strain gradient approach are considered and a variational approach is adopted to obtain the variationally consistent boundary conditions. The dependence of the buckling load on the nonlocal parameter has been det...

Recent experiments have shown that metallic materials display significant size effect at the micron and sub-micron scales. This has motivated the development of strain gradient plasticity theories, which usually involve extra boundary conditions and possibly higher-order governing equations. We propose a finite deformation theory of nonlocal plasticity based on the Taylor dislocation model. The...

Abstract We have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion obtain satisfactory accuracy when wavelength gets close spacing. Such applied displacement field lattice, resulting in novel SG...