Consideration of surface stress effects on the elastic field of nanocontact problem has extensive applications in several modern problems of solid mechanics. In this paper, the effects of surface stress on the contact problem at nanometers are studied in the frame of surface elasticity theory. Fourier integral transform method is adopted to derive the fundamental solution of the nanocontact problem under shear load. As two special cases, the deformations induced by a uniformly distributed shear load and a concentrated shear force are discussed in detail, respectively. The results indicate some interesting characteristics in nanocontact mechanics, which are distinctly different from those in macrocontact problem. At nanoscale, both the contact stresses and the displacements on the deformed surface transit continuously across the uniform distributed shear load boundary as a result of surface stress. In addition, the indent depth and the contact stress depend strongly on the surface stress for nanoindentation.
Considering the size-dependent influence ignored by classical continuum mechanics, a new non-classical Euler-Bernoulli beam model is proposed in this paper. The new fractional viscoelastic nanobeam model is set up by using the fractional viscoelastic Kelvin-Voigt model and Hamilton's principle. And the new model studies the total effects of nonlocal elasticity, modified couple stress, and surface energy. The model represented the fractional integral-partial differential governing equation is solved by Galerkin's and predictor-corrector method. Firstly, the effects of nonlocal elasticity, modified couple stress, surface energy, and their coupling impact on the nonlinear time response of free vibration of fractional viscoelastic nanobeam are analyzed. Secondly, the nonlinear time response of free and forced vibration of fractional viscoelastic nanobeam are studied in the context of the nonlocal couple-stress elasticity and the surface energy theory. Finally, the effects of initial displacement, fractional order, viscoelasticity coefficient, damping coefficient, length-to-thickness ratio, force amplitude, and excitation frequency on the nonlinear vibration time response of the fractional viscoelastic nanobeam are analyzed.
Elastic wave propagation at nanoscale exhibits some special properties due to surface/interface effect. Scattering of plane compressional waves (P-wave) by two nanocylindrical core-shell inclusions in an elastic solid medium is investigated in this study. The wave fields of the core-shell structure are given by the eigenfunction expansion method and Graf addition theorem. The effect of factors such as surface energy, center distance, and thickness of the liner under different incident wave frequencies has been discussed. The results show that as the radius of the core-shell inclusions shrinks to nanometers, surface energy becomes a dominant factor that affects the scattering of elastic waves. The interaction between two core-shell inclusions in multiple scattering phenomena is discussed at the same time.
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