One of the assumptions Linear Elastic Fracture Mechanics is that crack faces are traction-free or, at most, loaded by bounded tractions. The standard Irwin’s closure integral, widely used for computation Energy Release Rate, also relies upon this assumption. However, there practical situations where load acting on boundaries singular. This case, instance, in hydraulic fracturing, fluid inside e...

Abstract We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing thermal convection, analysing these detail, and deriving critical Rayleigh wave numbers the onset convective fluid motion. In addition to linear instability theory we present careful analysis fully nonlinear stability theory. theories analysed all possess bi-Laplacian term n...

In this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (FDM). The uniform temperature change is utilized to study thermal effect. The surface energy effects are taken into account using the Gurtin-Murdoch’s theory. Using the principle of virtual work, the...

This paper discusses boundary conditions appropriate to a theory of single-crystal plasticity (Gurtin, 2002) that includes an accounting for the Burgers vector through energetic and dissipative dependences on the tensor G = curlH, with H the plastic part in the additive decomposition of the displacement gradient into elastic and plastic parts. This theory results in a flow rule in the form of N...

in this article, surface stress and nonlocal effects on the biaxial and uniaxial buckling of rectangular silver nanoplates embedded in elastic media are investigated using finite difference method (fdm). the uniform temperature change is utilized to study thermal effect. the surface energy effects are taken into account using the gurtin-murdoch’s theory. using the principle of virtual work, the...

Nanosprings made of metallic or semiconducting materials hold promise for a wide range of important applications. In this letter, we extend the classical Kirchhoff rod model by incorporating surface effects on the mechanical response of quasi–one-dimensional nanomaterials. The refined model is then employed to derive the elastic constants of a nanospring by accounting for the effect of surface ...

In this paper, we investigate the stabilization of a system piezoelectric beams under (Coleman or Pipkin )-Gurtin thermal law with magnetic effect. First, study Piezoelectric-Coleman-Gurtin and obtain an exponential stability result. Next, consider Piezoelectric-Gurtin-Pipkin establish polynomial energy decay rate type $t^{-1}$