Narrow Results

This research focuses on studying the influence of the Hall current on the propagation and reflection of elastic waves in a non-local isotropic rotating solid. The dispersion relation is derived to determine the speed of propagation, revealing the presence of three coupled quasi-waves within the solid: coupled qP-wave, qT-wave and qSV-wave. The rotational motion and the Hall current introduce anisotropic characteristics to the medium, leading to the emergence of quasi-type waves. The rotation disrupts the isotropic nature of the solid, transforming it into an anisotropic medium. Consequently, the purely longitudinal and transverse waves are converted into quasi-longitudinal and quasi-transverse waves. The speed of the propagating waves is dependent on specific elastic parameters. By employing free boundary conditions, the mathematical calculation and graphical representation of wave amplitude ratios are determined. The influence of rotational frequency, non-locality, fractional order and Hall current parameters on the computed results is investigated. The conservation of energy validates the accuracy of the obtained results. Furthermore, it is observed that the previously reported results in the literature can be obtained as a special case when rotation and the Hall current are absent.

The propagation and reflection of thermo-elastic waves through diffusive nonlocal isotropic medium had been studied in this paper. The Green–Lindsay model of thermo-elasticity is incorporated in the context of Temperature Rate Dependent Theory. Using Helmholtz vector decomposition rule, the system of governing equations has been transformed to their respective components. The dispersion relation in frequency indicates the existence of three coupled waves and one independent wave propagating through the medium. The coupled waves are affected by non-locality, temperature field and diffusivity in the medium; anyhow, un-coupled shear vertical wave is only affected by the non-local parameter. The reflection of $P$-wave is also studied at the free boundary of the solid and their corresponding amplitude ratios are computed using set of suitable boundary conditions. The obtained results are further discussed graphically for significant physical parameters of interest. The results in the literature are obtained as a special case after ignoring the diffusivity in the solid.

In this paper, the buckling characteristic of FGM plate considering the surface effect is studied based on general third-order plate theory and non-local theory. The surface effect of FGM plate is captured by the surface elasticity theory. The Kirchhoff hypothesis is released by employing parabolic variation of transverse shear strains. By using Navier solution technique, analytical solutions of buckling loads of FGM plate with surface effect are given, and detailed parametric studies are presented to show the relationship between surface effects and the plate thickness, power-law index, surface residual stress, surface moduli and non-local parameter. Furthermore, the surface effect on the buckling characteristic of FGM plate is also discussed.

This paper discusses a coupled mechanics–phase-field model that can predict microstructure evolution in metallic polycrystals and in particular evolution of lattice orientation due to either deformation or grain boundary migration. The modeling framework relies on the link between lattice curvature and geometrically necessary dislocations and connects a micropolar or Cosserat theory with an orientation phase-field model. Some focus is placed on the underlying theory and in particular the theory of dislocations within a continuum single crystal plasticity setting. The model is finally applied to the triple junction problem for which there is an analytic solution if the grain boundary energies are known. The attention is drawn on the evolution of skew–symmetric stresses inside the grain boundary during migration.