Finite Element Analysis of Thermal-Diffusions Problem for Unbounded Elastic Medium Containing Spherical Cavity under DPL Model

In this work, the thermo-diffusions interaction in an unbounded material with spherical cavities in the context dual phase lag model is investigated. The finite element technique has been used to solve the problem. The bounding surface of the inner hole is loaded thermally by external heat flux and is traction-free. The delay times caused in the microstructural interactions, the requirement for thermal physics to take account of hyperbolic effects within the medium, and the phase lags of chemical potential and diffusing mass flux vector are interpreted. A comparison is made in the case of the presence and the absence of mass diffusions between coupled, Lord-Shulman and dual phase lag theories. The numerical results for the displacement, concentration, temperature, chemical potential and stress are presented numerically and graphically.

Dynamic Stresses Around Elliptical Discontinuities

The influence of an elliptical discontinuity on the stress distribution in an otherwise uninterrupted and unbounded elastic medium subjected to the passage of both P- and SV-waves is examined. The elliptical scatterer is either empty or filled with a rigid and infinitely dense material. Ratios of the maximum stresses on the elliptical scatterer boundary to the maximum stress of the incident wave are computed to demonstrate the effect of dynamic stress concentrations. Results are presented which show the influence on the stresses of the ellipse eccentricity, the normalized wave number as well as the ratio of nondimensional source distance to wavelength.