Generalized magneto‐thermo‐microstretch elastic solid under gravitational effect with energy dissipation

Abstract

Purpose

The purpose of this paper is to study the effect of gravity on the general model of the equations of generalized magneto‐thermo‐microstretch for a homogeneous isotropic elastic half‐space solid whose surface is subjected to a mode‐I crack. The problem is in the context of the Green and Naghdi theory of both types (II and III).

Design/methodology/approach

The normal mode analysis is used to obtain the expressions for the displacement components, the force stresses, the temperature, the couple stress and the microstress distribution.

Findings

The variations in variables against distance components are given graphically in 2D and 3D.

Practical implications

The linear theory of elasticity is of paramount importance in the stress analysis of steel, which is the commonest engineering structural material. To a lesser extent, the linear elasticity describes the mechanical behavior of the other common solid materials, e.g. concrete, wood and coal. However, the theory does not apply to the behavior of many of the newly synthetic materials of the elastomer and polymer type, e.g. polymethyl‐methacrylate (Perspex), polyethylene and polyvinyl chloride.

Originality/value

Comparisons are made with the results in the presence and absence of gravity and initially applied magnetic field with two cases: the first for the generalized micropolar thermoelasticity elastic medium (without stretch constants) between both types (II, III); and the second for the generalized magneto‐thermoelastic medium with stretch (without micropolar constants) between both types (II, III).

Citation

Othman, M.I.A., Atwa, S.Y., Jahangir, A. and Khan, A. (2013), "Generalized magneto‐thermo‐microstretch elastic solid under gravitational effect with energy dissipation", Multidiscipline Modeling in Materials and Structures, Vol. 9 No. 2, pp. 145-176. https://doi.org/10.1108/MMMS-01-2013-0005