Published by AMSS Press, Wuhan, China Acta Mechanica Solida Sinica, Vol. 25, No. 2, April, 2012 ISSN 0894-9166 RESPONSE OF MICROPOLAR THERMOELASTIC SOLID WITH VOIDS DUE TO VARIOUS SOURCES UNDER GREEN NAGHDI THEORY Mohamed Ibrahim Ahmed Othman 1 ⋆ Sarhan Youssef Atwa 1,2,3 ( 1 Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt) ( 2 Higher Institute of Engineer, Dept. of Eng. Math. and Physics, Shorouk Academy, Egypt) ( 3 Faculty of Science, Department of mathematics, Shaqra University, AL-Quwaiyah, Saudi Arabia) Received 28 June 2011, revision received 30 December 2011 ABSTRACT Green-Naghdi (G-N) theory of thermoelasticity is employed to study the deforma- tion of micropolar thermoelastic solid with voids considering the influence of various sources acting on the plane surface. The normal mode analysis is used to obtain the analytical expressions of the displacement components, force stress, coupled stress, variation of volume fraction field and tem- perature distribution. The computed results are presented graphically when the volume source is applied. Comparisons of type II and type III with and without micropolarity effect are made with the results predicted in the context of (G-N) theory. KEY WORDS micropolar, thermoelastic solid, volume fraction, coupled stress, energy dissipation, voids I. INTRODUCTION The linear theory of micropolar elasticity is adequate to represent the behavior of materials with microstructures. Metals, polymers, composites, soils, rocks and concrete are typical media with mi- crostructures. More generally, most of the natural and manmade materials including engineering, geo- logical and biological media possess a microstructure. For ultrasonic waves i.e., for the case of vibrations characterized by high frequencies and small wavelengths, the influence of the body microstructure be- comes significant. This influence of the microstructure results in the development of new type of waves, not found in the classical theory of elasticity. Eringen and S ¸uhubi [1, 2] and Eringen [3] developed the linear theory of micropolar elasticity. The difference between the micropolar theory and the classical theory is the introduction of an independent microrotation vector. Also, there exist not only traditional stress tensors but also couple stress tensors for micropolar theory. Othman and Baljeet [4] have studied micropolar theory under generalized thermoelastic theory for a half-space. The classical uncoupled theory of thermoelasticity predicts two phenomena not compatible with physical observations. First, the equation of heat conduction in this theory does not contain any terms produce heat effects. Second, the heat equation is of a parabolic type predicting infinite speeds of propa- gation for heat waves. Lord and Shulman (L-S) [5] introduced the theory of generalized thermoelasticity with one relaxation time by postulating a new law of heat conduction to replace the classical Fourier law. This new law contains the heat flux vector as well as its time derivative. It contains also a new ⋆ Corresponding author. E-mail: m i othman@yahoo.com