A HOMOGENIZATION METHOD FOR THERMOMECHANICAL CONTINUA USING EXTENSIVE PHYSICAL QUANTITIES
K.K. Mandadapu, A. Sengupta and P. Papadopoulos Proc. Royal Soc. A, 468, pp. 1696-1715, (2012)

Abstract
This article proposes a continuum thermomechanical homogenization method inspired by the Irving-Kirkwood procedure relating the atomistic equations of motion to the balance laws of continuum mechanics. This method yields expressions for the macroscopic stress and heat flux in terms of microscopic kinematic and kinetic quantities. The resulting equation for macroscopic stress affords a rational comparison to the widely used Hill-Mandel stress-deformation condition, while the one for heat flux reduces, under certain assumptions, to a Hill-Mandel like condition involving heat flux and the gradient of temperature.


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