A homogenization method for thermomechanical continua using extensive physical quantities

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 with 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. © 2012 The Royal Society.