A thermomechanical approach to the development of micropolar constitutive models of granular media

Summary.

In this paper, we lay the groundwork for the development of micropolar (Cosserat) constitutive relations for granular media within the framework of the theory of thermomechanics. Expressions for the free energy and the dissipation function have been derived using a micromechanical analysis of a cluster consisting of a particle and its immediate neighbors (i.e., “the first ring”). Fluctuations in particle displacements and rotations within this mesoscale assembly as well as fluctuations in strain and curvature are represented by internal variables. Using thermomechanical techniques previously employed for classical materials, a non-local micropolar model is constructed and then subsequently applied to a granular material undergoing simple shear. The effects of the boundaries through particle rotations are discussed.