A DYNAMICAL THEORY OF STRUCTURED SOLIDS .2. SPECIAL CONSTITUTIVE-EQUATIONS AND SPECIAL CASES OF THE THEORY

This paper is a continuation of Part I under the same title and is con cerned with derivation of some special cases of the general theory of Part I applicable to elastic-plastic and elastic-viscoplastic single c rystals. The main object here is to identify several existing macrosco pic theories of inelastic material behaviour and to shed light on the range of their validity in relation to accepted notions of various phy sical scales associated with the motion of crystal lattice. Included a mong the results obtained are: (i) the identification of the elastic p art of the intrinsic lattice force with the so-called 'energy-momentum tensor' using Eshelby's terminology; (ii) the development of special elastic-viscoplastic and elastic-plastic theories of material behaviou r in which the inertia effect associated with the rate of plastic defo rmation is neglected but other microstructural effects are retained; a nd (iii) the reduction, within the framework of the rate-independent t heory, to Prandtl-Reuss type equations in which all microstructural ef fects are suppressed.