A dynamical theory of structures solids. II Special constitutive equations and special cases of the theory

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Abstract
This paper is a continuation of Part I under the same title and is concerned with derivation of some special cases of the general theory of Part I applicable to elastic-plastic and elastic-viscoplastic single crystals. The main object here is to identify several existing macroscopic theories of inelastic material behaviour and to shed light on the range of their validity in relation to accepted notions of various physical scales associated with the motion of crystal lattice. Included among the results obtained a re : (i) the identification of the elastic part 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 behaviour in which the inertia effect associated with the rate of plastic deformation is neglected but other m icrostructural effects are retained; and (iii) the reduction, within the framework of the rate-independent theory, to Prandtl-Reuss type equations in which all microstructural effects are suppressed.

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