KINEMATICS OF PLASTICITY RELATED TO THE STATE AND EVOLUTION OF THE MATERIAL MICROSTRUCTUREt U.F. Kocks 1 , P.R. Dawson 2 , and C. Fressengeas 3 1 Los Alamos Nat. Lab., MS K-765, Los Alamos, NM 87545, USA 2 Dept. Mech.& Aero.Eng., Cornell Univ., Ithaca, NY 14853, USA 3 LPMM, Fac.des Sciences, He du Saulcy, 57045 Metz, FRANCE ABSTRACT The kinematics of plasticity is essentially concerned with shape changes. Some of these are observed on a macroscopic scale, some on a microscopic one: an example of the first is the change in the relation between external features that describe the "sample" shape; an example of the second is the change in the shape of grains in a polycrystal. While the first does not describe a property of the "state" of the material, the second one does. When the grain shape changes through plastic deformation, it can be described by the "left stretch" tensor V: its eigenvalues give the principal lengths, its eigenvectors the orientation of the principal axes of the grain shape ellipsoid. The kinematics of plasticity provides the means to update grain shape with deformation. When there are differences in shear strain components between a grain and its surroundings, differences in spins ensue. This is important for the development of texture in polycrystalline materials. The set of grain axes (those aligned with the eigenvectors of V) constitute a frame that is bound to the material, describes part of the "state" of the material, and stays orthogonal; it is thus an especially appropriate frame to use in constitutive descriptions based on the physical behavior of materials. 1. INTRODUCTION In Materials Science, the structure of a material plays a pre- dominant role. Aspects of a material's "structure" are the lattice structure (the arrangement of the atoms in a crystal), the substructure t Work supported by the U. S. Department of Energy.wvtsrponlkihfedcaTGA A prior version of this paper was presented at the International Conference on Mechanics, Physics, and Structure of Materials, Thessaloniki, Greece, 1990 107