T zyxwvutsrq 302 3 GAMER, zyxwvutsrqp U.; BENGERI, M. V.: Residual stress at the periphery of a coldworked hole, Z. angew. Math. Mech. (to be published). 4 GAMER, U.: The effect of a special hardening law on continuity in elastic-plastic problems with rotational symmetry. Forsch. 1ng.-Wes. zy 5 GAMER, U.: The expansion of the elastic-plastic spherical shell with nonlinear hardening. Int. J. Mech. Sci. 30 (1988), 415-426. zyx Address; Prof. Dr. U. GAMER; M. BENGERI, Institut fur Mechanik, Technische Universitat Wien, Wiedner HauptstraDe 8 zy - 10, ZAMM . Z. angew. Math. Mech. zyxwvuts 73 (1993) 4-5 zyxwvut 55 (1989), 60-64. A-1040 Wien, Osterreich ZAMM . Z. angew. Math. Mech. 73 (1993) 4-5, T 302-T 304 LE, K. C.; STUMPF, H. A New Look at Finite Strain Elastoplasticity from the Thermodynamic Viewpoint Akademie Verlag MSC (1980): 73U05 1. Introduction When dealing with elastoplasticity at finite strain, one should take into account the following two phenomena. The first one is the irreversibility of the plastic deformation leading to the dissipation of energy [l] and the increase of entropy [2]. The second one concerns the microscopical mechanism of slip and the crucial idea of the relaxed intermediate configuration used for expressing the explicit independence of the free energy on the preceding plastic strain [3], [4]. Therefore, thermodynamic requirements formulated with respect to the relaxed intermediate configuration should play a key role in establishing the constitutive equations for elastoplastic bodies. The present paper is devoted to this problem. To introduce the intermediate configuration we decompose the motion of an elastoplastic body into a plastic motion in some relaxed space .g3, considered as Riemannian manifold ([5], [6]), and an elastic motion cp = (pe0(pp. (1) zy F = FeFP. (2) This leads to the multiplicative decomposition of the deformation gradient [3], [4] (see Fig. 1) Fig. 1. Schematic sketch of reference, intermediate and spatial configu- rations, their tangent spaces and the associated multiplicative de- composition of the deformation gradient In contrast to [3], [4] we view the relaxed space rather as a primitive concept not implied by the multiplicative decomposition law. The kinematics of strain is next developed 171, with strain measures defined on tangent spaces to the reference, spatial and intermediate configuration, respectively. Of special interest is the definition of objective rates for tensors referred to the intermediate and spatial configuration. This problem becomes very actual in our case, because the time-dependent intermediate configuration is chosen as reference configuration for the thermodynamical requirements. In this paper we use the intermediate Lie derivatives as objective rates for the intermediate strain tensors ([7,8]). 2. Balance equations in intermediate description Within the framework of classical mechanics and field theories, we formulate a set of balance equations and entropy production inequality in integral form with respect to the spatial configuration for an arbitrary volume. Equivalent sets of equations in material and intermediate description for an elastoplastic body at finite strain can be obtained by