International Journal of Plasticity, Vol. 8, pp. 271-314, 1992 0749.-6419/92 $5.00 + .00 Printed in the U.S.A. Copyright © 1992PergamonPress Ltd. FINITE ELASTO-PLASTIC ANALYSIS OF TORSION PROBLEMS USING DIFFERENT SPIN TENSORS GEORGE Z. VOYIADJIS and PETER I. KATTAN Louisiana State University (Communicated by K.W. Neale, Universit6 de Sherbrooke) Abstract- In this work three tests are selected for evaluating the anticipated material behavior of ductile metals subjected to finite strains. The objective of this work is to test the appropri- ateness of certain expressions for the plastic spin used to describe the corotational stress rates, and the evolution equations for the backstress. The constitutive model used is based on a yon Mises type yield function that incorporates both isotropic and kinematic hardening. The for- mulation is presented in a Eulerian reference system and involves finite deformation. Three tor- sion problems are selected. In the first problem the outer surface of a hollow circular cylinder bounded by two rigid casings is twisted while the inner surface is fixed. The second and third problems are the torsion of a cylindrical bar with free ends and fixed ends, respectively. Dif- ferent spin tensors are used in the definitions of the corotational rates of stress and backstress. In particular, a spin tensor that involves the plastic spin is investigated and the results are com- pared with those of other spins. !. INTRODUCTION In the analysis of finite plastic deformation, stress and strain rates play an important role in the constitutive equations. Among other things, stress rates must satisfy the ob- jectivity and frame-indifference requirements. This is particularly important when for- mulating theories of plasticity in the Eulerian reference system where all the quantities are referred to the deformed configuration of the body. The use of an appropriate stress rate mainly depends on the choice of a modified spin tensor. In the past two decades, researchers in this field proposed several stress rates and recommended their use in the constitutive equations. These include the classical stress rates of JAUMANN [1911]; OLD- ROYD [1950]; TRUESDELL [1955]; and GREENand NAGttDI [1965], as well as modified ones recently proposed by DroNES [1979]; NAGTEGAAL and DE JONG [1982]; DAFALIAS[1983]; LEE et al. [1983]; JOHNSONand B ~ N N [1984]; and PAULUNand PECF_ERSKI[1985]. In an earlier article VOYIADSIS and KATTAN[1989] proposed a modified spin tensor to be used in the corotational stress equations. This mainly depends on the introduction of a scalar function w (can be taken as a constant) that defines the modified spin. It was shown that the use of this modified stress rate leads to a satisfactory solution of the sim- ple shear problem. No oscillations were observed in the stress-strain curve for specific values of w. These values were recommended for use in more general problems. It should be noted, however, that previous researchers have noticed oscillations in the stress-strain curve for this problem where a monotonically increasing relation should have been ob- tained. These results were attributed to the inadequacy of the corotational stress rates used and, therefore, to the improper choice of the associated spin tensor. The main objectives of this work are to show the applicability of the corotational rate proposed by VOYIAD~ISand KATTAN[1989] tO a selected number of torsion prob- 271