The finite element method (6th edn) (Its Basic and Fundamentals by O. C. Zienkiewicz, R. L. Taylor and J. Z. Zhu, ISBN 07506-6320-0, $54.99, Solid and Structural Mechanics by O. C. Zienkiewicz and R. L. Taylor, ISBN 07506-6321-9, $47.99 and Fluid Dynamics

In this paper, energy dissipation and residual stress developments are numerically studied in threedimensional closed deformation paths. Different objective stress rates coded in a finite element program are compared. In order to update the stresses, implicit integration algorithm based on mid-point rule for corotational and non-corotational objective rates is used. Several corotational objective rates such as Jaumann, Green–Naghdi, Eulerian and Lagrangian triad-based rates and non-corotational rates such as Truesdell and Cotter–Rivlin rates are considered. It is shown in this work that in some cases also a non-integrable model may exhibit no dissipation energy at the end of a closed deformation path. This study underlines some results previously obtained by other researchers, i.e. among all considered stress rates the logarithmic rate manifests the best result in respect of elasticity requirements. Copyright 2006 John Wiley & Sons, Ltd