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Incremental continuum mechanics
Published in I. Vardoulakis, J. Sulem, Bifurcation Analysis in Geomechanics, 1995
The constitutive equation 3.2.44 for the Jaumann increment of the relative Kirchhoff stress with a stiffness tensor given by Hooke’s law 3.2.48 is not truly elastic, i.e. hyperelastic; of. the remark below, and the papers by Hutchinson (1973) and McMeeking and Rice (1975). This is generally not considered as a major deficiency of such a theory, and in large strain analyses equation 3.2.44 with equation 3.2.48 are used; cf. Dorris and Nemat-Nasser (1980). It should be noticed also that Christoffersen (1991) discussed a simple class of hyperelastic relations with isotropic rate forms. These rate equations do not involve the Jaumann derivative of the Kirchhoff stress but other suitably chosen objective stress rates.
Stresses in deformable bodies
Published in Jamshid Ghaboussi, David A. Pecknold, Xiping Steven Wu, Nonlinear Computational Solid Mechanics, 2017
Jamshid Ghaboussi, David A. Pecknold, Xiping Steven Wu
The Jaumann and Truesdell rates of Cauchy stress are both objective stress rates and therefore can be used in material models expressed in rate form, as is necessary in general for incremental-iterative nonlinear finite element analysis.
Prediction of residual stresses of second kind in deep drawing using an incremental two-scale material model
Published in Philosophical Magazine, 2020
J. Hofinger, H. Erdle, T. Böhlke
In finite element analysis, objective stress rates are often used for the internal formulation of the equilibrium equations. In order to correctly implement a material law, understanding these different stress rates is key for a correct solution. ABAQUS for example uses the Jaumann rate of Cauchy stress (ABAQUS theory manual, [25]), which is defined asThe steps to formulate the material law (14) with respect to the Jaumann rate of Cauchy stress are given in Appendix 2 of Meissonnier et al. [26], and stated explicitly using the notation of this paper in Appendix 2. These steps lead to the following relation of the tangent moduliand allow to formulate the material law (14) formulated in