Kinematic hardening represents the anisotropic component of strain hardening by a shift of the center of the yield surface in stress space. The current approach in stress analysis at finite deformation includes rotational effects by using the Jaumann derivatives of the shift and stress tensors. This procedure generates the unexpected result that oscillatory shear stress is predicted for monotonically increasing simple shear strain. A theory is proposed that calls for a modified Jaumann derivative based on the spin of specific material directions associated with the kinematic hardening. This eliminates the spurious oscillation. General anisotropic hardening is shown to require a similar approach.
Stress Analysis for Anisotropic Hardening in Finite-Deformation Plasticity
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Lee, E. H., Mallett, R. L., and Wertheimer, T. B. (September 1, 1983). "Stress Analysis for Anisotropic Hardening in Finite-Deformation Plasticity." ASME. J. Appl. Mech. September 1983; 50(3): 554–560. https://doi.org/10.1115/1.3167090
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