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Based on the existed experimental results of 304 stainless steel, the evolution of fatigue damage during the stress-controlled cyclic loading was discussed first. Then, a damage-coupled visco-plastic cyclic constitutive model was proposed in the framework of unified visco-plasticity and continuum damage mechanics to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented during the uniaxial stress-controlled cyclic loading with non-zero mean stress. In the proposed model, the whole life ratcheting was described by employing a non-linear kinematic hardening rule, i.e., the Armstrong-Frederick model combined with the Ohno-Wang model I, and considering the effect of fatigue damage. The damage threshold was employed to determine the failure life of the material. The simulated whole-life ratcheting and predicted failure lives are in a fairly good agreement with the experimental ones of 304 stainless steel.

This technical note presents a numerical study on the stability of single degree of freedom (SDOF) systems with asymmetric bi-linear hysteretic restoring force, subjected to earthquake excitations. The aim is to report: (a) the existence of an unstable behavior in the response of such systems, under a specific ground motion, given small modifications of the yielding conditions of the hysteresis model, and (b) the introduction of a novel three-dimensional graphic visualization of the problem. The modifications of the yielding conditions were introduced via the symmetry-breaking produced by very small variations of the static equilibrium position of the system, equivalent to having an initial position and restoring force different from zero and symmetric yielding. The concise study comprises of nonlinear dynamic analyses of three system cases, one of them with symmetric (reference) and two with asymmetric yielding conditions. The results show that the system presented a stable response and severe ratcheting toward the weakest yielding direction for the symmetric and asymmetric cases, respectively. Differences as large as $\pm 2800$% between the asymmetric and reference cases were obtained for the residual displacement of the systems, due to variations as small as $\pm 7$% in the static-equilibrium position, and consequent $\pm 7$% variations of the positive/negative yielding displacements and forces. In turn, negligible variations of the velocity between the three cases were predicted. To conclude, the paper introduces novel three-dimensional representations of the solution-curve and of the hysteresis cycles of the systems, deepening the discussion on the identified bifurcation. The 3D hysteresis curve, in particular, can be of much use for seismic engineering and mechanical studies, either numerical or experimental, as it allows visualizing the sequence of events in the hysteresis plots in a much clearer fashion compared to the traditional two-dimensional counterparts.

Ratcheting and fatigue damage of thin-walled tube under cyclic bending and steady internal pressure is studied. Chaboche's nonlinear kinematic hardening model extended by considering the effect of continuum damage mechanics employed to predict ratcheting. Lemaitre damage model [Lemaitre, J. and Desmorat, R. [2005] Engineering Damage Mechanics (Springer-Verlag, Berlin)] which is appropriate for low cyclic loading is used. Also the evolution features of whole-life ratcheting behavior and low cycle fatigue (LCF) damage of the tube are discussed. A simplified method related to the thin-walled tube under bending and internal pressure is used and compared well with experimental results. Bree's interaction diagram with boundaries between shakedown and ratcheting zone is determined. Whole-life ratcheting of thin-walled tube reduces obviously with increase of internal pressure.

A new anisotropic continuum damage model was presented on the basis of irreversible thermodynamics. Second rank symmetric damage tensor, kinematic hardening tensor, and damage potential surface were introduced. The yield surface in this study has been modeled to distort in the stress space by the evolution of the damage tensor. The new model was applied in yield surface characterization and led to a well description of the subsequent yield surfaces. This model is then applied to predict experimental results of the cyclic nonproportional loading paths obtained by Kang et al. [2004], Hassan et al. [2002] and Taleb and Cailletaud [2011]. It is demonstrated that the new model can predict the yield surface distortion and the ratcheting strains of multiaxial nonproportional cyclic loading with acceptable accuracy and by using less material constants with respect to the previous models.

Based on the existed experimental results of 304 stainless steel, the evolution of fatigue damage during the stress-controlled cyclic loading was discussed first. Then, a damage-coupled visco-plastic cyclic constitutive model was proposed in the framework of unified visco-plasticity and continuum damage mechanics to simulate the whole-life ratcheting and predict the fatigue failure life of the material presented during the uniaxial stress-controlled cyclic loading with non-zero mean stress. In the proposed model, the whole life ratcheting was described by employing a non-linear kinematic hardening rule, i.e., the Armstrong-Frederick model combined with the Ohno-Wang model I, and considering the effect of fatigue damage. The damage threshold was employed to determine the failure life of the material. The simulated whole-life ratcheting and predicted failure lives are in a fairly good agreement with the experimental ones of 304 stainless steel.