A Multidimensional Hysteretic Model for Plastically Deforming Metals in Energy Absorbing Devices
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A one-dimensional hysteretic model from the field of passive vibration control in earthquake engineering is modified so that multi-dimensional loading conditions can be included. A procedure is given for extending a one-dimensional model of hysteresis to a three-dimensional tensorial representation. The resulting model is then reduced to meet the loading conditions of three special cases: uniaxial loading, shear loading, and non-proportional biaxial loading (combined axial-torsional loading). In each of these cases, the results calculated using the modeling scheme are consistent with experimentally observed behavior in plastically deforming metals. The uniaxial and shear results are verified via the von Mises criterion while the biaxial results are verified by comparison to experimental results from the literature. The model which is being considered, although nonlinear, is relatively simple in that only two evolutionary equations are required to model inelastic strain and backstress at a material point. Thus the model presented utilized only one internal variable, i.e. the backstress. Rate dependent characteristics are evaluated both analytically and numerically and show that the model being considered here is rate independent.