Elastic mimicry of elasto-plastic responses

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Abstract
A range of successively more elaborate elastic models is developed, with responses that in many ways mimic those of plastic specimens under load. The bilinear stiffness of a simple one degree-of-freedom elastic prop, which experiences a symmetric point of bifurcation, is first used to model the fundamental elasto-plastic response: the introduction of an imperfection corresponds to the Ramberg-Osgood approximation, rounding off the bilinearity. Upper and lower yield points are reproduced by a model termed the elastic hook, in which an elastic spring of the first model is itself replaced by an elastic prop with a bilinear stiffness. Finally, the normality relation of incremental plasticity theory is reproduced by two props at right-angles: responses are also traced for two hooking models in this configuration, for which no real comparison in plasticity theory seems to exist at present.

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