This paper is concerned with a special class of hardening response functions for small deformation of elastic-plastic materials, its application to isotropic metals, and comparison of the theoretical results with experimental cyclic stress-strain curves for two different metals. The theoretical development is carried out within the scope of the existing purely mechanical theory for the “rate-independent” response of elastic-plastic materials, which admits the existence of a single loading function, as well as certain accepted idealizations. After summarizing the basic equations for small deformation, detailed attention is given to the development of a special form of the hardening response function, motivated mainly by the observation that the stress-strain curves for uniaxial cyclic loading of a fairly large class of metals attain—after several cycles—the so-called saturation hardening. We exploit this property; and, in the case of isotropic metals, systematically derive some restrictions on the constitutive coefficients in the loading function and the hardening response. Comparison of the results with two sets of experimental data, obtained from uniaxial cyclic loading of a 304 stainless steel and a 2024 aluminum alloy, shows good agreement within the understood idealizations of the basic theory.

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