By assimilating shape memory alloys with mathematical multifractal-type objects, a theoretical model based on Scale Relativity Theory in the form of The Multifractal Theory of Motion, in order to explain the mechanical behavior of such material, is proposed. The model is validated by analyzing the mechanical behavior of Cu-Al-Zn shape memory alloy with various chemical compositions. More precisely, the multifractal tunnel effect can "mime" the mechanical hysteresis of such a material, a situation in which a direct correspondence for several mechanical properties of Cu-Al-Zn is highlighted (the chemical composition can be correlated with the shapes of the curves controlled through the multifractality degree, while the areas delimited by the same curves can be correlated with the multifractal specific potential, as a measure of the mechanical memory degree).
Keywords: Scale Relativity Theory; hysteresis; mechanical behavior; multifractal tunnel effect; multifractality; shape memory alloy.