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).

By using SMAs formulations based on Cu-Zn-Al, the electrical resistivity by employment of an Agilent 4294A Precision Impedance Analyzer was analysed. It results that the different percentages of the metals which make up an SMA, do have an important influence upon resistivity. In particular, for one of the analyzed samples, it was observed that the SME was manifested as a form of “electric properties” memory. The experimental data was fitted using both Gaussian and polynomial fitting.

Shape memory alloys (SMA in short) exhibit a series of properties which are very different compared to regular metallic materials. One of their main characteristic is the ability to change their geometric shape when subjected to an increase from a low to a high temperature. In certain conditions, this shape change can be reversible, such that the material can “memorize” two geometric shapes: the high temperature shape (the “warm” shape) and the low temperature shape (the “cold” shape). These transformations occur due to an effect known as shape memory effect (SME in short). Moreover, through SME, the material is able to produce mechanical work when shifting from the “cold” shape to the “warm” one [1]. The discovery of these alloys is linked to the highlighting of a specific property which actually pertains to only several of said alloys (being uncommon for a metallic material) and which is known as “rubber-type behavior”. Many types of SMAs are very expensive, due to their composition (which includes noble metals) and their complex manufacturing technologies.. The most commonly encountered alloys nowadays are Ni-Ti, Cu-Al-Zn and Cu-Al-Ni which are employed in a plethora of practical applications.