A prismatic approach to describe the hysteretic behavior of smart materials: An application to shape memory alloys

Hysteretic response of smart materials has complex mathematical modeling. Thermodynamic-based constitutive models belong to an important class of models and data-driven models are interesting alternatives that avoid complex algorithms and parameter determinations. The classical Preisach model describes multidisciplinary hysteretic behavior employing mathematical operators in a triangular domain. The Everett function is an alternative build a surface from experimental data, replacing the original integral form to a summation. This paper proposes a novel approach, extending the Preisach triangular domain to a prismatic domain that allows a broader description of distinct phenomena. The idea is to use the Preisach approach for different triangles and then performing a interpolation for a prismatic domain, enabling the representation of distinct phenomena that, otherwise would not be described. Shape memory alloys (SMAs) are employed as a representative example of smart materials. Experimental tests are developed in order to define reference cases to be analyzed. Numerical simulations are carried out and compared with experimental data, evaluating the model capabilities under different loading conditions. Specifically, temperature-dependent and cyclic-dependent behaviors are of concern. The results show the model ability to describe the general thermomechanical behavior of shape memory alloy hysteretic behavior, being in close agreement with experimental data.