Multiphysics description of smart materials using a prismatic data-driven approach

• Prismatic approach is a data-driven model to describe multiphysics behavior of smart materials. • The prismatic approach is based on the Preisach model allowing the description of complex phenomena by incorporating a third dimension. • Numerical simulations show the model ability to describe several complex multiphysics phenomena. • Shape memory alloys, magnetic shape memory alloys, magnetostrictive materials, and piezoelectric materials are described. Smart materials are characterized by their ability to adapt to environmental changes due to the coupling among different physical domains. The hysteretic response is a typical behavior of smart materials, representing a challenging topic for its mathematical modeling. The literature presents different approaches to deal with this modeling, and the use of data-driven, experimental-based models is an alternative that avoids the characterization of material properties, presenting simplicity as the main advantage. This paper investigates the use of a data-driven prismatic approach for the multiphysics description of the smart material hysteretic behavior. The prismatic approach promotes an extension of the classical Preisach triangular domain, allowing a broader description of material behaviors. The Preisach model is based on mathematical operators that allow the definition of the Everett function to build a surface that describes the material behavior, characterizing the hysteresis. Subsequent interpolations allow the prismatic domain description. Numerical simulations are carried out and compared with experimental data available in the literature to investigate the capabilities of the model to represent the multiphysics hysteretic behavior of smart materials. On this basis, distinct smart materials are evaluated including shape memory alloys, magnetic materials and piezoelectric materials. Results show a close agreement between numerical and experimental data, demonstrating that the proposed model is a powerful tool to describe the multiphysics aspects of smart material complex behaviors.