A multi-block-spin approach for martensitic phase transformation based on statistical physics

Current strategies in modeling shape memory alloy (SMA) behavior follow either the concept of classical irreversible thermodynamics or the methodology of phenomenological approaches at the micro as well as at the macro space scale. The objective of the present study is to show a new approach in modeling SMA's by using a statistical physics concept without the requirement of evolution equations for internal variables. Thermodynamic principles in connection with the mathematical apparatus of statistical physics allow deriving relevant system properties in analogy to the formalism used for paramagnetic-ferromagnetic systems. As a result the macroscopic strains and the volume fractions of the martensitic variants and their rates are obtained. The multi-block-spin approach further maps the tension compression asymmetry of multivariant SMA's.