  This paper presents a comparative study between two micro-macro modeling
approaches to simulate stress-induced martensitic transformation in shape
memory alloys (SMA). One model is a crystal plasticity based model and the
other describes the evolution of the microstructure with a Boltzmann-type
statistical approach. Both models consider a self-consistent scheme to perform
the scale transition from the local thermomechanical behavior to the global
one. The way the two modeling approaches describe the local behavior is
analyzed. Similarities and differences are pointed out. Numerical simulations
of the thermo-mechanical behavior of an isotropic titanium-niobium SMA are
performed. These alloys have known a growing interest of scientific community
given their high potential for application in the biomedical field.
Stress-strain curves obtained from the two simulations are compared with
experimental results. Evolutions of volume fractions of martensite variants
predicted by the two approaches are compared for <100>, <110> and <111> tensile
directions. Due to the absence of comparative studies between multiscale models
dedicated for SMA, this paper fills a gap in the state of the art in this field
and provides a significant step toward the definition of an efficient numerical
tool for the analysis of SMA behavior under multiaxial loadings.
