Analytical modeling of the shape memory effect in SMA beams with rectangular cross section under reversed pure bending

An analytical model is developed for a prismatic SMA beam with rectangular cross section subjected to alternating bending at temperature below the austenitic transformations. The loading path consists in loading-unloading cycle under and then reversed bending. Two opposite martensitic variants take place, whose volume fractions evolve linearly axial stress. Different Young’s moduli are taken phases. As moment increased, transformation starts from top bottom it extends inwards. If maximum applied large enough, complete Martensitic takes place upper lower parts of section. During unloading following bending, reorientation Martensite variant into one starting boundary between fully region intermediate transforming region. Special attention devoted calculate analytically stress distributions within each stage process. A closed form moment-curvature relation provided elastic integral rest approach validated by comparison results available literature.