On the strain differential effect in the theory of shape memory membranes

Abstract

A theory of thin shells made of shape memory alloys is developed. Such thin-walled elements could be used in various structures as sensors, actuators, vibration dampers, etc. The new incremental constitutive equations for a thin shape memory membrane shell are derived accounting for the strain differential effect taking the once coupled phenomenological model of thermoelastic phase transitions as a background. The solutions for spherical and cylindrical shape memory alloy shells loaded by the internal or external pressure and axial loads are obtained. It is shown that the ratio of second invariant of the deviatoric stress and the stress intensity impacts significantly on the strains accumulated by the shell during martensite phase transitions, as well as on the temperature ranges of phase transforms.