On the Theory of Shape Memory Membrane Shells Undergoing Thermoelastic Phase Transitions

Based on the once coupled phenomenological model of thermoelastic phase transitions, the new linearized intrinsic formulation of the theory of membrane shells with shape memory effect is proposed. The shell model is formulated on the cotangent fibration of a two-dimensional manifold by the tangent strain tensor while the phase state is determined by the scalar field of martensite volume ratio. The linearized evolution equation defines a small increment of the phase state parameter through the increments of the thermodynamical temperature and the tangent force tensor. The incremental constitutive equation for the tangent strain induced by the phase transforms is derived from three-dimensional relation while the constitutive relations for elastic and temperature-induced strains could remain finite. The solutions for cylindrical membrane shells undergoing complete or incomplete direct and inverse phase transforms induced by temperature impacts are shown.