Constitutive relations and compatibility equations for thin shape memory alloy shells

Abstract

A new formulation of constitutive equations for thin shape memory alloy shells is obtained within the Kirchhoff’s theory on the basis of the once coupled constitutive model of thermoelastic martensite transitions. The inverse martensite transitions are considered, the tangent and bending strains are expressed through the tangent forces, couples, martensite volume ratio, and temperature; such constitutive equations do not require numerical inversion at a point on the deformation pattern. The compatibility equations for a thin shape memory shell are also derived, and the intrinsic formulation of a shape memory shell theory is proposed.