An Explicit Modeling for the Pseudoelastic Response of Porous SMA Thick-Walled Cylinders under Internal and External Pressure

Abstract

Shape-memory alloy (SMA) structures, either dense or porous, are widely used because of their functional characteristics arising from shape-memory effect and pseudoelasticity. Hence, the precise modeling of these materials is essential due to design issues. In this study, the solution algorithm based on an explicit phenomenological constitutive model is investigated to analyze pressurized cylinders. The proposed method is extracted following return mapping scheme to find the evolution of phase transformation in these structures. The formulation is validated by comparing uniaxial tension–compression curves during loading, unloading and thermal actuation against published literature. By the aid of this model, assuming elastic and phase transformation strains, a comprehensive study is presented to inspect stress, strain and displacement fields along the thickness of internally and externally pressurized thick-walled cylinders. To this end, the governing nonlinear equation in elastic–inelastic zones is discretized by the efficient method of generalized differential quadrature (GDQ) and the resultant relations are solved numerically. The influences of internal and external pressure on stress distribution along the cylinder wall during loading–unloading for different temperatures including phase transformation and saturation states are discussed. Also, the closed-form solution for critical pressure at the onset of the phase transformation is studied.