One-dimensional constitutive SMA model with two martensite variants: Analytical and numerical solutions

• Published in: European journal of mechanics, A, Solids Vol. 40; pp. 166 - 185
• Main Authors: Marfia, Sonia, Rizzoni, Raffaella
• Format: Journal Article
• Language: English
• Published: Elsevier Masson SAS 01-08-2013
• Subjects: Analytical and numerical solutions; Elastic constants; Evolution; Laminates; Martensite; Mathematical analysis; Mathematical models; Non-constant elastic properties; One-dimensional SMA model; Pseudo-elastic and shape memory effects; Shape memory alloys; Tension–compression asymmetry; Three phase; Two martensite variants; One-dimensional SMA model; Non-constant elastic properties; Two martensite variants; Analytical and numerical solutions; Pseudo-elastic and shape memory effects; Tension–compression asymmetry
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2013.01.007

This paper deals with the one-dimensional modeling of a shape memory alloy (SMA) in order to reproduce the special thermo-mechanical response of the material. In particular, new analytical solutions are developed using a simple one-dimensional SMA model based on the introduction of three phases: tensile martensite, compressive martensite and austenite; the ability to reproduce the pseudo-elastic and shape memory effects; the different behavior in tension and compression; the different elastic properties of the three phases; and the reorientation process of the martensite. The model assumes the martensite volume fractions as internal variables, whose evolution is governed by stress and temperature. Analytical solutions, which take into consideration the axial loads and thermal processes, are developed to solve the axial problem. Furthermore, a numerical procedure is developed in order to time-integrate the kinetic laws that rule the evolution of the internal variables during the phase transformations and a 2-node finite element beam is implemented. Considering the constant and non-constant elastic properties for the three SMA phases, some applications are presented in order to verify the effectiveness of the proposed model and the analytical and numerical solutions. Comparisons with experimental data related to the axial response of SMA wires and laminae are carried out. Finally, a numerical application concerning a SMA lamina, which is subjected to bending load at high temperatures inducing the pseudo-elastic effect in the material, is presented.
► New analytical solutions are proposed based on a 1D SMA model. ► The model reproduces the pseudo-elastic and the shape memory effects. ► Tension–compression asymmetry and variants reorientation are considered. ► Analytical and numerical solutions are given for axial loads and thermal processes. ► Applications considering constant and non-constant elastic properties are presented.