An improvement on the Brinson model for shape memory alloys with application to two-dimensional beam element

Abstract

In this article, the one-dimensional phenomenological constitutive model originally proposed by Brinson for shape memory alloys is improved to predict asymmetric behavior in tension and compression. We propose an approach that decomposes stress-induced martensite volume fraction into two parts, one in tension and one in compression. Results of numerical examples show reasonable agreement with experimental data. Moreover, we implement the proposed model in a user-defined material subroutine in the nonlinear finite element software ABAQUS/Standard as a two-dimensional Euler–Bernoulli beam element. We simulate several beam problems and a shape memory alloy staple. Regarding the results, the proposed shape memory alloys constitutive model, employed in a two-dimensional beam element, can be used to simulate various shape memory alloys applications in the design and analysis.

Effects of asymmetric material response on the mechanical behavior of porous shape memory alloys

“…It is also supposed that the martensite transformation is just associated with the shear component of microplane stresses (Kadkhodaei et al, 2007a(Kadkhodaei et al, , 2007b. Based on this assumption, the volumetric and deviatoric parts of the normal component of the strain vector can be related to the corresponding stresses using Hook's law, and the shear strain is calculated using the 1D relation proposed for SMAs by Poorasadion et al (2013) …”

“…To evaluate the value of martensite volume fractions in tension and compression, in this article, the evolution function of martensite volume fraction presented by Poorasadion et al (2013) is modified based on this phase diagram as follows if T M s and s cr s \ŝ\s cr f :…”

“…As a result, unlike the studied 13% porous NiTi, the asymmetric response of dense SMA has a considerable effect on the stress-strain response of 42% porous specimen. Since stress state in porous materials, especially near their pore walls, is too complicated, asymmetric material response of dense SMAs should be considered using a suitable equivalent stress rather than separate material parameters in tension and compression similar to the approach proposed by Mehrabi et al (2014b) and Poorasadion et al (2013).…”

Effects of superelastic shape memory springs on the aeroelastic behavior of a typical airfoil section: passive vibration attenuation and energy harvesting applications

“…A "shape memory" material can change its shape through external stimuli such as temperature (BUEHLER; WANG, 1968), magnetic field (KIEFER; LAGOUDAS, 2005) and several other forms of excitation (MENG et al, 2013). Among different materials which exhibit shape memory behavior are the shape memory polymers (LIU et al, 2014;SCALET et al, 2015) and the SMAs (such as the CuAlBe, CuZnAl, CuAlNi, CuAlZnMn and NiTi alloys) (HUANG, 2002;POORASADION et al, 2014). The near-equiatomic NiTi alloys usually exhibit attractive properties (with reasonable cost) and are widely used in academy and industry.…”

“…The SMA behavior is represented based on classical models, mainly on the works of Liang and Rogers (1990, 1997 and Brinson (1993). Additional features are included mainly based on the works of Bucchi et al (2014) and Poorasadion et al (2014) and described later in Chapter 2. The two-state approximation of Edwards, Ashley and Breakwell (1979) to the classical aerodynamics of Theodorsen (1935) is used to determine the unsteady aerodynamic loads (pitch moment and lift).…”