Shape memory alloys (SMA) are metals which can restore their initial shape after having been subjected to a deformation. They exhibit in general both nonlinear shape memory and pseudoelastic effects. In this paper, shape memory alloy (SMA) and its constitutive model with an empirical kinetics equation are investigated. A new formulation to the martensite fractiondependent Young modulus has been adopted and the plastic deformation was taken into account. To simulate the variations, a onedimensional constitutive model was constructed based on the uniaxial tension features.
Recently, smart metals and alloys have been extensively used in several metallurgical applications, due to their great potential in updated structures and design [
In the present work, an attempt is made to model typical martensitic transformations occurring in shape memory alloys, taking into account pseudoplasticity patterns. In this martensitic transformation, austenite undergoes transformation to form different variants of martensite under a controlled mechanical loading. The formation of martensite in the material is monitored through the coexistence of the initial austenite phases and martensite inside periodic units. Solutions for the implemented governing equations are obtained numerically via explicit numerical protocols and compared to some records presented in the recent related literature [
The studied system is a monodimensional rod subjected to axial solicitation (Figure
The studied model.
The main assumptions of the present model consists of setting one scalar internal variable
Young modulus
Since the martensite fraction
As per the model of derived by Tanaka and Nagaki [
In the case of pure mechanical constraint, and taking into accounts the presumptions of Chen et al. [
In the actual model, the transformation tensor
This expression refers to the Boubaker polynomials expansion scheme (BPES) [
The main advantage of this formulation (
Young modulus
Numerical simulation was achieved for the values of parameters gathered in Table
Values of
Parameters  Value  Unit 


6.0 10^{5}  MPa 

7.5 10^{3}  MPa 
Rod diameter  1.49  mm 
Solution plots represented in the StrainStress plane.
Numerical stressstrain plots obtained from the actual model confirm that the patterns of hysteresis loop generated in the positive quadrant (Figure
Strain span shows also a good agreement with the model performed by Motahari and Ghassemieh [
In summary, we have implemented constitutive model for shapememory alloys capable of undergoing austenite to martensite phase transformation using fundamental thermodynamic laws and the principle of martensite fractiondependence. The stressstrain plots obtained from uniaxial monitored load were predicted using the finiteelement simulations. A key parameter of the performed model consists of avoiding avoids singularity of the main equilibrium equation during the transition since the derivative of the preset
Although applied to a particular geometry, the model should be suitable to study other configurations since it was based on a single scalar internal variable: the martensite fraction. This model may be extended to 2D and 3D, while other possible future developments are the inclusion of permanent inelastic effects, the prediction of coupled thermomechanical behavior, and the nonlinear hardening mechanisms.