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 fraction-dependent Young modulus has been adopted and the plastic deformation was taken into account. To simulate the variations, a one-dimensional constitutive model was constructed based on the uniaxial tension features. 1. Introduction Recently, smart metals and alloys have been extensively used in several metallurgical applications, due to their great potential in updated structures and design [1–10]. Among these materials, shape memory alloys (SMA) have attracted more attention, due to their ability to develop extremely large recoverable strains and great forces in the field of biomedical, metallurgy, aerospace, and civil structures [5–10]. In SMA matrices, pseudoplastic effect creates different stress strain behavior resulting in a stress strain curve which lies on the curve produced by the initial linear elastic response during loading. Consecutive and continued unloading may produce linear elastic behavior that eventually returns the structure to the zero stress strain state. 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 [11–18]. 2. Model Patterns 2.1. Governing Equations The studied system is a mono-dimensional rod subjected to axial solicitation (Figure 1). The phase transformations in this considered structure occur by nucleation and growth of platelet inclusions perpendicular to -axis (Figure 1). In this configuration, elastic modulus local expression can be obtained considering the medium as a succession of austenite-martensite periodic units (Figure 1). Figure 1: The studied model. The main assumptions of the present model consists of setting one scalar internal variable which represents the
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