On size-dependent bending behaviors of shape memory alloy microbeams via nonlocal strain gradient theory

Abstract

This paper focuses on the size-dependent behaviors of functionally graded shape memory alloy (FG-SMA) microbeams based on the Bernoulli-Euler beam theory. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus and critical transformation stresses vary continuously along the longitudinal direction. According to the simplified linear shape memory alloy (SMA) constitutive equations and nonlocal strain gradient theory, the mechanical model was established via the principle of virtual work. Employing the Galerkin method, the governing differential equations were numerically solved. The functionally graded effect, nonlocal effect and size effect of the mechanical behaviors of the FG-SMA microbeam were numerically simulated and discussed. Results indicate that the mechanical behaviors of FG-SMA microbeams are distinctly size-dependent only when the ratio of material length scale parameter to the microbeam height is small enough. Both the increments of material nonlocal parameter and ratio of material length-scale parameter to the microbeam height all make the FG-SMA microbeam become softer. However, the stiffness increases with the increment of FG parameter. The FG parameter plays an important role in controlling the transverse deformation of the FG-SMA microbeam. This work can provide a theoretical basis for the design and application of FG-SMA microstructures.

Finite Element Method of Functionally Graded Shape Memory Alloy Based on UMAT

“…When the shape memory factor decreases to 0, the shape memory strain fully recovers. The relationship between the shape memory factor and martensite volume fraction is [2]:…”

“…Based on the isotropic assumption, when the temperature T satisfies T > M s , it is assumed that the initial state of the SMA is completely in the austenitic phase, for the positive phase transformation process (σ ms ≤ σ eq ≤ σ mf ) [2]:…”

“…C M is the temperature influence coefficient of the critical stress of the martensitic phase transformation, and M s represents the martensitic starting temperature. When the ambient temperature T > A s , for the inverse phase transition process (σ af < σ eq < σ as ) [2]:…”

“…Shape memory alloys (SMAs) are promising candidates as materials in the fields of automotive, aerospace, biomedical, industrial process control, electronic instrumentation, telecommunications, and military applications because of their ability to undergo a structural displacive phase transformation [1,2], known as a martensitic transformation [3], which occurs between austenite of a crystallographic more-ordered phase (stable at high temperature and low stress) and martensite of a crystallographic less-ordered phase (stable at low temperature and high stress). Owing to exhibiting a reversible martensitic transformation, SMAs can recover their original shapes from large deformations well beyond their elastic strain limits upon unloading or heating, which are referred to as pseudo-elasticity and the shape memory effect, respectively [4,5].…”

Hygro-magneto-thermally induced vibration of spinning viscoelastic Y-shaped bifurcated tubes containing magnetic fluid based on nonlocal strain gradient theory

“…Recent studies illustrated that applying the classical continuum theory offers reliable results only for the dynamical analysis of macro-scale structures (Dabbagh and Ebrahimi, 2021; Guo et al, 2019; Nopour et al, 2022; Shojaeefard et al, 2018; Talebitooti and Fadaee, 2019). In fact, considering small-scale effects in the mathematical modeling of micro-and nanostructures is a mandatory engineering requirement (Ebrahimi et al, 2021b, 2021e; Li et al, 2016; Zhou et al, 2021). As a result, different size-dependent higher-order continuum theories are developed for accurate modeling and precise designing of small-size systems (Kiani et al, 2018; Waksmanski and Pan, 2017).…”