Finite Element Method on Shape Memory Alloy Structure and Its Applications

Abstract

It is significant to numerically investigate thermo-mechanical behaviors of shape memory alloy (SMA) structures undergoing large and uneven deformation for they are used in many engineering fields to meet special requirements.To solve the problems of convergence in the numerical simulation on thermo-mechanical behaviors of SMA structures by universal finite element software. This work suppose a finite element method to simulate the super-elasticity and shape memory effect in the SMA structure undergoing large and uneven deformation. Two scalars, named by phase-transition modulus and equivalent stiffness, are defined to make it easy to establish and implement the finite element method for a SMA structure. An incremental constitutive equation is developed to formulate the relationship of stress, strain and temperature in a SMA material based on phase-transition modulus and equivalent stiffness. A phase-transition modulus equation is derived to describe the relationship of phase-transition modulus, stress and temperature in a SMA material during the processes of martensitic phase transition and martensitic inverse phase transition. A finite element equation is established to express the incremental relationship of nodal displacement, external force and temperature change in a finite element discrete structure of SMA. The incremental constitutive equation, phase-transition modulus equation and finite element equation compose the supposed finite element method which simulate the thermo-mechanical behaviors of a SMA structure. Two SMA structures, which undergo large and uneven deformation, are numerically simulated by the supposed finite element method. Results of numerical simulation show that the supposed finite element method can effectively simulate the super-elasticity and shape memory effect of a SMA structure undergoing large and uneven deformation, and is suitable to act as an effective computational tool for the wide applications based on the SMA materials. which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Processing of shape memory alloys research, applications and opportunities: a review

“…From the study, it is evident that the finite element equation is an excellent tool for developing models that would be used to predict the behavior of SMA and therefore make use of them in direct applications [198]. Figures 23(a), (b), and C shows the deformation mechanism of an SMA bar, including two punch heads, one die, and one support, respectively [199]. The purpose of the study is to draw the curve of proportion between the moment of force and the rotation angle of the punch head at 317 K and 300 K constant temperatures.…”

“…The SMA bar generates strain-induced martensite transformation causing the hysteresis loop. The 300 K curve, on the other hand, does not show a hysteresis loop, as the SMA bar does not transform under these conditions [199]. This method permits the investigation of a variety of SMA configurations, including SMA cirques and SMA bars with punch heads, dies, and supports.…”

A review on Nitinol shape memory alloy heat engines

“…SME is a phenomenon that, when SMA with a given configuration at high temperature is cooled down to low temperature, it could be deformed easily to a new configuration like plastic material by external stress, and keep the deformed configuration when the load is removed. When it is heated up to high temperature again, it regains back its original configuration [54][55][56][57]. The mechanism behind this phenomenon is shown in detail in figure 1.…”

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

“…There are four characteristic temperatures, including martensitic starting temperature M s , martensitic finishing temperature M f , austenitic starting temperature A s and austenitic finishing temperature A f , in an SMA at a free-stress state (Brinson, 1993;Chen et al, 2018;Liang and Rogers, 1990). They are generally satisfied with the relationship M f \ M s \ A s \ A f (Zhou et al, 2019).…”