An analytical model for a shape memory alloy beam accounting for tension-compression stress asymmetry effect

Author(s):  
Nguyen V. Viet ◽  
Wael Zaki
10.5772/7228 ◽  
2009 ◽  
Vol 6 (3) ◽  
pp. 29 ◽  
Author(s):  
Hu Bing-Shan ◽  
Wang Li-Wen ◽  
Fu Zhuang ◽  
Zhao Yan-zheng

Wall climbing robots using negative pressure suction always employ air pumps which have great noise and large volume. Two prototypes of bio-inspired miniature suction cup actuated by shape memory alloy (SMA) are designed based on studying characteristics of biologic suction apparatuses, and the suction cups in this paper can be used as adhesion mechanisms for miniature wall climbing robots without air pumps. The first prototype with a two-way shape memory effect (TWSME) extension TiNi spring imitates the piston structure of the stalked sucker; the second one actuated by a one way SMA actuator with a bias has a basic structure of stiff margin, guiding element, leader and elastic element. Analytical model of the second prototype is founded considering the constitutive model of the SMA actuator, the deflection of the thin elastic plate under compound load and the thermo-dynamic model of the sealed air cavity. Experiments are done to test their suction characteristics, and the analytical model of the second prototype is simulated on Matlab/simulink platform and validated by experiments.


Author(s):  
Fabrizio Niccoli ◽  
Valentina Giovinco ◽  
Cedric Garion ◽  
Carmine Maletta ◽  
Paolo Chiggiato

Recent studies on Shape Memory Alloy rings have been undertaken at the European Organization for Nuclear Research (CERN) to develop smart and leak-tight couplers for Ultra High Vacuum systems of particle accelerators. A special thermo-mechanical process (training) is needed to provide SMA rings with proper functional properties, that is to allow thermal mounting, dismounting, and leak tight coupling within a given service temperature window. Low temperature ring expansion is a crucial part of the training process as it gives suitable size, shape recovery properties, and thermal stability range to the SMA element. An analytical model, based on simplified elastic-plastic axisymmetric concepts, has been developed and implemented in a commercial software to simulate isothermal SMA rings expansions. It is particularly useful to predict the final size of a martensitic SMA coupler as a function of the initial dimensions and of the pre-deformation parameters. The effectiveness of the model has been demonstrated by analyzing the stress/deformation field occurring in a wide range of ring geometries for different load cases including martensite reorientation and plasticity. The predictions of the analytical model have been systematically compared with those obtained by axisymmetric finite element (FE) analyses based on elastic-plastic constitutive models and experimental measurements.


Author(s):  
Wael Zaki ◽  
N. V. Viet

Based on the ZM model for shape memory alloys, an analytical model is derived for a functionally graded material (FGM)/shape memory alloy (SMA) laminated composite cantilever beam subjected to concentrated force at the tip. The beam consists of a SMA core layer bonded to identical FGM layers on both sides. The FGM layer is considered to be elastic with an equivalent Young’s modulus related to those of the constituents by means of a power law. Phase transformation within the SMA layer is accounted for in deriving the analytical relations, which are validated against finite element analysis results.


2018 ◽  
Vol 29 (20) ◽  
pp. 3902-3922 ◽  
Author(s):  
Nguyen Van Viet ◽  
Wael Zaki ◽  
Rehan Umer

We propose a new analytical model for a superelastic shape memory alloy prismatic cantilever beam subjected to a concentrated force at the tip. The force is gradually increased and then removed and the corresponding distribution of phase transformation fields in the beam is determined, analytically, in both the transverse and longitudinal directions. Analytical moment–curvature and shear force–shear strain relations are also derived during loading and unloading of the beam. The proposed model is validated against an exact numerical beam model as well as a three-dimensional finite element analysis model for the same beam, with very good agreement in each case. Moreover, an experiment is proposed and carried out to characterize the load–deflection response of a shape memory alloy beam under the same boundary conditions as those considered in deriving the model. The obtained response is in good agreement with the analytical model as well as three-dimensional finite element analysis simulations. The analytical method provides a direct mathematical way for describing the material and structural properties of the beam and the distribution of the different solid phase regions as they change under the influence of an applied load and allows the determination of details such as the boundaries of solid phase regions immediately and accurately using equations. The same would require postprocessing at possibly significant computational cost and personal effort if finite element analysis or similar numerical methods are used.


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