Shape Memory Alloy Beam Research Articles

Finite‐Element Analysis of an Antagonistic Bistable Shape Memory Alloy Beam Actuator

A finite‐element (FE) analysis of the active bistability of an antagonistic shape memory alloy (SMA) beam actuator of TiNiCu is presented. The actuator comprises two coupled SMA beams that are clamped at both ends and coupled in their center by a spacer having different memory shapes being deflected in opposite out‐of‐plane directions. The actuator is characterized by two equilibrium positions. To determine bistable behavior as a function of geometrical parameters, a force criterion is defined by the coupling force of the beams in austenitic and martensitic states. Bistable behavior is achieved, if the coupling force does not change sign in the entire displacement range. This implies that the austenitic beam dominates the opposing martensitic beam. Thus, selective heating of the SMA beams results in a snap‐through motion of the coupled SMA beams. Depending on which of the two beams is in austenitic state, either of the two equilibrium positions is reached without the need for an external force. It is demonstrated that geometrical parameters like initial predeflection and spacer length have a crucial effect on the bistable performance. Bistable regions as well as critical limits characterized by geometry‐dependent stability ratios, beyond which the actuator's performance becomes monostable, are identified.

Experiment and simulation study on the functional fatigue of shape memory alloy beam actuators

The functional fatigue behavior of shape memory alloy (SMA) beam actuators is gaining importance as their utilization in engineering applications becomes more widespread. However, research on the functional fatigue behavior of SMA beam actuators under bending conditions is not as extensive as that on SMA wires. In this paper, an experimental study and theoretical analysis of the functional fatigue behavior of SMA beam actuators were conducted. A measuring method for bending deflection and an automatic thermal cyclic test bench was designed. A series of functional fatigue tests were conducted on SMA beam actuators under different bias load conditions and the functional fatigue patterns were obtained. The material damage factor is defined and calculated through specimen tests. By incorporating the damage factor to modify the existing constitutive model, a model considering functional fatigue and tension-compression asymmetry is obtained. Finite element analysis (FEA) is performed based on this modified model to simulate the actuating performance of SMA beam actuators and to compute the deflection at different numbers of cycles. Additionally, a small parameter study on the actuator shape is conducted using FEA. By comparing the FEA results with functional fatigue experimental data, the effectiveness of the modified model is validated, demonstrating its capability to describe functional fatigue and predict actuator lifespan.

Topology optimization structure design of shape memory alloy with multiple constraints

As an emerging functional material, shape memory alloy (SMA) exhibits remarkable mechanical properties and finds diverse applications across industries. This paper presents a topology optimization framework based on the bi-directional evolutionary structural optimization (BESO) method for designing SMA structures, which maximizes structural stiffness under multiple constraints of specified volume fraction, displacement, and fundamental frequency. A phenomenological constitutive model is utilized to simulate the mechanical behavior of SMA accurately. The unit virtual load method is employed to determine sensitivities. Several optimized SMA beam structures and simply-supported cube structures are designed under different thermal-mechanical loads, and their displacement, mean compliance, and fundamental frequency are evaluated throughout the optimization process. The results demonstrate that the proposed framework successfully customizes the SMA topology structure with adjustable displacement and fundamental frequency, and the optimized schemes exhibit more considerable deformation and more uniform mechanical properties than their initial counterparts. The proposed framework has higher computational efficiency than the traditional SIMP-based SMA topology optimization design method.

Research and simulation on the thermal mechanical properties of functionally graded shape memory alloy composite beam considering tension-compression asymmetry

Considering the tension-compression asymmetry of Shape Memory Alloy (SMA), the tension and compression constitutive equations of the Functionally Graded Shape Memory Alloy (FG-SMA) beam are established based on the simplified constitutive relation of SMA. The influences of the power exponent, temperature, tension-compression asymmetry coefficient, and strain (along the length direction of the beam) on the martensite volume fraction and stress of the beam are analyzed, and the correctness of the theory is verified by comparing the results of theory with finite element analysis. The research shows that when the height of the beam is constant, the power exponent, temperature, tension-compression asymmetry coefficient are proportional (inversely proportional) to the stress (martensite volume fraction) of the cross-section, and the strain is proportional to both the stress and martensite volume fraction of the cross-section. When the other conditions are fixed, compared with compression, the martensite volume fraction (stress) under tension is larger (slightly less) at the same layer cross-section position.

Fully analytic approach to study bifurcation phenomenon for a shape memory alloy beam under temperature variation and lateral white-noise excitation

The main aim of this article is to obtain the probability density function of the response of an SMA beam under lateral white-noise excitation and study the bifurcation phenomenon through a fully analytic approach. Firstly, an efficient constitutive stress–strain relation for a shape memory alloy material supporting both martensite and austenite phases is considered. Secondly, the governing equation of motion for a typical SMA simply supported beam is derived using some dimensionless parameters. Thirdly, the corresponding probability density function of the response is computed analytically using the powerful Fokker–Planck–Kolmogorov equation, and finally, the bifurcation phenomenon for parameter variations of the beam is investigated. The results show how geometric (beam aspect ratio), force (the mean value of the white-noise excitation), and environmental (working temperature) factors can affect the nonlinear behavior and response bifurcation of the beam. A numerical validation is also done that guarantees the correctness of the method and results.

Bistable Actuation Based on Antagonistic Buckling SMA Beams

Novel miniature-scale bistable actuators are developed, which consist of two antagonistically coupled buckling shape memory alloy (SMA) beams. Two SMA films are designed as buckling SMA beams, whose memory shapes are adjusted to have opposing buckling states. Coupling the SMA beams in their center leads to a compact bistable actuator, which exhibits a bi-directional snap-through motion by selectively heating the SMA beams. Fabrication involves magnetron sputtering of SMA films, subsequent micromachining by lithography, and systems integration. The stationary force–displacement characteristics of monostable actuators consisting of single buckling SMA beams and bistable actuators are characterized with respect to their geometrical parameters. The dynamic performance of bistable actuation is investigated by selectively heating the SMA beams via direct mechanical contact to a low-temperature heat source in the range of 130–190 °C. The bistable actuation is characterized by a large stroke up to 3.65 mm corresponding to more than 30% of the SMA beam length. Operation frequencies are in the order of 1 Hz depending on geometrical parameters and heat source temperature. The bistable actuation at low-temperature differences provides a route for waste heat recovery.

A new approach for nonlinear transient dynamic analysis of micro SMA beam considering size effect and instantaneous phase transformation

Shape Memory Alloys (SMAs) have attracted lots of attraction in the recent years due to their unique characteristics. However, studies in the field of behavior of SMAs at micro scale is not enough and more research is required. The present paper presents a nonlinear dynamic solution for a micro made of NiFeGa SMA, located on a viscoelastic foundation. The recommended approach takes into account instantaneous variations of martensite volume fraction and size effect which are the main novelties of the present study. In this regard, the formulation proposed by Hernandez and Lagoudas is used to capture and model the size effect of the SMAs. The governing differential equations obtained for Euler-Bernoulli micro beam using the Hamilton’s principle, considering the Von-Karman nonlinear strain. The nonlinear equation of motion is solved applying the semi-exact method. In this study, the return mapping convex cutting plane is used, in order to overcome the material nonlinearity of the problem. The obtained results are compared with the reference papers which shows the accuracy of the present model. Results show that with considering the size effect, the loss factor of vibration will increase by increasing the thickness of the micro SMA beam. While regardless of the size effect, this factor remains almost constant. The reason for this phenomenon is that when size effect is taken into account, the thermodynamic properties and critical stresses of phase transformation will change with resizing the SMA. Outputs also show that by increasing the damping coefficient and decreasing the stiffness of foundation, more energy is wasted in the vibration of the micro SMA beam. In addition, it was observed that micro beams with lower thicknesses are more sensitive to foundation characteristics meanwhile the loss factor of vibration with lesser thicknesses changes more by changing the foundation stiffness and damping coefficients.

On the nonlinear analysis of pre-strained shape memory alloy beams

We present a theoretical and numerical investigation of the transverse dynamic response of monolithic Shape Memory Alloy (SMA) beams under the effect of axial pre-strains. The SMA beam is taken as benchmark structure to evaluate the effect of (axial) pre-strain on either the free or the forced dynamics. The combination of the static stress, produced by the pre-loading conditions, with the dynamic stress, associated with the vibratory response, affects the occurrence of the stress-induced SMA phase transformation hence providing a mechanism to passively tune the dynamic response. Particular attention is given to the effect that different pre-strain levels have on the overall ability to dissipate mechanical energy, that is on the effective damping. The numerical model of the SMA beam accounts for both material and geometric nonlinear behaviors. The nonlinear material behavior is due to the SMA phase-transformation and it is modeled via the one-dimensional improved Brinson’s model (including tension–compression asymmetry), while the geometric nonlinear behavior is due to large displacements occurring during the phase transformation and it is accounted for via von Kármán assumptions. The resulting model is solved numerically via the finite element method and used to evaluate both the free and the forced response of the beam. The free response analysis suggests the existence of optimal pre-strain levels to achieve maximum damping capacity, while the forced response highlights the occurrence of nonlinear dynamic features, such as bifurcation. In both cases, it is found that the level of pre-strain can significantly affect the dynamic response as well as the effective damping. The results presented in this work provide useful guidelines to understand the dynamics of continuous SMA structures under pre-strain and the ability to tune either their resulting dynamics or dissipation properties.

Bending of shape memory alloy nanobeams incorporating surface effects based on the Euler-Bernoulli beam model

Shape memory alloys (SMA) are widely used in micro-electro-mechanical systems due to shape memory effect and hyperelasticity. The surface effects on mechanical properties cannot be ignored because of their small structure size. Based on Euler Bernoulli beam theory and Gurtin-Murdoch surface elasticity theory, the influence of tension-compression asymmetry factors on SMA beams is considered, and a phase transformation mechanical model of SMA nanobeams considering surface effects is established. The effects of surface effects on load, curvature and neutral axis displacement are investigated The study demonstrates that regardless of whether considering the surface effect, the neutral axis displacement initially increases and subsequently decreases with the growth of the dimensionless bending moment. The neutral axis displacement of nanobeams can be significantly affected by taking surface effects into account. When considering the surface effect, the difference in neutral axis displacement of the nanobeam increases as the nanobeam’s size diminishes. Neglecting surface effects will underestimate the bending stiffness of the microbeam.

Investigation of the Damping Performance of a Shape Memory Alloy Beam

Investigation of the Damping Performance of a Shape Memory Alloy Beam

A 3D finite-strain beam model for thermo-mechanical deformations of 2D shape memory alloys in 3D space

In this paper, a robust constitutive model adapted to a 3D beam theory in the finite strain regime is proposed to simulate thermo-mechanical behaviors of shape memory alloys (SMAs) under triaxial normal-shear loadings. For the first time, four internal parameters are considered to capture martensitic transformation, orientation/reorientation of martensite variants, normal-shear deformation coupling, and asymmetric/anisotropic strain generation in polycrystalline SMAs. Solution algorithms of the model are presented for stress- and strain-control cases based on the elastic-predictor inelastic-corrector return mapping process. To develop the Cauchy-Green deformation tensor, a 3D exact displacement field is proposed based on the centroid movements and rotations of the cross-section. A finite element formulation along with the Newton-Raphson and Riks techniques is also established to trace the non-linear equilibrium path of 3D SMA beam structures in the large defamation regime. Higher-order shape functions are also considered to avoid shear and membrane locking issues. To explore and demonstrate the capabilities of the proposed model, the results of the triaxial and 3D SMA constitutive models are compared with existing experimental results on uniaxial tension, and combined tension-torsion tests. Afterwards, the results of 3D solid element and proposed 3D beam element are compared with experimental results of deep stretch SMA helical springs under three loading/unloading cycles. An excellent qualitative and quantitative correlation is observed between numerical and experimental results verifying the model accuracy and the solution procedure. The combination of the proposed triaxial SMA constitutive model with 3D beam theory leads to a significant reduction in computational time and storage requirements without any accuracy loss. Extra simulations are then conducted for a simplified model of a 3D biomedical vascular SMA stent under various loading/unloading conditions. The simulations reveal that the new 3D finite-strain SMA-beam element is well appropriate for modeling of 3D spatial lattice-based stents. Due to simplicity and accuracy, the 3D SMA beam model could serve in future efforts for a computationally efficient modeling of large defamations of complicated 3D SMA structures with 2D members (e.g., SMA lattices). • A robust constitutive model is developed to simulate behaviors of SMAs under triaxial normal-shears loadings. • The solution algorithms combined is extended to trace the non-linear equilibrium path of 3D SMA beam structures. • The results of present 3D Beam model has been compared with existing experimental results as well as 3D solid elements. • A good qualitative and quantitative correlation is observed between numerical and experimental results. • The proposed triaxial SMA beam model leads to a significant reduction in computational time without loss inaccuracy.

A Nonlinear Analysis of the Mechanical Behavior of Functionally Graded Shape-Memory Alloy Beams

A Nonlinear Analysis of the Mechanical Behavior of Functionally Graded Shape-Memory Alloy Beams

A nonlinear analysis of the mechanical behavior of functionally graded shape-memory alloy beams

С использованием теории изгиба балок и соотношений между напряжениями и деформациями для материалов из сплавов с памятью формы проанализировали нелинейное механическое поведение балок из функционально-градиентных сплавов с памятью формы, подверженных нечистому изгибу. Предположили, что объемное содержание сплава изменяется по толщине балки по закону степенной функции. Распределение напряжений в её поперечном сечении на каждой стадии фазового преобразования определили путем введения коэффициента асимметрии растяжения–сжатия. Перемещение нейтральной оси балки, кривизну поперечного сечения и изменение границы раздела фаз в осевом направлении рассчитали путем решения уравнения равновесия. Результаты показали, что влияние изменения показателя степени на асимметрию растяжения–сжатия намного больше, чем изменение коэффициента асимметрии растяжения–сжатия. Перемещение нейтральной оси и кривизна поперечного сечения нелинейно отрицательно связаны с показателем степени. С увеличением показателя степени граница фазового преобразования смещалась ближе к срединному сечению. Перемещение нейтральной оси того же поперечного сечения нелинейно положительно связано с коэффициентом асимметрии растяжения–сжатия, а кривизна – нелинейно отрицательно. Фазовая граница на сжатой стороне балки смещалась ближе к срединному сечению по мере увеличения коэффициента асимметрии растяжения– сжатия. Результаты расчетов могут быть использованы в качестве ориентира при разработке и применении таких материалов.

Analytic detection of chaos zones in response of a shape memory alloy beam under simultaneous external and parametric excitations

ABTRACT In this article, the dynamic stability and chaotic behavior of a shape memory alloy (SMA) beam with large deformation under simultaneous lateral and axial excitations is investigated through a fully analytic approach. First, the nonlinear governing equation of motion is derived. Second, Melnikov’s method, as an analytic approach, is employed to obtain the chaos zones. After that, by introducing non-dimensional parameters, border curves of chaotic areas were evaluated and plotted for some case studies which give a reader a precise and clear look at how the material and load properties can affect the chaos zones. Finally, the sufficient condition is approved via corresponding poincaré maps.

Concept of Elastocaloric Granular Material Made from SMA Wires in Bending

Shape memory alloys (SMAs) are promising materials for the creation of heating or cooling systems due to their elastocaloric character. The paper proposes a concept of elastocaloric “porous” SMA beam working in bending. The beam was made with superelastic nickel-titanium SMA wires of different diameters placed in a flexible tube. While water was flowing through the tube, bending was manually applied using 3D printed wavy profiles with portions of arcs with constant curvatures. Preliminary results showed an oscillation of the fluid temperature at the outlet of the flexible tube (containing the SMA wires) at the same frequency as the mechanical loading, validating therefore the concept of elastocaloric porous SMA beam operating in bending.

Design methodology of the Ni50Ti50 shape memory alloy beam actuator: Heat treatment, training and numerical simulation

Shape memory alloy (SMA) beam actuators are widely used in morphing structures, which leads to a surgent demand for a comprehensive design method. Previous methods have not considered the heat treatment and the evolution of actuation performance during training. In this study, an in-depth investigation was conducted into the Ni50Ti50 (at%) SMA beam actuator from the perspective of heat treatment, training, numerical simulation for developing a comprehensive and novel design methodology. The proper heat treatment conditions that result in the relatively high actuation performance for the Ni50Ti50 SMA beam were determined. The dependence of the thermomechanical behavior evolution on the training load was established. Moreover, a numerical analysis method for the SMA beam actuator based on a 3-D constitutive model with tension-compression asymmetry considered was detailed, followed by the calibration of material parameters. A forward design method for the SMA beam actuator was proposed with the shape and actuation performance evolution during training under various training loads fully considered in the design process. The proposed design method was applied for a design case and the accuracy of the design results demonstrated its feasibility.

Coupled thermomechanical modelling of shape memory alloy structures undergoing large deformation

Shape Memory Alloys (SMAs) exhibit strain recovery capabilities even after undergoing large deformation, out of underlying stress and temperature dependent diffusionless martensitic transformation. Modelling its behaviour accurately requires coupled thermomechanical analysis, considering absorption and emission of latent heat during phase transformation, thermoelastic effects, thermomechanical loading and boundary conditions. Moreover, the variation of material properties, e.g., modulus of elasticity and thermal expansion coefficient, during phase transformation, significantly affects the response of the system. In addition, appropriate stress and strain measures are required to model the large deformation of SMA-based components under practical thermomechanical loads. In this study, a nonlinear finite element formulation based on Total Lagrangian (TL) approach has been developed to address geometric as well as material non-linearity arising out of the SMA behaviour. Furthermore, considering all the above-mentioned effects, both the stress and thermal equilibrium equations are solved simultaneously in an incremental–iterative finite element (FE) framework, simulating the coupled SMA response. The SMA constitutive model, using Green–Lagrange strain and Second Piola–Kirchhoff stress measures, proposed by Qidwai and Lagoudas (2000), has been implemented. Using the developed FE model, the thermomechanical responses of SMA wire actuator, beam and biomedical staple are simulated to demonstrate the need for the coupled analysis while considering large deformation of the SMA structures.

Parametric Random Vibration Analysis of an Axially Moving Laminated Shape Memory Alloy Beam Based on Monte Carlo Simulation.

The study of the bifurcation, random vibration, chaotic dynamics, and control of laminated composite beams are research hotspots. In this paper, the parametric random vibration of an axially moving laminated shape memory alloy (SMA) beam was investigated. In light of the Timoshenko beam theory and taking into consideration axial motion effects and axial forces, a random dynamic equation of laminated SMA beams was deduced. The Falk’s polynomial constitutive model of SMA was used to simulate the nonlinear random dynamic behavior of the laminated beam. Additionally, the numerical of the probability density function and power spectral density curves was obtained through the Monte Carlo simulation. The results indicated that the large amplitude vibration character of the beam can be caused by random perturbation on axial velocity.

Study on the effect of phase transformation of a shape memory alloy on post-buckled restoring force characteristics

To develop a vibration isolator for the vertical direction using a post-buckled shape memory alloy (SMA), it is important to understand the restoring force and the mechanism of the negative stiffness characteristics of a post-buckled SMA beam. In this study, we investigated the relationship between the restoring force characteristics and the phase transformation of a post-buckled thin plate SMA beam. The Finite Element Analysis was used for the investigation. As a result, we confirmed a qualitative correlation between the restoring force characteristics and the volume fraction of the phase transformed SMA material.

Phase transformation mechanical behavior of functionally graded shape memory alloy beams

Based on the bending deformation theory of the beam, combined with stress-strain relationship and the critical stress-temperature relationship of the shape memory alloy materials, the nonlinear governing equation of the functionally graded shape memory alloy statically indeterminate beam was obtained, and its mechanical behavior under the thermal-mechanical load was investigated. The phase transformation process of the beam was analyzed by a step-by-step method, and the influence of mechanical load, the tension-compression asymmetry coefficient, power exponent and temperature on the displacement of the neutral axis, curvature and phase boundary were obtained. The results draw that as the increase of the load, the displacement of neutral axis and the curvature become larger and the phase boundary is farther away from the edge of the section; the more the temperature and the power exponent are, the smaller the displacement of neutral axis and curvature will be, and the phase boundary become closer to the edge of the section; the tension-compression asymmetry coefficient has a greater influence on the phase boundary of the compressive side, but it has a weak influence on the phase boundary of the tensile side.