Constitutive Model For Shape Memory Alloys Research Articles

Actuation Frequency Modeling and Prediction for Shape Memory Alloy Actuators

This article proposes a numerical model to predict actuation frequencies (strain-cycling frequencies) for 1-D shape memory alloy (SMA) actuators. The numerical model is designed by comprehensively considering the factors that significantly affect an SMA actuator's strain-cycling frequency, i.e., heat convection methods, constant or nonconstant bias loads, and Joule heating methods. For computing strain cycles of SMA actuators, we develop a computation framework that effectively integrates an SMA constitutive model, a phase transformation kinetic model, stress-strain models for different types of bias stress, and a heat transfer model of SMA wires. The strain and temperature rates are formulated by nonlinear ordinary differential equations. The strain and temperature cycles can be accurately approximated by numerical iterative methods. Experimental verification was conducted to investigate the effectiveness of the proposed model. By initially identifying the SMA characteristic parameters, we employed Latin hypercube sampling method to generate 30 sets of design parameters for comparing the predicted and measured actuation frequencies. In addition, we investigated how the uncertainty of premeasured SMA characteristic parameters affect the numerical prediction of actuation frequency by conducting sensitivity analysis. The experiments demonstrate 0.7%-9.03% and 2.65%-17.57% differences between predicted and measured actuation frequencies for constant bias loads and spring bias loads, respectively.

Transformation and Plasticity of Shape Memory Alloy Structures: Constitutive Modeling and Finite Element Implementation

In this work, we extend a well-known three-dimensional phenomenological shape memory alloy (SMA) constitutive model known as Souza model. The proposed model describes more precisely the hardening behavior observed during forward- and reverse-phase transformation as well as evolution of plastic strain and its effects on transformation behavior. Moreover, we present a solution algorithm for low temperatures and evolution of plastic strains which considerably reduces the computational cost. Through calibration of material parameters, the model is able to predict pseudo-elasticity and shape memory properties of SMAs more accurately compared to Souza model. Moreover, the plasticity and its effect on transformation are well predicted by the proposed model. Through finite element implementation, we can perform simulations on complex SMA structures. Finally we compare the run time for the present algorithm with the iterative Newton method used for solving equations of Souza model. The comparisons show that the computational cost of the proposed algorithm is considerably lower than previous algorithms.

A Temperature-Dependent Model of Shape Memory Alloys Considering Tensile-Compressive Asymmetry and the Ratcheting Effect.

Tensile-compressive asymmetry and the ratcheting effect are two significant characteristics of shape memory alloys (SMAs) during uniaxial cyclic tests, thus having received substantial attention in research. In this study, by redefining the internal variables in SMAs by considering the cyclic accumulation of residual martensite, we propose a constitutive model for SMAs to simultaneously reflect tensile-compressive asymmetry and the cyclic ratcheting effect under multiple cyclic tests. This constitutive model is temperature dependent and can be used to reasonably capture the typical features of SMAs during tensile-compressive cyclic tests, which include the pseudo-elasticity at higher temperatures as well as the shape-memory effect at lower temperatures. Moreover, the proposed model can predict the cyclic mechanical behavior of SMAs subjected to applied stresses with different peak and valley values under tension and compression. Agreement between the predictions obtained from the proposed model and the published experimental data is observed, which confirms that the proposed novel constitutive model of SMAs is feasible.

Design, Modeling, and Control of a Compact SMA-Actuated MR-Conditional Steerable Neurosurgical Robot

The letter presents a compact shape memory alloy (SMA)-actuated magnetic resonance (MR)-conditional neurosurgical robotic system. It consists of a 2-degree of freedom (DoF) cable-driven steerable end effector, an antagonistic SMA springs-based actuation module, and a quick-connect module, packaged into a single integrated device measuring 305 mm length × 76 mm diameter. The system is also highly adaptable, such that it could operate a cable-driven end effector up to a maximum of 4-DoFs and its length can be easily modified due to the acrylic plate-based modular construction. In addition to the kinematics of the robotic end effector and the SMA constitutive model, we also present the antagonistic SMA springs model under the known tension and cable displacement from the robotic end effector. We performed extensive characterization experiments to obtain SMA model parameters and integrated a feedforward component in our controller to achieve improved tracking of a sinusoidal reference up to 80° bending angle amplitude and 100 s period. Lastly, proof-of-concept robot demonstrations were performed in a gel phantom and in the MRI that confirmed the robot motion capability in the brain and MRI compatibility of the robot.

Analysis of One-Dimensional Ivshin-Pence Shape Memory Alloy Constitutive Model for Sensitivity and Uncertainty.

Shape memory alloys (SMAs) are classified as smart materials due to their capacity to display shape memory effect and pseudoelasticity with changing temperature and loading conditions. The thermomechanical behavior of SMAs has been simulated by several constitutive models that adopted microscopic thermodynamic or macroscopic phenomenological approaches. The Ivshin–Pence model is one of the most popular SMA macroscopic phenomenological constitutive models. The construction of the model requires involvement of parameters that possess inherent uncertainty. Under varying operating temperatures and loading conditions, the uncertainty in these parameters propagates and, therefore, affects the predictive power of the model. The propagation of uncertainty while using this model in real-life applications can result in performance discrepancies or failure at extreme conditions. In this study, we employed a probabilistic approach to perform the sensitivity and uncertainty analysis of the Ivshin–Pence model. Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods were used to perform the sensitivity analysis for simulated isothermal loading/unloading at various operating temperatures. It is evident that the model’s prediction of the SMA stress–strain curves varies due to the change in operating temperature and loading condition. The average and stress-dependent sensitivity indices present the most influential parameters at several temperatures.

An analytical model for crack monitoring of the shape memory alloy intelligent concrete

A theoretical model for the crack monitoring of the shape memory alloy intelligent concrete is presented in this work. The mechanical properties of shape memory alloy materials are first given by the experimental test. The one-dimensional constitutive model of the shape memory alloys is reviewed by degenerating from a three-dimensional model, and the behaviors of the shape memory alloys under different working conditions are then discussed. By combining the electrical resistivity model and the one-dimensional shape memory alloy constitutive model, the crack monitoring model of the shape memory alloy intelligent concrete is given, and the relationships between the crack width of the concrete and the electrical resistance variation of the shape memory alloy materials for different crack monitoring processes of shape memory alloy intelligent concrete are finally presented. The numerical results of the present model are compared with the published experimental data to verify the correctness of the model.

Sensitivity and Uncertainty Analysis of One-Dimensional Tanaka and Liang-Rogers Shape Memory Alloy Constitutive Models.

A shape memory alloy (SMA) can remember its original shape and recover from strain due to loading once it is exposed to heat (shape memory effect). SMAs also exhibit elastic response to applied stress above the characteristic temperature at which transformation to austenite is completed (pseudoelasticity or superelasticity). Shape memory effect and pseudoelasticity of SMAs have been addressed by several microscopic thermodynamic and macroscopic phenomenological models using different modeling approaches. The Tanaka and Liang-Rogers models are two of the most widely used macroscopic phenomenological constitutive models for describing SMA behavior. In this paper, we performed sensitivity and uncertainty analysis using Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods for the Tanaka and Liang-Rogers models at different operating temperatures and loading conditions. The stress-dependent and average sensitivity indices have been analyzed and are presented for determining the most influential parameters for these models. The results show that variability is primarily caused by a change in operating temperature and loading conditions. Both models appear to be influenced by the uncertainty in elastic modulus of the material significantly. The analyses presented in this paper aim to provide a better insight for designing applications using SMAs by increasing the understanding of these models’ sensitivity to the input parameters and the cause of output variability due to uncertainty in the same input parameters.

3D reconstitution and numerical analysis of superelastic behavior of porous shape memory alloy

In this work, a CAD 3D foam structure of Ni-Ti Shape Memory Alloy (SMA) is rebuilt using ellipsoid unit cells in order to study the superelastic behavior of porous SMAs. A taking and placing algorithm based on a uniform and a normal distributions is adopted for the 3D reconstitution process. In the design sample, dimensions, positions and orientations of the ellipsoid unit cells are randomly selected. A SMA constitutive model including phase transformation, martensitic reorientation and twins accommodation is selected to simulate the superelastic behavior of the SMA foam. As an application, the compression of SMA porous sample with random ellipsoid unit cell distribution is simulated by finite element in order to show the efficiency of the proposed methodology to predict its superelastic response and to analyze the porosity effect. The obtained results show that the force-displacement or stress-strain responses of the porous material are highly depend on the foam porosity. The effects of porosity, size, orientation, ratio of long axis and short axis, and distribution of unit cell on the superelastic behavior of SMA porous material are also discussed in both closed cells and open cells cases.

Uncertainty quantification of the parameters and predictions of a phenomenological constitutive model for thermally induced phase transformation in Ni–Ti shape memory alloys

In this work, a probabilistic calibration approach has been adopted to quantify the uncertainties of the parameters and predictions of a phenomenological shape memory alloys (SMAs) constitutive model which has been used to predict the thermally induced phase transformation of Ni–Ti SMAs. Furthermore, the impact of the adopted calibration method, which enables the determination of the uncertainty bounds of the model predictions, on the design of robust engineering applications has been discussed. To this end prior to the probabilistic model calibration, a design of experiments has been performed in order to identify the most influential parameters on the response of the system and thus reduce the dimensionality of the problem. Subsequently, uncertainty quantification (UQ) of the influential parameters has been carried out through Bayesian Markov Chain Monte Carlo (MCMC). The assessed uncertainties in the model parameters has been then propagated to the model predictions using an approximate approach based on the variance–covariance matrix of the MCMC-calibrated model parameters and then an explicit propagation of uncertainty through MCMC-based sampling. The determined 95% Bayesian confidence intervals of the model predictions, by the latter methods, have been demonstrated and compared. Additionally, good agreement between the experimentally measured and model predicted SMA hysteresis loops has been observed where the experimental data are situated within the predicted 95% Bayesian confidence intervals. Finally, the application of the MCMC-based UQ/UP approach in decision making for experimental design has also been shown by comparing the information that can be gained by performing multiple repetitive experiments under identical thermo-mechanical conditions versus experiments under different conditions.

Construction and mechanical analysis of finite element model for bending property of controlled memory wire nickel-titanium rotary file

To construct a model for a controlled memory (CM) nickel-titanium (NiTi) file and another M-wire NiTi file with the same geometry by using finite element analysis. To evaluate the flexibility of a CM NiTi file by using three dimensional finite element method and to compare its mechanical responses with that M-wire NiTi. Based on the reverse engineering, the 21 mm long, 25#/08 taper Hyflex NT NiTi file and Hyflex CM NiTi file were fixed by the cantilever bending model at a distance of 9.5 mm from the tip of the file. The mechanical tester's indenter was loaded/unloaded at a distance of 3 mm from the tip of the file. The maximum displacement was 3 mm, the load displacement curve was obtained. Subsequently, by using a micro-CT to scan (layer spacing of 8 μm) NiTi files, and ABAQUS (6.10) was introduced to construct a geometric model. Hyflex NT was considered as a shapememory alloy constitutive model, Hyflex CM was considered as a power-hardening plastic constitutive model, respectively. Comparing the load-displacement curve of cantilever bending in the three-dimensional finite element model with the load-displacement curve in the experiment. Two tetrahedral element models were constructed, the total number of nodes was 99 353 and the total number of cells was 63 744. When the loading displacement was 1 mm, the stress distribution of the cross section at 6.1 mm from the tip of the file was observed. The upper and lower surfaces were subjected to the maximum bending stress and entered the phase transformation yield stage. The finite element simulation could clearly show the deformation of the file. Various information such as deformation characteristics and stress distribution in the process were well fitted to the actual experimental curve. The constitutive behavior of the material has a significant effect on the mechanical behavior of NiTi file. The finite element model established for the NiTi file of the CM wire can accurately capture the characteristics of various deformation processes of the NiTi root canal file, and it has a good fit with the actual experimental curve. The finite element model can be used for study on bending properties of CM wire.

Evolution of internal damage during actuation fatigue in shape memory alloys

Shape Memory Alloys (SMAs) are subject to multiple types of fatigue including structural fatigue due to cyclic load application as well as functional fatigue due to cyclic phase transformation. Due to the thermomechanical nature of the phase transformation, the area of functional fatigue can be further subdivided into pseudoelastic fatigue, which is fatigue due to stress induced phase transformation, or actuation fatigue which is fatigue due to repeated thermally induced phase transformation. In the area of actuation fatigue, many works have attempted to predict the actuation fatigue lifetime, however the evolution of the microstructure during the actuation fatigue lifetime has yet to be examined. This work utilizes X-ray computed microtomography to examine the evolution of internal damage during actuation fatigue and has found that internal damage evolves in a non-linear manner unique to SMAs. Specifically, internal damage is shown to nucleate quickly during initial actuation cycling, followed by a steady state growth and leading to rapid coalescence at the end of the actuation fatigue lifetime. This experimentally observed non-linear internal damage growth has been introduced into a SMA constitutive model and the model is shown to give good lifetime predictions both for uniaxial as well as multiaxial loading conditions.

Constitutive model of shape memory alloy under the effect of martensite plasticity for finite‐element applications

This study is focused on the superelastic Ni-based shape memory alloy (SMA) for finite-element applications. SMA has presented excellent characterisations in biomedical application, mechanical application, aerospace application, seismic prevention, disaster reduction and so on. In this study, a SMA constitutive model is proposed that is capable of describing SMA superelastic features and its plasticity effects. Finally, the analysed results show good ability to predict the experimental data.

Simulation of Eccentric Impact of Square and Rectangular Composite Laminates Embedded with SMA.

In the present work, we study the low velocity impact, both central and eccentric, on square and rectangular laminated composite plates with embedded shape memory alloy (SMA) wires, which are stitched on the top and bottom surfaces of the plate, by using the finite element method. In finite element methods (FEM) simulations, a super-elastic SMA constitutive model is implemented in Abaqus/Explict by using a user defined material subroutine to describe the behaviors of SMAs. The three-dimensional (3D) Hashin failure criterion is adopted to model the damage initiation of laminated composite plates. To model the delamination failure, a cohesive damage zone model is introduced in interface elements. A comprehensive parametric study has been carried out to analyze the effects of eccentricity for the case of square and rectangular laminated composite plates.

Shape Memory Alloys: identification of the parameters necessary for constitutive models

The purpose of this research is to identify the Shape Memory Alloy (SMA) parameters necessary for SMA actuators analysis using SMA constitutive models. The behavior of a material is primarily a function of three variables: stress, strain and temperature, and their associated rates. These variables are interdependent, and the material behavior is a non-linear function of these variables. A number of constitutive models for shape memory alloys have been proposed and found to be relatively convenient to use in predicting and describing shape memory alloys’ behaviors quantitatively. However, the application of these models in designing and analyzing an actuator requires the determination of the thermomechanical properties of these materials such as transformation temperatures, thermoelastic tensor, Young’s modulus, Transformation tensor) and recovery strain. This research has been conducted to identify the thermomechanical properties of a commercial NiTi SMA wire. The paper shows in details how these parameters can be identified.

Robust fluid-structure interaction analysis of an adaptive airfoil using shape memory alloy actuators

In the present paper, an aero-structure interaction model for the rapid simulation of morphing structures realized through shape memory alloy (SMA) actuators is presented. The aerodynamic simulation method implements a potential flow method strongly coupled with an integral boundary layer method in the context of a viscous-inviscid interaction approach, which includes a transition prediction model and a simplified shear stress-transport equation for the turbulence closure. The structural analysis model of the airfoil integrates a well-established SMA constitutive model for the prediction of the actuator behavior into finite element software. The two numerical models are loosely interconnected by exchanging geometrical and loading data at each iteration. An articulated 2-link adaptive mechanism for load alleviation purposes in horizontal axis wind turbine blades is investigated considering two different morphing scenarios: (1) operation of a single hinged flap; (2) combined movement of two sequential airfoil segments is attempted to achieve a smoother camber variation. The present fluid-structure interaction (FSI) model is employed with the aim to quantify its effect and benefits on the active shape control of the morphing airfoil, the actuator response, and the aerodynamic performance including lift and drag coefficients. The presented results demonstrate the robustness and numerical performance of the developed FSI method.

Uniaxial, pure bending, and column buckling experiments on superelastic NiTi rods and tubes

Many existing shape memory alloy (SMA) devices consist of slender beams and frames. To better understand SMA beam behavior, we experimentally examined the isothermal, room temperature response of superelastic NiTi rods and tubes, of similar outer diameters, subjected to four different modes of loading. Pure tension, pure compression, and pure bending experiments were first performed to establish and compare the baseline uniaxial and bending behaviors of rods and tubes. Column buckling experiments were then performed on rod and tube columns of several slenderness ratios to investigate their mechanical responses, phase transformation kinetics under combined uniaxial and bending deformation, and the interaction between material and structural instabilities. In all experiments, stereo digital image correlation measured local displacement fields in order to capture phenomena such as strain localization and propagating phase boundaries.Superelastic mechanical behavior and the nature of stress-induced phase transformation were found to be strongly affected by specimen geometry and the deformation mode. Under uniaxial tension, both the rod and tube had well-defined loading and unloading plateaus in their superelastic responses, during which stress-induced phase transformation propagated along the length of the specimen in the form of a high/low strain front. Due to the dependence of strain localization on kinematic compatibility, the high/low strain front morphologies differed between the rod and tube: for the rod, the high/low strain front consisted of a diffuse “neck”, while the high/low strain front in the tube consisted of distinct, criss-crossing “fingers.” During uniaxial compression, both cross-sectional forms exhibited higher transformation stresses and smaller transformation strains than uniaxial tension, highlighting the now well-known tension-compression asymmetry of SMAs. Additionally, phase transformation localization and propagation were absent under compressive loading. During pure bending, the moment-curvature response of both forms exhibited plateaus and strain localization during forward and reverse transformations. Rod specimens developed localized, high-curvature regions that propagated along the specimen axis and caused shear strain near the high/low curvature interface; whereas, the tube specimens exhibited finger/wedge-like high strain regions over the tensile side of the tube which caused nonlinear strain profiles through the thickness of the specimen that did not propagate. It was therefore found that classical beam theory assumptions did not hold in the presence of phase transformation localization (although, the assumptions did hold on average for the tube). During column buckling, the structures were loaded into the post-buckling regime yet recovered nearly-straight forms upon unloading. Strain localization was observed only for high aspect ratio (slender) tubes, but the mechanical responses were similar to that of rods of the same slenderness ratio. Also, an interesting “unbuckling” phenomenon was discovered in certain low aspect ratio (stout) columns, where late post-buckling straightening was observed despite continuous monotonic loading. Thus, these behaviors are some of the challenging phenomena which must be captured when developing SMA constitutive models and executing structural simulations.

Co-rotational thermo-mechanically coupled multi-field framework and finite element for the large displacement analysis of multi-layered shape memory alloy beam-like structures

A thermo-mechanically coupled finite element (FE) for the simulation of multi-layered shape memory alloy (SMA) beams admitting large displacements and rotations (LDRs) is developed to capture the geometrically nonlinear effects which are present in many SMA applications. A generalized multi-field beam theory implementing a SMA constitutive model based on small strain theory, thermo-mechanically coupled governing equations and multi-field kinematic hypotheses combining first order shear deformation assumptions with a sixth order polynomial temperature field through the thickness of the beam section are extended to admit LDRs. The co-rotational formulation is adopted, where the motion of the beam is decomposed to rigid body motion and relative small deformation in the local frame. A new generalized multi-layered SMA FE is formulated. The nonlinear transient spatial discretized equations of motion of the SMA structure are synthesized and solved using the Newton–Raphson method combined with an implicit time integration scheme. Correlations of models incorporating the present beam FE with respective results of models incorporating plane stress SMA FEs, demonstrate excellent agreement of the predicted LDRs response, temperature and phase transformation fields, as well as, significant gains in computational time.

The Mechanical Behavior and Martensitic Transformation of Porous NiTi Alloys Based on Geometrical Reconstruction

The finite element analysis (FEA) of porous NiTi shape memory alloys (SMAs) remains a challenge due to irregularity and complexity of pore structure. In this paper, the real finite element model (FEM) is established based on the geometrical reconstruction. Through a SMA constitutive model, the mechanical behavior and stress-induced martensitic (SIM) phase transformation are analyzed with the real FEM. The results show that the stress–strain curve of FEA is in good agreement with the experimental curve and the calculation can reflect the mechanical behavior well in the compressive process. With the increase of load, the SIM first appears pore walls or weak parts of struts, then spreads to the center of matrix, and finally happens to most of matrix. When the slope of the stress–strain curve shows obvious changes, the SIM has happened in quite a part of matrix.

形状記憶合金を用いた超軽量月惑星探査ローバの提案

Planetary surface mobility is one of the key technologies for future deep space missions. However conventional rovers are so big and expensive. To enhance robotic surface exploration missions, small, light-weight explorers are required. Therefore this paper proposes a new hopping locomotion system for small planetary rover using shape-memory-alloy(SMA) actuator. The proposed mechanism is analysed based on SMA constitutive mathematical model. Simulation results show that proposed mechanism has the capability of horizontally 2.5 m jump under the 1/6 gravity environment.

Influence of the SMA Constitutive Model on the Response of Structures

Strong earthquakes may impose significant displacements in structures, which can result in excessive displacements at structural joints. Previous numerical studies have shown that the recentring capability of shape memory alloys (SMA) can be applied to limit joint openings and maximum longitudinal displacements. However, these studies do not focus on the influence of the SMA constitutive model adopted on the estimated displacements. A sensitivity analysis was performed using simplified two-degree-of-freedom models, which represent two-frame reinforced concrete bridges with various ratios of natural periods of vibration, connected by SMA bars. These models were implemented in a MATLAB based program for nonlinear dynamic analysis. The obtained results show that the relative displacements are more sensitive to the SMA model than the absolute displacements.