Constitutive Model For Shape Memory Alloys Research Articles

A fast actuated soft gripper based on shape memory alloy wires

The application of shape memory alloy (SMA) actuated soft grippers is limited by their slow recovery speed. In order to further expand their application range, as one of the solutions to address this limitation, this paper proposes a fast actuated soft gripper based on SMA wire active heat dissipation and elastic rib combination to meet the rapid actuation and recovery. The structure primarily consists of a heat dissipation module capable of winding SMA wire and a soft structure resembling a scorpion tail with embedded supper elastic SMA wire. The geometric structure model, dynamics and SMA constitutive model and finite element model of the soft gripper are established, and the lateral deformation of soft bionic scorpion tail end is analyzed through simulations and experiments. In addition, the force in designed soft gripper tip and its ability to grasp different objects are also studied through experiments. The results show that the addition of a cooling fan increased the recovery rate by about 25%, and the force in soft bionic scorpion tail end can reach about 0.12 N. The designed soft gripper can successfully grasp objects with different softness, shape, size and weight. It lays a theoretical foundation and technical support for the development of soft grippers actuated by SMA in the future.

A new constitutive model of shape memory alloy and its seismic mitigation capacity compared with existing models

The existing constitutive models of shape memory alloy (SMA) cannot accurately describe the mechanical behavior in martensitic strengthening segment since their loading and unloading paths in strengthening segment completely overlap. This study proposes a multi-segment linear mathematical model for SMA, which realizes the separation of loading path and unloading path in strengthening segment. A four-story steel frame structure and corresponding braced structures with various SMA constitutive models are designed, and seismic control effects of SMA braces with these models are analyzed and compared through time history analysis. The results show that the sub-cycle unloading mode of SMA constitutive model affects the seismic mitigation capacity of SMA brace in a certain extent. The position of the inflection point of unloading path has very little influence on the structural control ability of SMA braces. The SMA brace using the SMA constitutive model with a single linear sub-cyclic unloading path has the minimal seismic response and the highest seismic reduction ratio. For most evaluation indexes, the seismic mitigation ability calculated by the proposed path separation constitutive model is in the middle of the results calculated by the existing models. SMA models without considering the mechanical behavior of strengthening segment may lead to an erroneous estimation of the energy consumption of SMA brace and the structural damage. The difference of simulation results among various SMA constitutive models is almost independent with ground motion.

A novel energetic approach for predicting fatigue crack growth in pseudoelastic NiTi alloys

A novel strain energy-based method for analyzing fatigue crack growth (FCG) in pseudoelastic Nickel-Titanium (NiTi) -based shape memory alloys (SMAs) is proposed. It uses the dissipated energy to predict the FCG. This parameter can be computed either by volume integration of near-crack-tip strain energy or by the force–displacement hysteresis measured at the loading pins of the sample. Eccentrically-loaded single Edge Crack tension samples (ESE(T)) were used for FCG tests. High resolution Digital Image Correlation (DIC) was used to capture near-crack-tip displacement and strain fields. DIC data were also used to estimate the effective stress intensity range by regressing the William’s expansion series. Furthermore, a constitutive model for SMAs was used for FE simulations of ESE(T) samples, and the evolution of the dissipated energy during FCG tests was computed. Experimental FCG rate, plotted against the cyclic dissipated energy, are well fitted by a power law equation (R2 = 0.99). This result would open new perspectives to develop predictive models for FCG in SMAs considering intricate thermomechanical coupling mechanisms and material non-linearities.

A three-dimensional constitutive model for shape memory alloy considering transformation-induced plasticity, two-way shape memory effect, plastic yield and tension-compression asymmetry

In this paper, a three-dimensional phenomenological constitutive model for shape memory alloys (SMA) is proposed with consideration given to various thermomechanical mechanisms. This model includes, for the first time in literature, the major mechanisms influencing the behaviors of SMA actuators in a unified thermodynamics framework: transformation-induced plasticity (TRIP), two-way shape memory effect (TWSME), plastic yield as well as tension-compression asymmetry. Furthermore, a new method to address the characteristics of transformation strain varying with stress levels was proposed. Moreover, a new transformation hardening function was proposed which can give a more accurate prediction of the transformation process. The three-dimensional constitutive model is solved using return mapping algorithm for an increment in a material point in the form of strain and temperature increment. The complete algorithm is proposed and the user-defined material subroutine (UMATs) for finite element problem is established. To validate the proposed SMA constitutive model, the parameters of the SMA material are determined through uniaxial tensile tests. The SMA tubes of the same material are used to conduct both experiments and simulation, with tension-compression asymmetry considered. Training experiments and simulations have been carried out on the SMA tubes, with evident TWSME observed. The typical loading conditions to trigger simultaneous transformation and plastic yield were designed, with experiments and simulations performed. According to the results, the SMA constitutive model is effective in capturing the thermomechanical response of SMA structures under various loading conditions.

Comprehensive shape memory alloys constitutive models for engineering application

The current shape memory alloys (SMA) constitutive models have the problems of complicated calculation, inaccurate results, measuring difficult parameters, and inconvenient application, which brings about challenges for designing, analyzing, and simulating SMA’s macroscopic behavior in engineering. This paper proposed practical SMA constitutive models for accurate engineering calculation, which apply to both the single loading-unloading process and the multiple loading-unloading cycles. The more accurate SMA theoretical tensile curve and temperature-stress phase transformation diagram is introduced to derive the constitutive model. The more accurate calculation method of elastic modulus, phase transformation modulus, and critical phase transformation stress is proposed in this paper. The proposed constitutive model considers the incomplete phase transformation phenomenon and the variation of critical phase transformation stress under multiple loading and unloading conditions. It can accurately evaluate the critical phase transformation stress and stress-strain relationships at various temperatures. Tensile tests under various working conditions were conducted. The results demonstrated that the proposed constitutive model could well simulate the SMA’s macroscopic mechanical behavior at various temperatures, loads, and multiple loading-unloading cycles with accuracy, practicality, and efficiency.

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 Shape Memory Alloy Constitutive Model with Polynomial Phase Transformation Kinetics

A Shape Memory Alloy Constitutive Model with Polynomial Phase Transformation Kinetics

Numerical simulations of spherical indentation of superelastic-plastic thin films

Depth sensing indentation is a useful tool to characterize the mechanical behavior of shape memory alloys (SMAs), which are often used in small volumes, such as thin films. However, it is difficult to interpret these test results since SMAs exhibit various phenomena such as superelasticity (SE), shape memory effect and plasticity. Hence, in this work, a finite element investigation of spherical indentation of a SMA thin film bonded to a stiff elastic substrate as well as a bulk SMA specimen is performed pertaining to two fixed temperatures, which are below and above the austenite finish temperature (Af). A SMA constitutive model which can represent the combined effects of SE and plasticity is employed. The simulations are aimed at revealing the roles of above two phenomena as well as influence of the substrate on the indentation response. While the load-depth (P−h) curve for the thin film rises well above that of the bulk SE sample as h increases, the inclusion of plasticity reduces this deviation. The Oliver–Pharr modulus is close to the Young’s modulus pertaining to the parent austenite phase at small h and tends to that of martensite at large h for bulk samples, whereas it reaches a minimum and thereafter increases corresponding to the thin film specimens. The mean contact pressure versus indentation strain curves for both specimens agree quite well which enables interpretation based on expanding cavity models. The results are rationalized from the evolution of transformed martensite and plastic zone underneath the indenter.

A multi-featured shape memory alloy constitutive model incorporating tension–compression asymmetric interpolation

The mechanical response of shape memory alloys is heavily governed by phase transformation and plasticity. These inelastic mechanisms present added complexities in the form of asymmetries with respect to the stress state (tension–compression asymmetry) and the direction (forward or reverse) of transformation, leading to the formation of internal loops. With this in mind, a constitutive model is developed incorporating phase transformation and yield plasticity. The model represents the tension–compression asymmetry through a novel approach by interpolating the maximum transformation strain, the Young’s modulus of martensite and a plasticity factor in the deviatoric plane of the transformation strain direction. Internal loops are also considered by scaling the transformation hardening and the hysteresis width based on memory points. The interaction between the processes of reorientation and phase transformation is also taken into account. The model is validated with several proportional and non-proportional loading tests with considerable success. The capability of the model to simulate complex loading scenarios is demonstrated by simulating the manufacturing and loading of a stent structure.

Multiparameter Optimization Design of Self-centering Friction Damper Using Shape Memory Alloy Bars

ABSTRACT In this study, the superelasticity of shape memory alloy (SMA) bars was used to develop a new self-centering friction damper (SCFD). A modified SMA constitutive model was established and verified using cyclic tensile test results of the SMA bars to establish the theoretical model of the SCFD. An effective method for the multiparameter optimization design of the SCFD was developed, which is applicable to other hybrid dampers. This optimal method using the genetic algorithm was based on defining an optimization calculation that reflects the dissipative coefficient and equivalent viscous damping as the evaluation indices and the SCFD design variables as the optimal parameters.

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.

Modelling fatigue crack growth in shape memory alloys

AbstractWe present a phase field‐based framework for modelling fatigue damage in Shape Memory Alloys (SMAs). The model combines, for the first time: (i) a generalized phase field description of fracture, incorporating multiple phase field formulations, (ii) a constitutive model for SMAs, based on a Drucker–Prager form of the transformation surface, and (iii) a fatigue degradation function, with damage driven by both elastic and transformation strains. The theoretical framework is numerically implemented, and the resulting linearized system is solved using a robust monolithic scheme, based on quasi‐Newton methods. Several paradigmatic boundary value problems are addressed to gain insight into the role of transformation stresses, stress‐strain hysteresis, and temperature. Namely, we compute Δε − N curves, quantify Paris law parameters, and predict fatigue crack growth rates in several geometries. In addition, the potential of the model for solving large‐scale problems is demonstrated by simulating the fatigue failure of a 3D lattice structure.

Nonlinear dynamic characteristics and stability analysis of energy storage flywheel rotor with shape memory alloy damper

In this paper, the nonlinear dynamic characteristics and stability of an energy storage flywheel rotor with shape memory alloys (SMA) damper are studied. A new type of SMA constitutive model is proposed to express SMA's hysteresis properties, and the nonlinear dynamic model of an energy storage flywheel rotor with SMA damper is established. A developed multi-scale method is proposed to obtain the natural frequency of the system with high accuracy in strong nonlinear condition, and the nonlinear dynamic characteristics of the system are analyzed. To a cracked flywheel rotor, a time-varying function is proposed to express the effect of the crack depth on the system's stiffness, and the variation of the system's area with different parameters is discussed. Simulation results show that the nonlinearity and crack will both affect the stable area of the system. To a flywheel rotor subjected to stochastic excitation, a developed analysis method for the stability is proposed to obtain the global stability of the system. Finally, the conditions on stochastic bifurcation are determined. Simulation results show that the stochastic system's motion will change from balance point to periodic orbit, and will also jump from one orbit to another in special cases. The results of this paper are helpful for the design of energy storage flywheel rotor.

Design, modeling and evaluation of a millimeter-scale SMA bending actuator with variable length

Millimeter-scale continuum bending actuators are useful in minimally invasive surgery to allow distal visualization and manipulation outside the line of sight. This paper presents a new continuum bending actuator based on shape memory alloy (SMA) with variable bending length. It consists of two SMA wires antagonistically configured to produce bidirectional bending under Joule heating. A linearly actuated rigid tube along the longitudinal axis enables continuous bending length adjustment, thus enhancing its workspace and force range. The proposed fabrication method tackles the challenging assembly tasks of maintaining the antagonistic configuration of long SMA wires, and robust electrical and mechanical connection during actuation. A quasi-static model of the actuator based on beam model and SMA constitutive model is presented and verified. The bending actuator was evaluated comprehensively for its workspace, blocked force, and trajectory tracking capability at different bending lengths and under different cooling conditions. It is the first work that demonstrates real-time continuous bending length adjustment in SMA-based bending actuator, leading to the potential development of compact and compliant robotic end effectors with improved distal workspace and force.

Implementation of visco-pseudo-elastic dampers for vibration reduction of sandwich shells using a large deformation FE technique

This study introduces a numerical method for investigating the appropriate arrangement of visco-pseudo-elastic dampers applicable to shell and plate structures under large deformation. These passive dampers are considered as discrete shape memory alloy (SMA) wires and viscoelastic layers. The SMA constitutive model is adopted and developed based on carried out experimental tests (i.e., calorimetry and tensile tests) on Ni-rich Nitinol alloy samples. Pseudoelastic, pseudoplastic, strain recovery and de-twinning phenomena are perceived experimentally. The presented model characterizes pseudoelastic response of shape memory alloys. The current finite element formulation is based on an incremental updated Lagrangian (UL) approach along with the Newmark's integration technique. The used sandwich element is capable of accurate modeling of the viscoelastic core damping behavior, as a result of independent rotation of element's layers. Also, the creep functions regarding to the viscoelastic constitutive model are estimated using Dirichlet-Prony series. Employing the state variables, the viscoelastic deferred strain is presented in a proper incremental form. A nonlinear FE program is developed to assess the proposed procedure. Obtained results demonstrate that quick vibration mitigation may be possible using visco-pseudo-elastic dampers while overcoming their individual drawbacks.

Response sensitivity studies of a cable-stayed bridge with shape memory alloy damping system considering temperature effects

This paper presents response sensitivity analyses of a cable-stayed bridge equipped with shape memory alloy (SMA) damping devices considering environmental temperature changes. The devices consist of an SMA-based damping brace (SMA-DB) system. An SMA constitutive model is extended to the SMA-DB to consider energy dissipation, rate dependencies, temperature effects, and asymmetry between tension and compression. Based on the direct differentiation method (DDM), an accurate and efficient sensitivity analysis algorithm is derived for the SMA-DB model. The methods of response and response sensitivity analyses are implemented in an open system for earthquake engineering simulation platform, OpenSees, for being used in various problems in civil engineering. A cable-stayed bridge in Shandong Binzhou Yellow River Highway is employed as an application example to verify the newly developed methods. Four SMA-DB components between piers and beams are added to the original finite element bridge model, and the seismic response and response sensitivity analyses are performed to study the complex behaviors of the cable-stayed bridge, e.g., the effect of SMA-DB on the energy dissipation, the changes of responses and response sensitivities due to the temperature change, the relative importance of various parameters on the system responses. The paper provides valuable references for seismic response studies of a cable-stayed bridge with the SMA-DB system.

A finite beam element multifunctional fabric modeling framework demonstrated with SMA knitted actuators

Multifunctional textiles have gained recent attention due their intrinsic properties that provide actuator, energy dampening, or sensory capabilities within small form factor textiles without external attachments. Such technologies are specifically appealing for medical and aerospace wearables, where active compression, haptic feedback, or the tracking of bodily functions are important tasks that are ideally conducted in a minimally-intrusive fashion. Current design capabilities of multifunctional textile are limited as present predictive tools lack accuracy and universality. This paper presents a finite beam element modeling tool for shape memory alloy (SMA) knitted architectures. The temperature-dependent variation of material properties within the SMA knitted loop affects the macroscopic force-extension behavior of SMA knitted architectures leading to an actuated and a relaxed knitted architecture response. This difference is exploited as the active property in SMA knitted architectures. The modeling architecture defines interfaces between sub-models organized in modules, specifically the material constitutive module, repetitive unit cell module, manufacturing module, contact module, and a boundary condition module. The SMA knitted architecture is modeled utilizing a 1D SMA constitutive model, quarter loop knit unit cell, a differential geometry-based manufacturing model, while assuming 3D Coulomb friction conditions. Kinematically-suitable boundary conditions are applied and the simulation predictions are compared quantitatively to macroscopic tensile experimental results, as well as qualitatively to microscopic x-ray diffraction phase analysis. The verification against experimental data supports the ability of the modeling tool to accurately predict the SMA knitted architecture thermo-mechanical performance with mean force-extension errors of less than 5%. The modeling tool provides the basis to understand, design, and optimize the lightweight, large force and deformation SMA knitted actuator textiles for novel applications. Additionally, the multifunctional textile modeling tool is implemented based on highly interchangeable sub-models to create synergies and propel the modeling of any multifunctional textile.

Introduction of the strain rate and cyclic loading effects on shape memory alloys constitutive law models

The superelasticity of shape memory alloys is a characteristic that permits to this smart material to dissipate significant energy during dynamic loads in addition to having the capacity to be used for seismic attenuation. Experimental studies have shown the strain rate and the cyclic loading caused by an earthquake influence on the residual strain and transformation stress of shape memory alloys. For this reason, this work consists of introducing the influence of the two latter parameters on constitutive laws of the most used shape memory alloy in the civil engineering field. A numerical model is then proposed and validated, and it represents residual strain–cyclic load and transformation stress–cyclic load relationships. A comparison between the original model, the built model and the experimental results is presented to show the consequence of taking into account the strain rate and cyclic loading effects. Finally, a parametric study is carried out to show cycles to be experimentally determined to get significant numerical results.

Shape Memory Alloy Bolted Joint for Medical Application by Finite Element Method

Shape memory alloy (SMA) have shown excellent ability for medical application. In this research, a three-dimensional SMA constitutive model with superelastic character is proposed based on the framework of general inelasticity and implemented successfully into the finite element software (e.g. ANSYS). The effectiveness of such implementation is verified by the experimental results of superelastic NiTi alloy taken from the literature. Finally, the stress distribution of a bolted joint for osteopathic medicine is analyzed by this model.

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.