Finite element analysis of 2D SMA beam bending

A thermomechanical model of a shape memory alloy beam bending under tip force loading is implemented in finite element codes.The constitutive model is a one dimensional model which is based on free energy and motivated by statistical thermodynamics.The particular focus of this paper is on the aspects of finite element modeling and simulation of the inhomogeneous beam bending problem.This paper extends previous work which is based on the small deformation Euler-Bernoulli beam theory and by treating an SMA beam as consisting of multi-layers in a twodimensional model.The flux terms are involved in the heat transfer equation.The simulations can represent both shape memory effect and super-elastic behavior.Different thermal boundary condition effect and load rate effect can also be captured.     

Three-dimensional modeling and numerical analysis of rate-dependent irrecoverable deformation in shape memory alloys

Shape memory alloys (SMAs) provide an attractive solid-state actuation alternative to engineers in various fields due to their ability to exhibit recoverable deformations while under substantial loads. Many constitutive models describing this repeatable phenomenon have been proposed, where some models also capture the effects of rate-independent irrecoverable deformations (i.e., plasticity) in SMAs. In this work, we consider a topic not addressed to date: the generation and evolution of irrecoverable viscoplastic strains in an SMA material. Such strains appear in metals subjected to sufficiently high temperatures. The need to account for these effects in SMAs arises when considering one of two situations: the exposure of a conventional SMA material (e.g., NiTi) to high temperatures for a non-negligible amount of time, as occurs during shape-setting, or the utilization of new high temperature shape memory alloys (HTSMAs), where the elevated transformation temperatures induce transformation and viscoplastic behaviors simultaneously. A new three-dimensional constitutive model based on established SMA and viscoplastic modeling techniques is derived that accounts for these behaviors. The numerical implementation of the model is described in detail. Several finite element analysis (FEA) examples are provided, demonstrating the utility of the new model and its implementation in assessing the effects of viscoplastic behaviors in shape memory alloys.     

On the thermomechanical modeling of shape memory alloys

In this work, a general inelastic framework for the derivation of general three-dimensional thermomechanical constitutive laws for materials undergoing phase transformations is proposed. The proposed framework is based on the generalized plasticity theory and on some basic elements from the theory of continuum damage mechanics. More specifically, a new elaborate formulation of generalized plasticity theory capable of accommodating the multiple and interacting loading mechanisms, which occur during the phase transformations, is developed. Furthermore, the stiffness variations occurring during phase transformations are taken into account by the proposed framework. For this purpose, the free energy is decomposed into elastic and inelastic parts, not in a conventional way, but in one which resembles the elastic-damage cases. Also, a rate-dependent version of the theory is provided. The concepts presented are applied for the derivation of a three-dimensional thermomechanical constitutive model for Shape Memory Alloy materials. Numerical simulations to show qualitatively the ability of the model to capture the behavior of the shape memory alloys are also presented. Furthermore, the model has been fitted to actual experimental results from the literature.     

Optimization of hysteretic characteristics of damping devices based on pseudoelastic shape memory alloys

In order to develop a fundamental understanding and the feasibility of SMA devices for passive vibration control, an undamped SDOF system with a pseudoelastic SMA restoring force is investigated to find the basic relationship between the shape of the hysteresis loop of SMA elements and their performance as a damping device. The dynamic characteristics of the device are evaluated by the steady-state response at the resonance point in order to focus on the damping effect. Dynamic analysis utilizing the equivalent linearization approach results in two major findings that, to the best of the authors’ knowledge, have not yet been reported in the literature. These results which characterize the unique behavior of the SMA hysteresis include: (a) for a given excitation amplitude, the “scale” of the hysteresis loop, which is a measure of displacement and restoring force, needs to be adjusted so that the response sweeps the maximum loop but does not exceed it; (b) the ratio of the area confined within the hysteresis loop to the area of a corresponding envelope of triangular shape should be as large as possible. The results of this study would be quite useful not only as a guideline for the design of actual SMA devices, but also as a basis for the development of new autoadaptive materials in future.     

Three-dimensional constitutive model for shape memory alloys based on microplane model

A new model for the behavior of polycrystalline shape memory alloys (SMA), based on a statically constrained microplane theory, is proposed. The new model can predict three-dimensional response by superposing the effects of inelastic deformations computed on several planes of different orientation, thus reproducing closely the actual physical behavior of the material. Due to the structure of the microplane algorithm, only a one-dimensional constitutive law is necessary on each plane. In this paper, a simple constitutive law and a robust kinetic expression are used as the local constitutive law on the microplane level. The results for SMA response on the macroscale are promising: simple one-dimensional response is easily reproduced, as are more complex features such as stress-strain subloops and tension-compression asymmetry. A key feature of the new model is its ability to accurately represent the deviation from normality exhibited by SMAs under nonproportional loading paths.     

形状记忆合金热力学行为的模拟

基于塑性流动法则和马氏体相变动力学 ,引入马氏体体积分数和相变应力间的关系 ,对形状记忆合金的热力学行为进行了模拟 ,算例表明本文提出的形状记忆合金本构模型与实验结果比较吻合 ,且实施起来简单易行 ;最后还用该本构模型进行了有限元分析     

SMA纤维复合材料梁振动半主动控制

分析了一类形状记忆合金(SMA)纤维混杂层合粱用于振动控制的动力学模型和作用机理．采用多胞模型、形状记忆合金一维本构关系分析方法，同时考虑横向剪切的影响，建立了层合梁的数学模型．半主动控制是通过改变受控结构的参数来减小结构振动的响应．根据开关控制原理确定可变刚度系统的控制律，进行SMA纤维混杂层合粱的半主动控制的数值仿真．结果表明，将半主动控制应用于梁的振动控制是一种有效的方法．     

Constitutive modeling of shape memory alloy wire with non-local rate kinetics

A constitutive modeling approach for shape memory alloy (SMA) wire by taking into account the microstructural phase inhomogeneity and the associated solid–solid phase transformation kinetics is reported in this paper. The approach is applicable to general thermomechanical loading. Characterization of various scales in the non-local rate sensitive kinetics is the main focus of this paper. Design of SMA materials and actuators not only involve an optimal exploitation of the hysteresis loops during loading–unloading, but also accounts for fatigue and training cycle identifications. For a successful design of SMA integrated actuator systems, it is essential to include the microstructural inhomogeneity effects and the loading rate dependence of the martensitic evolution, since these factors play predominant role in fatigue. In the proposed formulation, the evolution of new phase is assumed according to Weibull distribution. Fourier transformation and finite difference methods are applied to arrive at the analytical form of two important scaling parameters. The ratio of these scaling parameters is of the order of 10⁶ for stress-free temperature-induced transformation and 10⁴ for stress-induced transformation. These scaling parameters are used in order to study the effect of microstructural variation on the thermo-mechanical force and interface driving force. It is observed that the interface driving force is significant during the evolution. Increase in the slopes of the transformation start and end regions in the stress–strain hysteresis loop is observed for mechanical loading with higher rates.      

A NEW MODEL OF SHAPE MEMORY ALLOYS

A new constitutive model of shape memory alloys ( SMAs) based on Tanaka ' s martensite fraction exponential expression is produced. This new model can present recoverable shape memory strain during different phase transformation, and reflect the action of martensite reorientation . Also it can overcome the defect of Tanaka ' s Model when the SMAs ' microstructure is fully martensite . The model is very simple and suitable for using , and the correct behavior of the model is proved by test.     

Computational modeling of size-dependent superelasticity of shape memory alloys

We propose a nonlocal continuum model to describe the size-dependent superelastic responses observed in recent experiments of shape memory alloys. The modeling approach extends a superelasticity formulation based on the martensitic volume fraction, and combines it with gradient plasticity theories. Size effects are incorporated through two internal length scales, an energetic length scale and a dissipative length scale, which correspond to the gradient terms in the free energy and the dissipation, respectively. We also propose a computational framework based on a variational formulation to solve the coupled governing equations resulting from the nonlocal superelastic model. Within this framework, a robust and scalable algorithm is implemented for large scale three-dimensional problems. A numerical study of the grain boundary constraint effect shows that the model is able to capture the size-dependent stress hysteresis and strain hardening during the loading and unloading cycles in polycrystalline SMAs.     

A non-local implicit gradient-enhanced model for unstable behaviors of pseudoelastic shape memory alloys in tensile loading

In this paper, a gradient-enhanced 3-D phenomenological model for shape memory alloys using the non-local theory is developed based on a 1-D constitutive model. The method utilizes a non-local field variable in its constitutive framework with an implicit gradient formulation in order to achieve results independent of the finite element discretization. An efficient numerical approach to implement the non-local gradient-enhanced model in finite element codes is proposed. The model is used to simulate stress drop at the onset of transformation, and its performance is evaluated using different experimental data. The potential of the presented numerical approach for behavior of shape memory alloys in eliminating mesh-dependent simulations is validated by conducting various localization problems. The numerical results show that the developed model can simulate the observed unstable behaviors such as stress drop and deviation of local strain from global strain during nucleation and propagation of martensitic phase.     

Study on cyclic deformation and fatigue of thermal and magnetic shape memory alloys

形状记忆合金(包括热致和磁致形状记忆合金)由于其特有的超弹性和形状记忆效应, 一直以来受到学者和工程界人士广泛关注, 且已有诸多成功的工程应用案例.为了进一步拓展该类合金的工程应用范围, 对其热--力和磁--力耦合循环变形和疲劳失效行为的宏微观实验观察和理论模型研究成果进行了综述. 总结了NiTi和NiTiX两类合金材料的温度诱发(即热致)的热--力耦合循环变形和疲劳失效行为研究的最新成果; 对以NiMnGa合金为代表的磁场诱发(即磁致)的磁--力耦合循环变形和疲劳失效行为的研究现状进行了评述; 提出并预测了未来的研究方向及发展趋势.     

Three-dimensional phenomenological thermodynamic model of pseudoelasticity of shape memory alloys at finite strains

The familiar small strain thermodynamic 3D theory of isotropic pseudoelasticity proposed by Raniecki and Lexcellent is generalized to account for geometrical effects. The Mandel concept of mobile isoclinic, natural reference configurations is used in order to accomplish multiplicative decomposition of total deformation gradient into elastic and phase transformation (p.t.) parts, and resulting from it the additive decomposition of Eulerian strain rate tensor. The hypoelastic rate relations of elasticity involving elastic strain rate are derived consistent with hyperelastic relations resulting from free energy potential. It is shown that use of Jaumann corotational rate of stress tensor in rate constitutive equations formulation proves to be convenient. The formal equation for p.t. strain rate , describing p.t. deformation effects is proposed, based on experimental evidence. Phase transformation kinetics relations are presented in objective form. The field, coupled problem of thermomechanics is specified in rate weak form (rate principle of virtual work, and rate principle of heat transport). It is shown how information on the material behavior and motion inseparably enters the rate virtual work principle through the familiar bridging equation involving Eulerian rate of nominal stress tensor.

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A micromechanical continuum model for the tensile behavior of shape memory metal nanowires

We have previously discovered a novel shape memory effect and pseudoelastic behavior in single-crystalline face-centered-cubic metal (Cu, Ni, and Au) nanowires. Under tensile loading and unloading, these wires can undergo recoverable elongations of up to 50%, well beyond the recoverable strains of 5-8% typical for most bulk shape memory alloys. This phenomenon only exists at the nanoscale and is associated with a reversible lattice reorientation driven by the high surface-stress-induced internal stresses. We present here a micromechanical continuum model for the unique tensile behavior of these nanowires. Based on the first law of thermodynamics, this model decomposes the lattice reorientation process into two parts: a reversible, smooth transition between a series of phase-equilibrium states and a superimposed irreversible, dissipative twin boundary propagation process. The reversible part is modeled within the framework of strain energy functions with multiple local minima. The irreversible, dissipative nature of the twin boundary propagation is due to the ruggedness of strain energy curves associated with dislocation nucleation, glide, and annihilation. The model captures the major characteristics of the unique behavior due to lattice reorientation and accounts for the size and temperature effects, yielding results that are in excellent agreement with the results of molecular dynamics simulations.     

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source

In Part II of this two-part work, we apply an optimal linear control technique to suppress chaotic behavior in a SMA oscillator, driven by a DC motor with limited power supply (Nonideal sources). Nonideal sources of vibrations of structures are those whose characteristics are coupled to the motion of the structure. Thus, in this case, an additional equation of motion is written, related to the motor rotation. Special attention is focused into the resonance region, when the nonideal excitation frequency is near the natural frequency of the SMA oscillator. Numerical results are presented, which show the efficiency of the method in resonance region. The ideal case, when we do not consider the interaction between an energy source and structure was considered in Part I of this paper.