Development of a frequency-dependent constitutive model for hysteresis of shape memory alloys

Shakiba, Saeid; Yousefi‐Koma, Aghil; Ayati, Moosa

doi:10.1177/1464420720949583

Cited by 3 publications

(3 citation statements)

References 60 publications

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“…Meanwhile, when the variable stiffness instruction changes from increase to decrease or from decrease to increase the stiffness change of the SMA-TE has a certain hysteresis, where the hysteresis time of increasing stiffness and decreasing stiffness is about 1.8 s and 2.3 s, respectively. This specific hysteresis has a significant correlation with the phase change hysteresis of SMA [47] and the limited power of the temperature control devices in SMA-TE. The hysteresis effect of variable stiffness when the SMA-TE tracks square waves with different frequencies are shown in figure 12(b).…”

Section: Resultsmentioning

confidence: 92%

Design and experiment of a SMA-based continuous-stiffness-adjustment torsional elastic component for variable stiffness actuators

Xiong¹,

Sun²,

Jia³

et al. 2021

Smart Mater. Struct.

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The variable stiffness actuator (VSA) is widely applied in robotics and human-robot interactions, generating controllable torque with sufficient compliance to ensure safety and robustness. At present, typical VSA design usually adopted pure mechanical structures that integrated an additional motor for stiffness adjustment, making it hard to meet the demand of lightweight joint actuation due to large actuator size and weight. As a new functional material, shape memory alloy (SMA) shows the prospect of lightweight actuation due to its high power-to-weight ratio. In this paper, a compact SMA-based torsional elastic component (SMA-TE) for the VSA is proposed. The SMA-TE with torsional stiffness is implemented by the confrontational arrangement of paired spiral SMA springs. The ceramic heating plate and semiconductor refrigeration plate are installed in the elastic component shell, and the thermally conductive medium is filled between the internal gap. The torsional stiffness of the SMA-TE can be continuously adjusted via a feed-forward cascade controller. Repeated experimental results show that the SMA-TE can precisely maintain constant stiffness and continuously adjust its stiffness between 2.6 Nm rad −1 and 6.8 Nm rad −1 when performing precise square wave stiffness tracking under variable frequencies.

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Section: Resultsmentioning

confidence: 92%

Design and experiment of a SMA-based continuous-stiffness-adjustment torsional elastic component for variable stiffness actuators

Xiong¹,

Sun²,

Jia³

et al. 2021

Smart Mater. Struct.

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“…Zaki and Moumni [34,35] developed the Lagoudas model by introducing the martensite orientation strain, which enables to describe the reorientation and plastic deformation [36] of microstructures in SMAs. On the basis of Lagoudas model, Chemisky, Lagoudas, Hartl and Zhang et al have performed several analyses on the tensioncompression asymmetry [37,38], finite strain [39,40], large deformation [41], non-proportional loading [39,42], load rate influence [43][44][45], thermomechanical coupling [46][47][48][49], cyclic loading [32,50,51] and plastic fatigue [52][53][54][55][56][57] of SMAs, which have extended the assessment of the feasibility of this model.…”

Section: Introductionmentioning

confidence: 99%

A polynomial constitutive model of shape memory alloys based on kinematic hardening

Yang

Zhang

Scarpa

et al. 2023

Smart Mater. Struct.

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This paper describes the derivation of a phenomenological model for shape memory alloys under the framework of classical plasticity theory. The proposed model combines the Souza constitutive approach with kinematic hardening; the model requires solving only one nonlinear equation rather than several nonlinear ones, therefore improving the computational efficiency and convergence. Moreover, the original Souza model is improved by adding an odd polynomial function to describe the phase transformation of the shape memory alloys, making it possible to use a lower number of parameters for the inverse identification of the constitutive properties of SMAs from simple tensile tests. A tangent stiffness formulation is also derived to simulate the variation of the elastic modulus during the phase transformation. The tangent stiffness formulation proposed here extends the one used in classical plasticity theory and improves the convergence of the proposed model. The reliability and fidelity of the model described in this work are benchmarked against experimental data and other models. The numerical results show that the proposed phenomenological approach can describe well the pseudoelasticity and shape memory effect of shape memory alloys. The formulation described in this paper can be readily generalized to finite strains and other formulations based on existing works related to classical plasticity theory.

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“…16 Recently, many efforts have been done to boost constitutive models, but combining constitutive and phenomenological models was less discussed. [17][18][19][20] The main goal of this research is a feasibility study of using PI model for boosting constitutive models. LR model is selected as a constitutive model due to its simplicity and ability in transformation phases of martensite and austenite.…”

Section: Introductionmentioning

confidence: 99%

Development of Hybrid Prandtl–Ishlinskii and Constitutive Models for Hysteresis of Shape-Memory-Alloy-Driven Actuators

2021

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SUMMARY Prandtl–Ishlinskii (PI) model has an excellent compromise to characterize an asymmetric saturated hysteresis behavior of shape-memory-alloy (SMA)-driven systems, but it cannot consider thermomechanical relations between components of SMA-driven systems. On the other hand, constitutive models are composed of these relations, but their precision needs to be improved. In this paper, PI model is proposed to boost constitutive models in two cases. In the first case, PI model is used to characterize martensite volume fraction (MVF) called hybrid model. In the second case, the model is applied as a regulator in the output of a constitutive model called PI-based output (PIO) regulator. Due to simplicity and ability of Liang–Rogers (LR) model in transformation phases, it is considered as an MVF in the original constitutive model. The performance of both proposed models is compared with the original LR-based constitutive model. Unknown parameters of all three models are identified using genetic algorithm in MATLAB Toolbox. The performance of the three models is investigated at three different frequencies of \[\frac{{2\pi }}{8}\] , \[\frac{{2\pi }}{{15}}\] , and \[\frac{{2\pi }}{{30}}\] Hz because the excitation frequency changes the hysteresis behavior. Results show that the proposed hybrid model keeps the precision of the original constitutive model at different frequencies. In addition, the proposed PIO model shows the best performance to predict hysteresis behavior at different frequencies.

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Development of a frequency-dependent constitutive model for hysteresis of shape memory alloys

Cited by 3 publications

References 60 publications

Design and experiment of a SMA-based continuous-stiffness-adjustment torsional elastic component for variable stiffness actuators

Design and experiment of a SMA-based continuous-stiffness-adjustment torsional elastic component for variable stiffness actuators

A polynomial constitutive model of shape memory alloys based on kinematic hardening

Development of Hybrid Prandtl–Ishlinskii and Constitutive Models for Hysteresis of Shape-Memory-Alloy-Driven Actuators

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