Constitutive modeling of cyclic behavior in shape memory alloys

Mehrabi, Reza; Shirani, Milad; Kadkhodaei, Mahmoud; Elahinia, Mohammad

doi:10.1016/j.ijmecsci.2015.08.003

Cited by 23 publications

(7 citation statements)

References 32 publications

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“…The thermodynamic driving force is obtained by taking the partial derivative of the Gibbs free energy with respect to martensite volume fraction, which makes the physical meaning of thermodynamic driving force and critical driving force not very intuitive and easy to understand. Lagoudas and Brinson et al [30][31][32] also proposed several phase change hardening functions in exponential and trigonometric forms to better characterize the mechanical behaviors of the SMA phase transformation. Based on the temperature-stress phase diagram, Popov and Lagoudas [33] introduced the volume fraction of twinned martensite and detwinned and austenite to describe the transformation between different metal phases and complex mechanical behaviors in SMAs under various thermal and static loading paths.…”

Section: Introductionmentioning

confidence: 99%

“…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%

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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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Section: Introductionmentioning

confidence: 99%

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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“…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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“…Many researchers have used constitutive models to predict SMAs hysteresis. 29–31 Constitutive models include Tanaka, Liang-Rogers (LR) and Brinson. Although Tanaka and LR models describe the SMAs behavior in transformation phases and superelastic ranges, they cannot properly predict the behavior at low temperatures, which are not related to transformation temperatures.…”

Section: Introductionmentioning

confidence: 99%

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

Shakiba

Yousefi‐Koma

Ayati

2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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In this study, a constitutive model based on Liang-Rogers’s relations is developed to characterize the effect of the excitation frequency in the hysteresis of shape memory alloys. Shape memory alloys are good candidates as smart actuators because of their high strain and power density, although the complex hysteresis behavior barricades their usage. Although constitutive models are one of the most potent methods to predict the shape memory alloys behavior, they cannot consider the effect of excitation frequency in active applications. In this paper, the Liang-Rogers model is modified to consider this effect using a linear relation between the excitation frequency and martensite transformation temperatures. A shape memory alloy-driven actuator as a morphing wing is employed to characterize the frequency effect on shape memory alloy hysteresis. Experimental results show that the hysteresis is widened when the excitation frequency increases. The modeling results show that the original model significantly fails to predict the correct behavior when the frequency increases, whereas the proposed model can adequately handle the frequency effect on the behavior of the shape memory alloy-driven actuator.

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Constitutive modeling of cyclic behavior in shape memory alloys

Cited by 23 publications

References 32 publications

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

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

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

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