A model for shape memory alloy beams accounting for tensile compressive asymmetry

Việt, Nguyễn Văn; Zaki, Wael; Moumni, Ziad

doi:10.1177/1045389x19873407

Cited by 18 publications

(11 citation statements)

References 37 publications

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“…An equivalent reduction is performed also in other investigations of the pseudoelastic effect in SMA beam under bending, e.g. in Mirzaeifar et al (2012), Ostadrahimi et al (2015), Viet et al (2018Viet et al ( , 2019. Obviously, a 3D strain field arises in the beam so that the beam cross section can change his shape by expanding in the compressed zone and contracting in the tensile one, due also to the martensitic transformation and reorientation.…”

Section: Introductionmentioning

confidence: 99%

“…Viet et al (2018) worked out an analytical solution for the problem of SMA cantilever beams subjected to tip load throughout a full loading-unloading cycle. The analysis was based on Timoshenko beam theory and was later extended to account for tensile-compressive asymmetry in SMA response (Viet et al, 2019). The asymmetric tension-compression behavior of the SMA has been observed and modelled under direct bending by Rejzner et al (2002), Fahimi et al, (2019), and Viet et al (2019).…”

Section: Introductionmentioning

confidence: 99%

“…The analysis was based on Timoshenko beam theory and was later extended to account for tensile–compressive asymmetry in SMA response (Viet et al, 2019). The asymmetric tension-compression behavior of the SMA has been observed and modeled under direct bending by Rejzner et al (2002), Fahimi et al (2019), and Viet et al (2019).…”

Section: Introductionmentioning

confidence: 99%

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Analytical modeling of the shape memory effect in SMA beams with rectangular cross section under reversed pure bending

Radi

2021

Journal of Intelligent Material Systems and Structures

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An analytical model is developed for a prismatic SMA beam with rectangular cross section subjected to alternating bending at temperature below the austenitic transformations. The loading path consists in a loading-unloading cycle under bending and then under reversed bending. Two opposite martensitic variants take place, whose volume fractions evolve linearly with the axial stress. Different Young’s moduli are taken for the austenitic and martensitic phases. As the bending moment is increased, the martensitic transformation starts from the top and bottom and then it extends inwards. If the maximum applied bending moment is large enough, then the complete Martensitic transformation takes place at the upper and lower parts of the cross section. During unloading and the following reversed bending, reorientation of the Martensite variant into the opposite one takes place starting from the boundary between the fully martensitic region and the intermediate transforming region. Special attention is devoted to calculate analytically the axial stress and Martensite variant distributions within the cross section at each stage of the process. A closed form moment-curvature relation is provided for loading and elastic unloading and in integral form for the rest of the process. The approach is then validated by comparison with analytical results available in the literature.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analytical modeling of the shape memory effect in SMA beams with rectangular cross section under reversed pure bending

Radi

2021

Journal of Intelligent Material Systems and Structures

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“…An exact solution for deflection of a PE cantilever beam loaded at the tip is derived in and bending stress of PE beams considering asymmetric response in tensioncompression accurately calculated [4,30]. Several theoretical works were also studied for bending of laminated composite PE beams considering the constitutive equations with different material behavior in tension and compression [31][32][33]. More recently, assuming the effect of tension-compression asymmetry, a constitutive model to predict the response of PE and SME beams under a three-point bending test and pure bending is proposed in [34,35], respectively.…”

Section: Introductionmentioning

confidence: 99%

Effect of Tension-Compression Asymmetry Response on the Bending of Prismatic Martensitic SMA Beams: Analytical and Experimental Study

2021

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This paper aims to analytically derive bending equations, as well as semi-analytically predict the deflection of prismatic SMA beams in the martensite phase. To this end, we are required to employ a simplified one-dimensional parametric model considering asymmetric response in tension and compression for martensitic beams. The model takes into account the different material parameters in martensite twined and detwinned phases as well as elastic modulus depending on the progress of the detwinning process. In addition, the model considers the diverse slope of loading and unloading in martensite detwinned phases favored by tension and compression. To acquire general bending equations, we first solve the pure bending problem of a prismatic SMA beam. Three different phases are assumed in the unloading procedure and the effect of neutral fiber distance from the centerline is also considered during this stage. Then according to the pure bending solution and employing semi-analytical methods, general bending equations of an SMA beam are derived. Polynomial approximation functions are utilized to obtain the beam deflection–length relationship. To validate the attained analytical expressions, several three- and four-point bending tests were conducted for rectangular and circular SMA beams. Experimental data confirm the reasonable accuracy of the analytical results. This work may be envisaged to go deep enough in investigating the response of SMA beams under an arbitrary transverse loading and stress distribution during loading and unloading, as well as findings may be applicable to a good prediction of bending behavior.

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“…For example, Paiva et al [ 23 ] proposed a constitutive model considering both the tensile-compressive asymmetry and the plastic strains that occur in the thermomechanical processing of SMAs. Zaki et al [ 27 ] extended their original Zaki-Moumni model to account for tensile-compressive asymmetry over a wide temperature range, and they developed the asymmetry model to analyze SMA cantilever beams subjected to tip loads [ 32 ]. Poorasadion et al [ 28 ] further developed the original Brinson model [ 33 ] into a novel tensile-compressive asymmetry model for SMAs and successfully applied their model in a two-dimensional (2D) Euler–Bernoulli beam to predict its behavior through ABAQUS/Standard.…”

Section: Introductionmentioning

confidence: 99%

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

Wang¹,

Feng²

2020

Materials

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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.

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A model for shape memory alloy beams accounting for tensile compressive asymmetry

Cited by 18 publications

References 37 publications

Analytical modeling of the shape memory effect in SMA beams with rectangular cross section under reversed pure bending

Analytical modeling of the shape memory effect in SMA beams with rectangular cross section under reversed pure bending

Effect of Tension-Compression Asymmetry Response on the Bending of Prismatic Martensitic SMA Beams: Analytical and Experimental Study

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

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