Modeling of Shape Memory Alloys Based on Microplane Theory

Kadkhodaei, Mahmoud; Salimi, M.; Rajapakse, R. K. N. D.; Mahzoon, Mojtaba

doi:10.1177/1045389x07077837

Cited by 27 publications

(23 citation statements)

References 23 publications

(39 reference statements)

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“…Kadkhodaei et al (2007a) presented a one-dimensional coupled thermo-mechanical model of SMAs under non-quasistatic loading by defining a Helmholtz free energy function consisting of strain energy, thermal energy, and the energy of phase transformation. Kadkhodaei et al (2007bKadkhodaei et al ( , 2008 presented a three-dimensional microplane constitutive model which included the statically constrained formulation with volumetric-deviatoric split for the shape memory alloys. They described the shear stress within each microplane by the component of resultant shear on the plane and then used onedimensional stress-strain laws by considering proper adjustments between the macroscopic and the microscopic quantities.…”

Section: Constitutive Models For Smasmentioning

confidence: 99%

A review on shape memory alloys with applications to morphing aircraft

Barbarino

Flores

Ajaj

et al. 2014

Smart Mater. Struct.

309

176

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Shape memory alloys (SMAs) are a unique class of metallic materials with the ability to recover their original shape at certain characteristic temperatures (shape memory effect), even under high applied loads and large inelastic deformations, or to undergo large strains without plastic deformation or failure (super-elasticity). In this review, we describe the main features of SMAs, their constitutive models and their properties. We also review the fatigue behavior of SMAs and some methods adopted to remove or reduce its undesirable effects. SMAs have been used in a wide variety of applications in different fields. In this review, we focus on the use of shape memory alloys in the context of morphing aircraft, with particular emphasis on variable twist and camber, and also on actuation bandwidth and reduction of power consumption. These applications prove particularly challenging because novel configurations are adopted to maximize integration and effectiveness of SMAs, which play the role of an actuator (using the shape memory effect), often combined with structural, load-carrying capabilities. Iterative and multi-disciplinary modeling is therefore necessary due to the fluid-structure interaction combined with the nonlinear behavior of SMAs.

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Section: Constitutive Models For Smasmentioning

confidence: 99%

A review on shape memory alloys with applications to morphing aircraft

Barbarino

Flores

Ajaj

et al. 2014

Smart Mater. Struct.

309

176

View full text Add to dashboard Cite

show abstract

“…Accordingly, in this article, the static constraint formulation is utilized for the evolution of SMA constitutive relations. In this formulation, three main steps should be followed: first, the projection of stress tensor is found on each microplane as normal and shear stress vectors; then, a 1D constitutive relation is defined for each normal and shear component, and finally a homogenization process is utilized to generalize the 1D model to 3D one (Kadkhodaei et al, 2007a(Kadkhodaei et al, , 2007bMehrabi et al, 2014aMehrabi et al, , 2014bMehrabi et al, , 2014cMehrabi et al, , 2014dMehrabi and Kadkhodaei, 2013). Figure 1 shows the projected stress tensor on a generic microplane as shear and normal components.…”

Section: Constitutive Modelingmentioning

confidence: 99%

“…To generalize the 1D constitutive relations to 3D ones, the principle of complementary virtual work is utilized which yields (Kadkhodaei et al, 2007a(Kadkhodaei et al, , 2007b 4p…”

Section: Constitutive Modelingmentioning

confidence: 99%

“…The idea of utilizing microplane theory for this purpose was first proposed by Brocca et al (2002) and has been further developed by Kadkhodaei et al (2007aKadkhodaei et al ( , 2007b and Mehrabi et al (2013). This constitutive modeling approach has been shown to be thermodynamically consistent (Mehrabi et al, 2014c) and capable of modeling nonproportional loading paths (Kadkhodaei et al, 2007a(Kadkhodaei et al, , 2007bMehrabi et al, 2014cMehrabi et al, , 2014d. Mehrabi et al (2014b) used the microplane theory to develop a constitutive model for tension-torsion coupling and tensioncompression asymmetry in NiTi SMAs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Effects of asymmetric material response on the mechanical behavior of porous shape memory alloys

Karamooz-Ravari

Kadkhodaei

Ghaei

2015

Journal of Intelligent Material Systems and Structures

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The demand for lightweight devices attracts attention toward porous materials. Among them, porous shape memory alloys are of interest due to superior mechanical and biological properties. High cost related to fabrication and characterization of such materials makes it necessary to model their mechanical properties before fabrication. Experimental observations of dense shape memory alloys show tension-compression asymmetry which in turn can affect the mechanical response of porous ones. In this article, the effects of this asymmetric response on the mechanical response of porous shape memory alloys are investigated by comparing three models: asymmetric, symmetric with tensile, and symmetric with compressive material parameters. To this end, a constitutive model considering asymmetric material response is proposed based on microplane theory. Then, this model is used to simulate the stress-strain response of porous shape memory alloys. The results are compared with available experimental and numerical data, and a good agreement is observed. It is concluded that in comparison with the asymmetric model, the symmetric model with tensile material parameters under-predicts the stress level while the model with compressive one over-predicts the stress level. In addition, the effects of porosity on the asymmetric response as well as hysteresis of stress-strain curve in tension and compression are assessed.

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“…In the microplane model, all material parameters can be determined from uniaxial tension tests at different temperatures. The microplane model considers 1-D equations for some directions on arbitrary plane and is extended to 3-D model using homogenization process [54]. Mehrabi et al [40,41,55] developed this idea within the framework of thermo-dynamics and proved the capability of the proposed model under multiaxial loadings.…”

Section: Formulation Characteristics Limitationmentioning

confidence: 99%

Modeling and Simulation of Shape Memory Alloys using Microplane Model

Mehrabi¹

2015

Superalloys

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In this chapter, a three-dimensional phenomenological constitutive model for the simulation of shape memory alloys is introduced. The proposed macromechanical model is based on microplane theory. Microplane approach is chosen to have limited material parameters in that all of those are measurable by simple tests. User material subroutine is developed to implement the proposed model in a commercial finite element package. NiTi hollow tube specimens are under various loading conditions in order to experimentally study the superelastic response of shape memory alloys. Comparing experimental data with numerical results in simple tension and pure torsion as well as proportional and nonproportional tension-torsion loadings demonstrates the capability of proposed model in constitutive modeling of shape memory alloys.

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Modeling of Shape Memory Alloys Based on Microplane Theory

Cited by 27 publications

References 23 publications

A review on shape memory alloys with applications to morphing aircraft

A review on shape memory alloys with applications to morphing aircraft

Effects of asymmetric material response on the mechanical behavior of porous shape memory alloys

Modeling and Simulation of Shape Memory Alloys using Microplane Model

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