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Journal ArticleDOI

Thermomechanical modeling of hysteresis in SMAs using the dissipationless reference response

01 Feb 2007-Smart Materials and Structures (IOP Publishing)-Vol. 16, Iss: 1
TL;DR: In this article, the authors introduce a dissipationless band to model inner hysteresis loops of response of shape memory alloys (SMAs), which is critical to the modeling of hysteretic behavior.
Abstract: The main objective of this study is to introduce a 'dissipationless band' to model inner hysteresis loops of response of shape memory alloys (SMAs). Dissipation that occurs when the material undergoes phase transformation is critical to the modeling of hysteretic behavior. Emphasis is placed on modeling such dissipation in the proposed methodology. Using a dissipationless virtual response of the material, a logical framework for the onset transformation under reversal of cycles is presented. Characteristics of the material transformation with reference to a dissipationless band model the true inner hysteresis loops. It is identified that this dissipationless band occurs due to the difference between the starting states of forward and reverse transformations. The construction of the generalized driving force for the transformation along with the rate of dissipation function is formulated. A numerical example is presented to highlight the qualitative prediction capabilities of the model. The example involves simulating hysteresis loops for different kinds of partial and complete loading cycles in the pseudoelastic state of the material. The predictions show that the proposed one-dimensional model is capable of representing the actual hysteresis behavior of the stabilized shape memory alloys, by effectively incorporating the dissipation effects due to the loading history.
Citations
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01 Jan 2009
TL;DR: An overview of shape memory alloys (SMA) can be found in this article, where the authors provide a brief introduction to the SMA behavior and the underlying martensitic transformation.
Abstract: Shape memory alloys (SMA) have been known for over five decades and modeling of their response has attracted much attention over the last two decades. Recent increase in the range of applications of these materials has lead to an increased focus on modeling their thermomechanical response. Various approaches ranging from macroscopic phenomenology to microscopic lattice based methods are being pursued to model SMA behavior. Models ranging from simple tools as design aids to complex thermodynamic based models to understand the characteristic martensitic transformation responsible for the shape memory and superelastic response exist. In this report, following a brief introduction to the SMA behavior and the underlying martensitic transformation, an overview of models for SMAs is provided. This is aimed at providing an understanding of the state of the art and also to identify possible future directions. In this review, models are classified both on the basis of the approach and the level (scale) of continuum they address. General methodology of each type of approach is presented briefly followed by a review of the models that fall under that category. Certain liberties are taken in classifying these models to facilitate understanding and thus the present classification is by no means either unique or completely rigorous. Also, while an attempt is made to cover most of the approaches, review of all the models that exist in literature is practically impossible. Finally, summarizing the literature on models for SMAs, several interesting and relevant problems are identified for possible future developments.

65 citations


Additional excerpts

  • ...…Force Varyi ng Dissipation potential Popov and Lagoudas (2007) Helmholtz (notional) (ε , ξ , T) { ξs, ξT } Independent (Linear) Fixed Yield function Kishore Kumar et al (2007) Helmholtz (notional) (ε , ξ , T) { ξs } Driving force Varyi ng Dissipation potential 4.2.2 Mechanistic decomposition…...

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Journal ArticleDOI
TL;DR: In this article, the authors present experimental results of large complex loading and unloading torsional cycles which were conducted on superelastic SMA wires, under isothermal conditions with the purpose of elucidating the torsion internal loop response.

23 citations

Journal ArticleDOI
TL;DR: In this article, a memory parameter based on the concept of thermodynamic dissipation function is introduced to capture the transformation process under fluctuating loads. And the proposed model is compared with experimentally observed results for typical NiTi based SMAs for arbitrary thermomechanical loading.

17 citations

01 Jan 2009
TL;DR: In this article, a thermodynamically consistent three species (austenite, plus-martensite and minus-martenite) model for shape memory alloys (SMA) is proposed.
Abstract: A thermodynamically consistent three species (austenite, plus-martensite & minus-martensite) model for shape memory alloys (SMA) is proposed The uniaxial model proposed has been formulated with capabilities of simulating the characteristic response under general thermo-mechanical loading conditions It is shown that a minimal set of model variables, essentially, the volume fractions of the three species, describing the one dimensional state of the polycrystal SMA, is enough to capture its characteristic features including the pseudoelastic and the shape memory effects Primarily, two back stresses are defined within a dissipative setting - one to take care of polycrystalline nature of SMA and the other for the moving interfaces of the species within the sub grains The connection between the physical response of the material and the choice of the material parameters is illustrated using different conditions of the material and of the loading Simulation results exemplify the potential of the proposed model in predicting the characteristic behavior under loading paths such as isothermal, iso-stress and cyclic thermomechanical loading, that are typical in the applications

14 citations


Cites background or methods from "Thermomechanical modeling of hyster..."

  • ...Phenomenological models - plasticity or phase-diagram based (Bekker and Brinson, 1998; Lubliner and Auricchio, 1996; Lexcellent et al., 2000; Kumar et al., 2007), and, 3....

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  • ...Phenomenological models - plasticity or phase-diagram based (Bekker and Brinson, 1998; Lubliner and Auricchio, 1996; Lexcellent et al., 2000; Kumar et al., 2007), and, 3....

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  • ...In contrast Kumar et al. (2007), use the transformation surface notion to define the onset, while the finish of transformation is given by the underlying hardening law....

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Journal ArticleDOI
TL;DR: In this paper, the authors explored a link between a recently proposed macroscopic "smeared" approach and a microscopic/mesoscopic approach of sequential laminate type to model martensitic transformations.
Abstract: This paper explores a link between a recently proposed macroscopic “smeared” approach and a microscopic/mesoscopic approach of sequential laminate type to model martensitic transformations. In addition, a numerical simulation of the stress-induced martensitic transformation in a single crystal has been performed upon simplification to small deformations. One significant observation in the results of such a simulation is the counter-intuitive change of preferred martensitic plate even under proportional loading conditions. It remains to be seen if it is an artifact of the procedure adopted or the actual shift of active martensitic plate system. A further step toward modeling polycrystal behavior using homogenization with simple bounds has been attempted. Hysteresis results show that there is no clear demarcation of critical stress at which the transformation occurs. This may be critical to the functional fatigue behavior of shape memory materials.

11 citations

References
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Journal ArticleDOI
TL;DR: In this article, a one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka, and an internal variable ap-proach is used to deri...
Abstract: A one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka. An internal variable ap proach is used to deri...

1,444 citations

01 Jan 1993
TL;DR: In this paper, a one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka, where an internal variable approach is used to derive a comprehensive constitutive law for shape memory alloy materials from first principles without the assumption of constant material functions.
Abstract: A one-dimensional constitutive model for the thermomechanical behavior of shape memory alloys is developed based on previous work by Liang and Tanaka. An internal variable approach is used to derive a comprehensive constitutive law for shape memory alloy materials from first principles without the assumption of constant material functions. This constitutive law is of such a form that it is well suited to further practical engineering applications and calculations. A separation of the martensite fraction internal variable into temperature-induced and stress-induced parts is presented and justified which then allows the derived constitutive law to accurately represent both the pseudoelastic and shape memory effects at all temperatures. Several numerical examples are given which illustrate the ability of the constitutive law to capture the unique thermomechanical behavior of shape memory alloys due to their internal phase transformations with stress and temperature.

1,350 citations

Journal ArticleDOI
TL;DR: In this article, a complete, unified, one-dimensional constitutive model of shape memory materials is developed and presented in the form of a thermomechanical model for shape memory alloys.
Abstract: The use of the thermoelastic martensitic transformation and its reverse transformation has recently been proposed and demonstrated for several active control ap plications. However, the present constitutive models have lacked several important funda mental concepts that are essential for many of the proposed intelligent material system ap plications such as shape memory hybrid composites.A complete, unified, one-dimensional constitutive model of shape memory materials is developed and presented in this paper. The thermomechanical model formulation herein will investigate important material characteristics involved with the internal phase transformation of shape memory alloys. These characteristics include energy dissipation in the material that governs the damping behavior, stress-strain-temperature relations for pseudoelasticity, and the shape memory effect. Some numerical examples using the model are also presented.

1,222 citations

Journal ArticleDOI
TL;DR: In this paper, the shape memory effect due to martensitic transformation and reorientation of polycrystalline shape memory alloy (SMA) materials is modeled using a free energy function and a dissipation potential.

848 citations

Journal ArticleDOI
TL;DR: In this article, an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations was carried out, where attention was confined to infinitesimal deformations.
Abstract: An accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors, is carried out in this paper. For simplicity, attention is confined to infinitesimal deformations. The integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations. General rate-independent and rate-dependent behaviour, with plastic hardening or softening, associated or non-associated flow rules and nonlinear elastic response can be efficiently treated within the present framework. Isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding.

800 citations