Distributed-element Preisach model for hysteresis of shape memory alloys

Song, Chang Hun; Brandon, J. A.; Featherston, Carol Ann

doi:10.1243/0954406011524045

Cited by 5 publications

(5 citation statements)

References 22 publications

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“…These characteristic parameters of the models are directly connected with the macroscopic experimental facts. Typically, they are determined by means of simple interpolation of the limited experimental data or leastsquares fitting of a measured major loop or multiple loops for a pre-selected load (Torrie & Vajida, 1994;Song et al, 2001;Ktena et al, 2001). Such identification strategies are strongly sensitive to measurement errors.…”

Section: Discussionmentioning

confidence: 99%

Hysteresis Behaviour and Modeling of SMA Actuators

Luo¹,

Liao²,

Abel³

et al. 2010

Shape Memory Alloys

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Section: Discussionmentioning

confidence: 99%

Hysteresis Behaviour and Modeling of SMA Actuators

Luo¹,

Liao²,

Abel³

et al. 2010

Shape Memory Alloys

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“…We assume that there exists a classical Preisach model that satisfies the origin-crossing property of the mem-models, i.e., the input and output become zero simultaneously (e.g., Song et al (2001)). It will be shown that this subset of the classical Preisach model can be transformed into an equivalent time-invariant memcapacitive system model.…”

Section: Subset Of Classical Preisach Modelsmentioning

confidence: 99%

Connecting mem-models with classical theories

et al. 2021

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A family of mem-models, including the mem-dashpots, mem-springs, and most recently, mem-inerters, is emerging as a new and powerful way of capturing complex nonlinear behaviors of materials and systems under various types of dynamic loads involving different frequency, amplitude, and loading histories (e.g., hysteresis). Under the framework of nonlinear state-space representation and hybrid dynamical systems, mem-springs may be formulated to effectively represent an inherent degradation of material state. It is shown in this study, for the first time, how the absement (time integral of strain /displacement), a signature state variable for a mem-spring, can be connected with the damage variable, a key quantity in continuum damage mechanics (CDM). The generalized momentum (time integral of stress), on the other hand, is shown to be efficient in modeling strain ratcheting via the concept of mem-dashpot. It is also shown in this study, for the first time, how two formulations of the memcapacitive system models (for mem-springs) are special cases of the Preisach model.

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“…But a more detailed view (see Fig. 10) of the bifurcations for C ∈ [2,3] shows, that the two diagrams are slightly different. This is due to the fact, that Comparison of the bifurcation diagrams for the piecewise-smooth system with N = 20 000 ( ) spins and the system in its thermodynamic limit ( ).…”

Section: B Many-spin Dynamicsmentioning

confidence: 99%

“…This work is motivated by problems, which arise if a dynamical system contains a hysteretic subsystem. Hysteresis phenomena in general can be found in many different research fields, such as magnetic effects at oxide interfaces [1], shape memory alloys [2], ultrathin singlelayer films [3], organic ferroelectrics [4], soft porous crystals [5], atomtronics [6] and metallic nanoparticles [7]. An overview over the field of hysteresis can be found in [8].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields

2020

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In general we are interested in dynamical systems coupled to complex hysteresis. Therefore as a first step we did some investigation on the dynamics of a periodically driven damped harmonic oscillator coupled to independent Ising spins with a local quenched disorder at zero temperature in the past. Although such a system does not produce hysteresis, we showed how to characterize the dynamics of such a piecewise-smooth system, specially in case of a large number of spins [P. Zech, A. Otto, and G. Radons, Phys. Rev. E101,042217 (2020)]. In this paper we want to extend our model to spins dimers, thus spins with pairwise interaction. We will show in which cases two interacting spins can show elementary hysteresis and we will give a connection to the Preisach Model (PM), when superpose a infinite number of spin-pairs in the thermodynamic limit. We will see, that this will lead us to a dynamical system with an additional hysteretic force in form of a play operator. By using methods from general chaos theory, piecewise-smooth system theory and statistics we will investigate the chaotic behavior of the dynamical system for a few spins and also in case of larger number of spins by calculating bifurcation diagrams, fractal dimensions and self-averaging properties. In doing so we show, how the dynamical properties of the piecewise-smooth system for a large number of spins differs from the system in its thermodynamic limit.

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Distributed-element Preisach model for hysteresis of shape memory alloys

Cited by 5 publications

References 22 publications

Hysteresis Behaviour and Modeling of SMA Actuators

Hysteresis Behaviour and Modeling of SMA Actuators

Connecting mem-models with classical theories

Dynamics of a driven harmonic oscillator coupled to independent Ising spins in random fields

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