A model for an alloy with shape memory

Achenbach, M.

doi:10.1016/0749-6419(89)90023-5

Cited by 107 publications

(71 citation statements)

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“…In this approach, motivated by the shape memory alloy model developed by Müller, Achenbach, and Seelecke [1,2,23,27], a one-dimensional Helmholtz free energy potential consisting of two convex energy wells and a concave energy barrier (spinodal region) between the wells is proposed as a function of polarization. Depending on the applied electric field, dipoles jump from one energy well to another according to a competition between thermal activation and energy barriers.…”

Section: Supplementary Notesmentioning

confidence: 99%

A rate-dependent two-dimensional free energy model for ferroelectric single crystals

Seelecke

Kim

Ball

et al. 2005

Continuum Mech. Thermodyn.

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Abstract. The one-dimensional free energy model for ferroelectric materials developed by is generalized to two dimensions. The two-dimensional free energy potential proposed in this paper consists of four energy wells that correspond to four variants of the material. The wells are separated by four saddle points, representing the barriers for 90 • -switching processes, and a local maximum, across which 180 • -switching processes take place. The free energy potential is combined with evolution equations for the variant fractions based on the theory of thermally activated processes. The model is compared to recent measurements on BaTiO 3 single crystals by Burcsu et al. [8], and predicitions are made concerning the response to the application of in-plane multi-axial electric fields at various frequencies and loading directions. The kinetics of the 90 • -and 180 • -switching processes are discussed in detail.

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Section: Supplementary Notesmentioning

confidence: 99%

A rate-dependent two-dimensional free energy model for ferroelectric single crystals

Seelecke

Kim

Ball

et al. 2005

Continuum Mech. Thermodyn.

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“…[12][13][14] and references therein). The application of these models to the relatively large number of studied alloy systems has a very fragmentary character, because of the large mathematical processing needed and the difficulty for comparing results of different alloy systems.…”

Section: Introductionmentioning

confidence: 99%

Stress-induced Martensitic Transformation and Superelasticity of Alloys: Experiment and Theory

et al. 2005

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The superelasticity of alloys undergoing a stress-induced martensitic transformation is studied in both experimental and theoretical way. Experimental stress-strain dependencies illustrating the different types of superelastic behavior are taken from Ni-Mn-Ga alloys typifying thermoelastic martensites and then modeled theoretically using a statistical approach to describe the growth of stress-induced martensite in the matrix of parent (austenitic) phase. A good agreement between the experimental and theoretical results is achieved whereby a physical interpretation of the different types of stress-strain dependencies is made and a quantitative evaluation of the main parameters controlling transformational behavior of the alloys is carried out.

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“…The MAS model rationalizes this observation by considering ideal mesoscopic crystal layers in one of the three model phases austenite (A) and two martensitic twin phases (M+, M-) [1][2][3][4][5][6][7][8][9]. The model derivation adheres strictly to thermodynamics and roots in the idea of a three-well potential energy with minima indicating the stable locations of these three phases.…”

Section: The Mas Model and Its Fem Implementationmentioning

confidence: 99%

“…Assuming temperature homogeneity in simple geometries, the temperature can be calculated from the integral energy balance which represents an additional differential equation to be solved along with the rate equations for the phase fractions. Previously, this was accomplished by a standalone FORTRAN program [5,8]. An online version of this model considering a SMA wire is illustrated on the internet [14].…”

Section: The Mas Model and Its Fem Implementationmentioning

confidence: 99%

“…Hence, mechanical and thermal equations need to be solved simultaneously. This feature capable of reflecting all the characteristics of SMA [1][2][3][4][5][6][7][8][9]. Recently, a finite-element-method (FEM) implementation of the MAS model into the commercial software package ABAQUS (ABAQUS, Inc., Dassault Syst mes Simulia Corp., Providence, RI, USA) was elaborated at the Department of Materials Science of the Ruhr-University Bochum and tested upon pure pseudoelastic and quasiplastic settings [10].…”

Section: Introductionmentioning

confidence: 99%

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Finite – element model for simulations of fully coupled thermomechanical processes in shape memory alloys

Richter

Kastner

Eggeler

2009

ESOMAT 2009 - 8th European Symposium on Martensitic Transformations

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Abstract.-Achenbach-Seelecke model for shape memory alloys is able to address full thermomechanical coupling of mechanical and thermal fields. The model roots in a stringent interpretation of thermodynamical principles and interprets the behavior as resulting from an interplay of austenite with two generic martensite twin variants. Its constitutive behavior covers both pseudoplasticity, pseudoelasticity and the characteristic shape memory effect upon temperature changes. Thus, the model reflects the complex, nonlinear hysteretic and thermomechanically coupled material behavior of SMAs on a physically sound basis. In this contribution we investigate the capability of the MAS model in a typical engineering setting, viz. the shrink fitting of a SMA bushing onto a linear-elastic shaft. In this case, the shrink fitting is caused by a martensite-austenite phase transition of the bushing upon temperature change from low to high level (shape memory effect). To address all geometrical implications we employ a finitereliability of the FEM model is proven by comparison to the classical solutions for the linear-elastic and the ideally elastic-plastic case. The MAS model is implemented into ABAQUS using the UMAT interface. The results arrived at with this model are validated against the classical solutions and show the significance for the full thermomechanical coupling which becomes particularly evident in this setting.

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A model for an alloy with shape memory

Cited by 107 publications

References 1 publication

A rate-dependent two-dimensional free energy model for ferroelectric single crystals

A rate-dependent two-dimensional free energy model for ferroelectric single crystals

Stress-induced Martensitic Transformation and Superelasticity of Alloys: Experiment and Theory

Finite – element model for simulations of fully coupled thermomechanical processes in shape memory alloys

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