A hereditary type, discrete memory, constitutive equation with applications to simple geometries

Wack, B.; Terriez, J.M.; Guélin, P.

doi:10.1007/bf01170438

Cited by 21 publications

(7 citation statements)

References 7 publications

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“…For further details about the origin of this hysteresis model and its compatibility with the thermodynamic dissipation principle, see Favier and Guélin (1985), Wack et al (1983), Blès (2002). This model was first applied to electromagnetic and metallic materials and shape memory alloys, and some details of simulated tests can be found in Rio et al (1995), Manach et al (1996).…”

Section: Hysteresismentioning

confidence: 98%

Experimental and numerical study on the temperature-dependent behavior of a fluoro-elastomer

Laurent

Rio

Vandenbroucke

et al. 2014

Mech Time-Depend Mater

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The aim of this study is to investigate the mechanical behavior of a fluoro-polymer elastomer in the −8 to 100 • C temperature range. Several cyclic tension and compression tests and multi-step relaxation tests were performed in order to determine the effects of the temperature on the behavior of the material. The Hyperelasto-Visco-Hysteresis (HVH) phenomenological model was used to account for the thermo-mechanical properties of this material. In this model, which was implemented in the in-house Herezh++ code, three sets of branches stand for different modes of characteristic behavior: the hyperelasticity contribution stands for the reversible elastic phase which occurs at the onset of the loading, the viscosity contribution models the strain rate dependent phase and the hysteresis contribution stands for the irreversible plastic phase. Temperature-dependent parameters were determined using a simplified method based on tension and compression tests interrupted by relaxation steps. The model was found to accurately describe the stress-strain evolution of the elastomer investigated under various mechanical loading conditions at various temperatures.

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Section: Hysteresismentioning

confidence: 98%

Experimental and numerical study on the temperature-dependent behavior of a fluoro-elastomer

Laurent

Rio

Vandenbroucke

et al. 2014

Mech Time-Depend Mater

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“…As proposed in [1,2], the permanence of the simultaneous existence of reversible processes and hysteresis in the thermomechanical behaviour of shape memory alloys suggests to express the total stress σ as the addition of two partial stresses, the first σ r being hyperelastic while the second one is related to hysteresis of elastoplastic type [3][4][5]. A 1-D illustration of the "elastohysteresis model" is shown in figure 1a.…”

Section: The Elastohysteresis Modelmentioning

confidence: 99%

“…The hysteresis is described by an incremental model of hypoelastic type :σ = 2µD + βφ∆ t Rσ and an algorithm to manage discrete memory points σ R introduced by P.Guélin [3] and used in the model.D is the deviatoric strain rate tensor and ∆σ = σ(t) − σ R . More details can be found in [2,[4][5][6]9]. Figures 1b-e show the meaning of the parameters used in this work.…”

Section: The Elastohysteresis Modelmentioning

confidence: 99%

Elastohysteresis model implemented in the ﬁnite element sofware HEREZH++

Rio

Favier

Liu

2009

ESOMAT 2009 - 8th European Symposium on Martensitic Transformations

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Abstract. This short paper describes the simulation results obtained with the elasto-hysteresis model implemented in the finite element software Herezh++ and compares them with the experimental data of the Roundrobin SMA Modelling benchmark. The elastohysteresis modelAs proposed in [1,2], the permanence of the simultaneous existence of reversible processes and hysteresis in the thermomechanical behaviour of shape memory alloys suggests to express the total stress σ as the addition of two partial stresses, the first σ r being hyperelastic while the second one is related to hysteresis of elastoplastic type [3][4][5]. A 1-D illustration of the "elastohysteresis model" is shown in figure 1a. In the present work, the partial hyperelastic stress tensor is calculated from the hyperelastic potential proposed by Orgéas [6,7], which leads in the 1-D case (shear test) to the stress-strain curve shown in figure 1b. In the case of shape memory alloys [2], the potential ω = ω(V, Q ε , ϕ ε ) is expressed as function of 3 invariants of the Almansi strain tensor: the relative variation of volume V, the intensity of the deviatoric deformation Q ε , and ϕ ε a measure of the angle giving the direction of the deformation tensor in the deviatoric plane. The hysteresis is described by an incremental model of hypoelastic type :σ = 2µD + βφ∆ t Rσ and an algorithm to manage discrete memory points σ R introduced by P.Guélin [3] and used in the model.D is the deviatoric strain rate tensor and ∆σ = σ(t) − σ R . More details can be found in [2,[4][5][6]9]. Figures 1b-e show the meaning of the parameters used in this work. Process to parameter identificationFirstly, eight parameters independent of the temperature are used in this model, including 6 parameters involved in the hyperelastic potential and 2 parameters of the hysteresis scheme. The 6 parameters independent of the temperature of the hyperelastic potential (cf. fig. 1 b ) are: the 3 slopes: µ 1 µ 2 µ 3 , the 2 curvatures for the transitions: α 1 α 2 and the bulk modulus K. The 2 hysteresis parameters indepedent of the temperature (cf. fig. 1 c )are: the initial slope µ and the Prager parameter np which controls the transition to the saturation of the hypoelastic scheme). The bulk modulus K is chosen from the literature. The 7 other parameters independent of the temperature are determined from one isothermal tensile test performed at a temperature above Af.a

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“…Tension-compression asymmetry is taken into account using path direction history dependancy for the maximum transformation strain. Internal loops are considered by introducing discrete memory points formalism initiated by Wack et al [5]. The dissipation potential is expressed to account for the loop hysteresis.…”

Section: Fundamental Aspects Of Modelingmentioning

confidence: 99%

Numerical tool for Shape Memory Alloys structures simulations including twinning eﬀects

Chemisky

Duval

Piotrowski

et al. 2009

ESOMAT 2009 - 8th European Symposium on Martensitic Transformations

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Abstract. According to the S3T-RoundRobin effort, this paper presents the main results obtained using the SMA model developed by Chemisky et al. [6], from the calibration to the prediction results. This model is based on thermodynamics of the irrevesible processes. Three internal variables are used to model the macroscopic behavior of SMAs. Parameters identification procedure requires only a limited set of experimental data. Comparison between modeling and experimental results are presented for the four data sets of this RoundRobin. Finite Element Analysis was performed to capture tension-torsion tests. Major discrepancies are related to strain localization effects and R-phase transformation which are not included in the present model. Fundamental aspects of modelingThe present model is dedicated to the description of the macroscopic response of SMAs, as well as the simulation of the response of SMA-based structures, using Finite Element Analysis (FEA). The considered state variables are the average value of inelastic strains in martensite and twinned martensite volumes and the martensite volume fraction inside a representative volume element (RVE). Elastic, thermal and inelastic strains are related to the total strain using an additive decomposition law. Two inelastic strains are considered. The first one is the macroscopic transformation strain which is defined from the martensite volume fraction f and the mean transformation strainε V denotes the total volume of the considered representative volume element, and V M is the martensite phase volume.The second inelastic strain is the accommodation of twins which is expressed only in the formed self-accommodated martensite f F A , using the mean accommodation of twins strain [2][3]:This decomposition lead to a straightforward definition of the internal variables: the volume fraction of martensite (f ), the mean transformation strain (ε T ) and the mean accommodation of twins strain (ε tw ). The formed self-accommodated martensite volume is dependant on the amount of martensite formed and the mean transformation strain history (see [2][3] for details).

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A hereditary type, discrete memory, constitutive equation with applications to simple geometries

Cited by 21 publications

References 7 publications

Experimental and numerical study on the temperature-dependent behavior of a fluoro-elastomer

Experimental and numerical study on the temperature-dependent behavior of a fluoro-elastomer

Elastohysteresis model implemented in the ﬁnite element sofware HEREZH++

Numerical tool for Shape Memory Alloys structures simulations including twinning eﬀects

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