Elastohysteresis model implemented in the finite element sofware HEREZH++

Abstract

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

A simplified methodology to identify material parameters of a hyperelasto-visco-hysteresis model: application to a fluoro-elastomer

“…To implement this constitutive law in a numerical schema, a 3D finite deformation framework has been developed in a finite element software, called HEREZH++ [21]. An Eulerian formulation, the Cauchy stress tensor σ, the Almansi strain tensor ε and the Jaumann time derivative of the stress are chosen for this purpose [48,49].…”

“…With this assumption of stress decomposition, it is relatively easy to identify material parameters of hyperelastic σ e and hysteresis σ h contributions. Inverse analysis software package SiDoLo [30,31] and the finite element software program HEREZH++ [21] are used for this purpose. Experimental boundary and loading conditions are simulated with HEREZH++ on a single hexahedral finite element to reproduce the assumed homogeneous state at the centre of the specimen.…”

“…An original phenomenological model, called hyperelasto-visco-hysteresis (HVH), has also been used to simulate this complex behaviour. This model, written in 3D and implemented in an in-house code HEREZH++ [21], is based on the superimposition of three stress components which correspond to linear viscoelastic, hyperelastic and pure hysteresis behaviour. It takes the phenomena of viscosity, possible compressibility and hysteresis into account.…”

Bulge tests on ferroelastic and superelastic NiTi sheets with full field thermal and 3D-kinematical measurements: experiments and modelling

“…found in [13][14][15][16][17][18][19]. Figure 10b shows the meaning of the 2 parameters used in this work.…”