Parameter identification of a thermodynamic model for superelastic shape memory alloys using analytical calculation of the sensitivity matrix

Abstract

IThis paper presents an identification procedure for the parameters of a thermodynamically based constitutive model for Shape memory Alloys (SMAs). The proposed approach is a gradient-based method and utilizes an analytical computation of the sensitivity matrix. For several loading cases, including superelasticity, that are commonly utilized for the model parameters identification of such a constitutivemodel, a closed-form of the total infinitesimal strain is derived. The partial derivatives of this state variable are developed to find the components of the sensitivity matrix. A LevenbergeMarquardt algorithm is utilized to solve the inverse problem and find the best set of model parameters for specific SMA materials. Moreover, a pre-identification method, based on the second derivative of the total strain components is proposed. This provides a suitable initial set of model parameters, which increases theefficiency of the inverse method. The proposed approach is applied for the simultaneous identification of the non-linear constitutive parameters for two superelastic SMAs. The comparison between experimental and numerical curves obtained for different temperatures shows the capabilities of the developedidentification approach. The robustness and the efficiency of the developed approach are then experimentally validatedInternational audienceThis paper presents an identification procedure for the parameters of a thermodynamically based constitutive model for Shape memory Alloys (SMAs). The proposed approach is a gradient-based method and utilizes an analytical computation of the sensitivity matrix. For several loading cases, including superelasticity, that are commonly utilized for the model parameters identification of such a constitutivemodel, a closed-form of the total infinitesimal strain is derived. The partial derivatives of this state variable are developed to find the components of the sensitivity matrix. A LevenbergeMarquardt algorithm is utilized to solve the inverse problem and find the best set of model parameters for specific SMA materials. Moreover, a pre-identification method, based on the second derivative of the total strain components is proposed. This provides a suitable initial set of model parameters, which increases theefficiency of the inverse method. The proposed approach is applied for the simultaneous identification of the non-linear constitutive parameters for two superelastic SMAs. The comparison between experimental and numerical curves obtained for different temperatures shows the capabilities of the developedidentification approach. The robustness and the efficiency of the developed approach are then experimentally validate

Hybrid micromechanical-phenomenological modelling of anisotropic damage and anelasticity induced by micro-cracks in unidirectional composites

“…Then the two remaining parameters are obtained by minimizing a cost function formulated from the least squares between the numerical and experimental mechanical response of the specimen (Meraghni et al, 2011(Meraghni et al, , 2014. The obtained values of the parameters are listed in Table 3.…”

Modeling of coupled phase transformation and reorientation in shape memory alloys under non-proportional thermomechanical loading

“…A last set of experiment is complex tension/torsion and tension compression on NiTi tube Grabe and Bruhns (2009). Parameter identication was carried out using a proven method reliable in identifying complex modeling parameters for SMAs using inverse identication methods developed by Meraghni et al (2014) and extended for heterogeneous conguration in 340 Chemisky et al (2015). Table 4: Material constants for equiatomic NiTi utilized in loading simulations of experiments presented in (Sittner et al, 2009).…”

Identification of Model Parameter for the Simulation of SMA Structures Using Full Field Measurements

“…However, these solutions require more advanced characterization techniques than the uniaxial tension or thermal analysis recommended by the ASTM standards (F2004, 2005; F2082, 2003). For homogeneous tests, a recent method has been developed to identify the phase transformation parameters from a set of experiments, utilizing a gradient-based inverse approach (Meraghni et al, 2014). A similar approach has been adopted to determine the parameter of a SMA model from experimental data (Whitten and Hartl, 2014).…”