Parameter identification of a thermodynamic model for superelastic shape memory alloys using analytical calculation of the sensitivity matrix
| Autor: | Etienne Patoor, Rachid Echchorfi, Boris Piotrowski, Nadine Bourgeois, Fodil Meraghni, Yves Chemisky |
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| Přispěvatelé: | Laboratoire de physique et mécanique des matériaux (LPMM), Université Paul Verlaine - Metz (UPVM)-Institut National Polytechnique de Lorraine (INPL)-Ecole Nationale d'Ingénieurs de Metz (ENIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), IIMEC |
| Rok vydání: | 2014 |
| Předmět: |
State variable
Matériaux [Sciences de l'ingénieur] Materials science Computation Constitutive equation General Physics and Astronomy [SPI.MECA.MSMECA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Materials and structures in mechanics [physics.class-ph] 02 engineering and technology [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph] [SPI.MAT]Engineering Sciences [physics]/Materials Thermodynamical constitutive modeling Matrix (mathematics) 0203 mechanical engineering [SPI.MECA.MEMA]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of materials [physics.class-ph] Applied mathematics General Materials Science Sensitivity (control systems) Mécanique: Mécanique des matériaux [Sciences de l'ingénieur] Analytical sensitivity calculation Shape memory alloys Thermodynamical constitutive modeling Second derivative Mécanique [Sciences de l'ingénieur] business.industry Analytical sensitivity calculation Mechanical Engineering Mécanique: Mécanique des solides [Sciences de l'ingénieur] Mécanique: Matériaux et structures en mécanique [Sciences de l'ingénieur] Structural engineering [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph] Optimisation et contrôle [Mathématique] Inverse problem 021001 nanoscience & nanotechnology 020303 mechanical engineering & transports Shape memory alloys Mechanics of Materials Partial derivative [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] 0210 nano-technology business |
| Zdroj: | European Journal of Mechanics-A/Solids European Journal of Mechanics-A/Solids, Elsevier, 2014, 45, pp.226-237. ⟨10.1016/j.euromechsol.2013.12.010⟩ |
| ISSN: | 0997-7538 |
| Popis: | I; This 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 validated; International audience; This 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 validated |
| Databáze: | OpenAIRE |
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