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Finite Element Analysis of the Behavior of Shape Memory Alloys and their Applications.

Brinson, L.C. and Lammering, R. (1993) Finite Element Analysis of the Behavior of Shape Memory Alloys and their Applications. International Journal of Solids and Structures, Vol. 30, No. 23, pp. 3261-3280, 1993., No. 23, pp. 3261-3280. Pergamon Press.

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Abstract

A nonlinear finite element procedure is developed which incorporates a thermodynamically derived constitutive law for shape memory alloy material behavior. The constitutive equations include the necessary internal variables to account for the material transformations and are utilized in a one-dimensional finite element procedure that captures the unique shape memory alloy responses of pseudoelasticity and of the shape memory effect at all temperatures, stress levels and loading conditions. Detailed material properties for the alloy used are necessary for the analysis. The solution of the geometrically and physically nonlinear problem is achieved by application of a Newton's method in which a sequence of linear problems is numerically solved. Due to consistent linearization, a quadratic rate of convergence is obtained. Several test cases are presented to illustrate the potential of the finite element procedure. Cases simulating the stress-strain behavior of a bar of shape memory alloy under simple uniaxial loading as well as restrained recovery responses at different temperatures compare well with experimental and analytical results. Two further generalized applications are examined: the use of a shape memory alloy ring as a pipe connector and eigenfrequency tuning of a composite beam with embedded shape memory wires. The results of these analyses correlate well with analytical results and the methodology for the incorporation of the finite element procedure into general cases is demonstrated. The finite element procedure is thus shown to be a powerful tool for studying various applications of shape memory alloys.

Item URL in elib:https://elib.dlr.de/39624/
Document Type:Article
Additional Information: LIDO-Berichtsjahr=1993,
Title:Finite Element Analysis of the Behavior of Shape Memory Alloys and their Applications.
Authors:
AuthorsInstitution or Email of AuthorsAuthors ORCID iD
Brinson, L.C.UNSPECIFIEDUNSPECIFIED
Lammering, R.UNSPECIFIEDUNSPECIFIED
Date:1993
Journal or Publication Title:International Journal of Solids and Structures, Vol. 30, No. 23, pp. 3261-3280, 1993.
Refereed publication:Yes
Open Access:No
Gold Open Access:No
In SCOPUS:No
In ISI Web of Science:Yes
Volume:No. 23
Page Range:pp. 3261-3280
Publisher:Pergamon Press
Series Name:Vol. 30
Status:Published
Keywords:Shape memory alloys, Finite Element Method, Thermomechanics, Constitutive Relations, Smart Structures, Consistent Linearization.
HGF - Research field:UNSPECIFIED
HGF - Program:Space (old)
HGF - Program Themes:W RP - Raumtransport
DLR - Research area:UNSPECIFIED
DLR - Program:W RP - Raumtransport
DLR - Research theme (Project):UNSPECIFIED
Location: Göttingen
Institutes and Institutions:Institute of Aeroelasticity
Deposited By: DLR-Beauftragter, elib
Deposited On:02 Apr 2006
Last Modified:27 Apr 2009 10:49

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