Numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm

The numerical simulation of structures made of shape memory materials is of increasing interest in different fields. Among others, the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge. In such practical applications the pseudoelastic effect as w...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 69; no. 10; pp. 1997 - 2035
Main Author: Helm, D.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 05.03.2007
Wiley
Subjects:
Algorithms
Biological and medical sciences
Blood vessels and receptors
computational mechanics
Computational techniques
Computer simulation
Exact sciences and technology
Fundamental and applied biological sciences. Psychology
Fundamental areas of phenomenology (including applications)
integration algorithm
martensitic phase transitions
Martensitic transformations
Mathematical analysis
Mathematical methods in physics
Mathematical models
Phase transformations
Physics
Shape memory alloys
Solid mechanics
Structural and continuum mechanics
Surgical implants
thermomechanical constitutive theory
Vertebrates: cardiovascular system
Constitutive equation
Euler equation
integration algorithm
Numerical integration
Prosthesis
Evolution equation
Thermomechanical properties
Modeling
Stent
Phase transitions
Finite element method
shape memory alloys
Phase transformation
Shape memory alloy
Superelasticity
martensitic phase transitions
Shape memory effect
Martensitic transformation
computational mechanics
Endoscopy
Non linear effect
thermomechanical constitutive theory
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:The numerical simulation of structures made of shape memory materials is of increasing interest in different fields. Among others, the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge. In such practical applications the pseudoelastic effect as well as the one‐way and two‐way shape memory effects are utilized. These material properties are caused by martensitic phase transitions between austenite and martensite. In the present contribution, a recently proposed constitutive theory is numerically treated in the context of the finite element method. This constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys. For the numerical integration of the evolution equations, the backward Euler method is applied. In spite of the complexity of the constitutive theory, it is shown that an improved integration procedure can be formulated, which merely involves the solution of three non‐linear equations for three scalar‐valued unknown variables. Numerical examples show the capability of the proposed model and the improved integration algorithm. Copyright © 2006 John Wiley & Sons, Ltd.
Bibliography:istex:EFA29911BCCC7F0EF6B595294ECCFD60314BDB59
German Research Foundation
ark:/67375/WNG-7V1DGG6G-J
ArticleID:NME1822
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.1822