An implicit integration algorithm with a projection method for viscoplastic constitutive equations

1989 ◽  
Vol 28 (10) ◽  
pp. 2397-2421 ◽  
Author(s):  
K. Hornberger ◽  
H. Stamm
Keyword(s):  
Projection Method ◽  
Constitutive Equations ◽  
Implicit Integration ◽  
Integration Algorithm ◽  
Implicit Integration Algorithm

scholarly journals Time Integration and Assessment of a Model for Shape Memory Alloys Considering Multiaxial Nonproportional Loading Cases

2014 ◽  
Author(s):  
Wael Zaki ◽  
Xiaojun Gu ◽  
Claire Morin ◽  
Ziad Moumni ◽  
Weihong Zhang
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Time Integration ◽  
Implicit Integration ◽  
Proportional Loading ◽  
Simulation Data ◽  
Integration Algorithm ◽  
Implicit Integration Algorithm ◽  
User Material Subroutine ◽  
Martensite Reorientation

The paper presents a numerical implementation of the ZM model for shape memory alloys that fully accounts for non-proportional loading and its influence on martensite reorientation and phase transformation. Derivation of the time-discrete implicit integration algorithm is provided. The algorithm is used for finite element simulations using Abaqus, in which the model is implemented by means of a user material subroutine. The simulations are shown to agree with experimental and numerical simulation data taken from the literature.

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