FINITE ELEMENT IMPLEMENTATION OF A SUPER-ELASTIC CONSTITUTIVE MODEL FOR TRANSFORMATION RATCHETTING OF NiTi ALLOY

2012 ◽  
Vol 09 (01) ◽  
pp. 1240022 ◽  
Author(s):  
Q. H. KAN ◽  
G. Z. KANG ◽  
S. J. GUO
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Niti Alloy ◽  
Cyclic Stress ◽  
Euler Method ◽  
Convergence Criterion ◽  
Integration Algorithm ◽  
Finite Element Implementation ◽  
Backward Euler ◽  
Forward Transformation

In the previous work, a new constitutive model describing the transformation ratchetting of super-elastic NiTi alloy was proposed. The finite element implementation of the proposed model is discussed in this work, because such implementation is necessary to launch a numerical analysis for the cyclic stress–strain responses of NiTi alloy devices including the transformation ratchetting. During the implementation, a new stress integration algorithm is adopted, and a new expression of the consistent tangent modulus is derived for the forward transformation and the reverse transformation. The finite element implementation is elaborated by the user subroutine of UMAT in ABAQUS based on backward Euler method. The accumulated error during cyclic transformation is controlled by a robust convergence criterion. Finally, the validity of such implementation is verified by several numerical examples.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

scholarly journals Development of a continuum plasticity model for the commercial finite element code ABAQUS

2011 ◽  
Vol 2 (2) ◽  
pp. 275-283
Author(s):  
M. Safaei ◽  
W. De Waele
Keyword(s):  
Finite Element ◽  
Yield Surface ◽  
Euler Method ◽  
Integration Scheme ◽  
Isotropic Hardening ◽  
Implicit Integration ◽  
Backward Euler ◽  
User Material Subroutine ◽  
Von Mises ◽  
Future Work

The present work relates to the development of computational material models for sheet metalforming simulations. In this specific study, an implicit scheme with consistent Jacobian is used forintegration of large deformation formulation and plane stress elements. As a privilege to the explicitscheme, the implicit integration scheme is unconditionally stable. The backward Euler method is used toupdate trial stress values lying outside the yield surface by correcting them back to the yield surface atevery time increment. In this study, the implicit integration of isotropic hardening with the von Mises yieldcriterion is discussed in detail. In future work it will be implemented into the commercial finite element codeABAQUS by means of a user material subroutine.

Research on WALKER Constitutive Model Tangent Modulus

2012 ◽  
Vol 249-250 ◽  
pp. 113-117
Author(s):  
Yan Chen ◽  
Qing Wu Wang ◽  
Quan Shan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Constitutive Model ◽  
Constitutive Equations ◽  
Tangent Modulus ◽  
Finite Element Code ◽  
Numerical Examples ◽  
Rate Dependent ◽  
Backward Euler ◽  
Elasto Plasticity

In elasto-plasticity computation on materials by sub-increase finite element method, in general, it is necessary to calculate the consistent tangent modulus of elements. In this paper, based on the backward Euler integration, for an unified viscoplasticity constitutive equations, a new expression of consistent tangent modulus is derived for rate-dependent plasticity. The constitutive equations and consistent tangent modulus expression are implemented into a commercial finite element code-MARC. Numerical examples are given to verify the finite element implementation.This template explains and demonstrates how to prepare your camera-ready paper for Trans Tech Publications. The best is to read these instructions and follow the outline of this text.

scholarly journals Constitutive model of coupled damage-plasticity and its finite element implementation

2003 ◽  
Vol 12 (4) ◽  
pp. 381-405 ◽  
Author(s):  
Adnan Ibrahimbegović ◽  
Damijan Markovič ◽  
Fabrice Gatuingt
Keyword(s):  
Finite Element ◽  
Constitutive Model ◽  
Finite Element Implementation
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