Numerical Implementation of a Thermomechanical Constitutive Model for Shape Memory Alloys Using Return Mapping Algorithm and Microplane Theory

2012 ◽  
Vol 516-517 ◽  
pp. 351-354 ◽  
Author(s):  
Reza Mehrabi ◽  
Mahmoud Kadkhodaei ◽  
Abbas Ghaei
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Axial Stress ◽  
Numerical Procedure ◽  
Finite Element Program ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Element Program ◽  
Microplane Theory

In this work, a return mapping algorithm is utilized to implement the model into a finite element program and then Microplane theory is employed. A numerical procedure is also developed to implement the model as a user material subroutine for ABAQUS-Standard commercial code. Uniaxial tension test under a constant axial stress is simulated in order to study the behavior of shape memory alloys. A very good agreement is seen between the results obtained by the two approaches indicating the capability of microplane theory.

A Phenomenological Model for Shape Memory Alloys With Uniformly Distributed Porosity

2020 ◽  
Author(s):  
Wael Zaki ◽  
N. V. Viet
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Phenomenological Model ◽  
Free Energy Density ◽  
State Variables ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Generalized Standard Materials ◽  
Inelastic Strains

Abstract A phenomenological model is proposed for shape memory alloys considering the presence of uniformly distributed voids. The model is developed within a modified generalized standard materials framework, which considers the presence of constraints on the state variables and ensures thermodynamic consistency. Within this framework, a free energy density is first proposed for the porous material, wherein the influence of porosity is accounted for by means of scalar state variables accounting for damage and inelastic dilatation. By choosing key thermodynamic forces, derived from the expression of the energy, as sub-gradients of a pseud-potential of dissipation, loading functions are derived that govern phase transformation and martensite detwinning. Flow rules are also proposed for damage and inelastic dilatation in a way that ensures positive dissipation. The model is discretized and the integration of the time-discrete formulation is carried out using an implicit formulation, whereby a return mapping algorithm is implemented to calculate increments of dissipative variables including inelastic strains. Comparison with data from the literature is finally presented.

Parameter Inversion of Return Mapping Algorithm in Tunnel Engineering

2011 ◽  
Vol 243-249 ◽  
pp. 3360-3363
Author(s):  
De Hai Yu ◽  
An Nan Jiang ◽  
Jun Xiang Wang
Keyword(s):  
Finite Element ◽  
Differential Evolution Algorithm ◽  
Tunnel Engineering ◽  
Finite Element Program ◽  
C Language ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Element Program ◽  
Evolution Algorithm

The self-developed finite element program on return mapping algorithm is used to the simulation of the true tunnel with C + + language, while the finite element program is embedded into differential evolution algorithm to achieve the inversion parameter. Applying to Line 1 of Dalian Metro, rock mechanics inversion parameters and true parameters are close, which indicates the superiority and good prospects of return mapping algorithm and different evolution algorithm, and it can be used for quantitative analysis of actual tunnel.

Shape Memory Effect Behavior of NiTi Torque Tubes in Torsion

2012 ◽  
Author(s):  
Reza Mehrabi ◽  
Mahmoud Kadkhodaei ◽  
Masood Taheri ◽  
Mohammad Elahinia
Keyword(s):  
Shape Memory ◽  
Constitutive Models ◽  
Material Point ◽  
Macroscopic Model ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Strain Components ◽  
Plane Passing ◽  
Arbitrary Plane ◽  
Microplane Theory

In order to simulate the torsional behavior of NiTi torque tubes, two different 3D thermo-mechanical constitutive models are utilized. Firstly, an available incremental constitutive model is used in which a return mapping algorithm is implemented to numerically calculate the strains for any applied stresses. Secondly, Microplane theory is employed based on which 1D constitutive laws are considered for associated stress and strain components on any arbitrary plane passing through a material point followed by a homogenization process to generalize the 1D equations to a 3D macroscopic model. Both of the constitutive models are implemented in ABAQUS by developing UMAT. In order to compare the two approaches, torque-angle of rotation and shear stress-shear strain responses for torsion of thin-walled Nitinol torque tubes with different thicknesses are studied. The numerical results of these two approaches show to be in a good agreement indicating the capability of Microplane theory in constitutive modeling of shape memory alloys. This theory provides explicit relationships to calculate strains in terms of stresses, and this makes it very beneficial in obtaining the SMA responses in a fast and easy manner.

An Energy Dissipation Device Based on Shape Memory Alloys for Frame Structures

2014 ◽  
Vol 580-583 ◽  
pp. 1591-1594
Author(s):  
Yun Chen ◽  
Nai Long Zhu ◽  
Shuai Gao
Keyword(s):  
Energy Dissipation ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Analytical Study ◽  
Time History ◽  
Frame Structures ◽  
Finite Element Program ◽  
History Analysis ◽  
Element Program ◽  
Energy Dissipation Devices

This paper proposes an energy dissipation device based on shape memory alloys (SMA) for frame structures. By setting anchorage device below and near the inflection point of the first storey columns, a set of force cable and energy dissipation cable using SMA are installed symmetrically in the anchorage device and the bottom of them fixed in the ground. Analytical study including the push-over and time-history analysis were investigated by ANSYS finite element program to a new CFST frame and an ordinary CFST frame. Studies have shown that the device can effectively control the structural displacement response and acceleration response, dissipating large amounts of earthquake energy. Therefore, the energy dissipation devices had a better value and prospects in engineering.

Meshless Analyses of Fracture, Plasticity and Impact

2003 ◽  
Author(s):  
A. Eskandarian ◽  
Y. Chen ◽  
M. Oskard ◽  
J. D. Lee
Keyword(s):  
High Speed ◽  
Large Strain ◽  
Plastic Response ◽  
Governing Equations ◽  
Mapping Algorithm ◽  
High Speed Impact ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Large Strain Plasticity ◽  
Computational Plasticity

The governing equations for rate-independent large strain plasticity are formulated in the framework of meshless method. The numerical procedures, including return mapping algorithm, to obtain the solutions of boundary-value problems in computational plasticity are outlined. The crack growth process in elastic-plastic solid under plane strain conditions is analyzed. The large strain plastic response of material under high-speed impact is simulated. Numerical results are presented and discussed.

OS1001 A Constitutive Model for Stress and Temperature Induced Phase Transformation of Shape Memory Alloys under Multi-axial Stress

2008 ◽  
Vol 2008 (0) ◽  
pp. _OS1001-1_-_OS1001-2_ ◽  
Author(s):  
Akihiko Suzuki ◽  
Wakako Araki ◽  
Hideo Shibutani ◽  
Takaei Yamamoto ◽  
Toshio Sakuma
Keyword(s):  
Phase Transformation ◽  
Constitutive Model ◽  
Shape Memory Alloys ◽  
Shape Memory ◽  
Axial Stress
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