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.

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 proposed phenomenological model for shape memory alloys

2006 ◽  
Vol 15 (2) ◽  
pp. 393-400 ◽  
Author(s):  
Rongqiao Wang ◽  
Chongdu Cho ◽  
Changboo Kim ◽  
Qiang Pan
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Phenomenological Model

A phenomenological model for thermally-induced hysteresis in polycrystalline shape memory alloys with internal loops

2021 ◽  
pp. 1045389X2110482
Author(s):  
Yuxiang Han ◽  
Haoyuan Du ◽  
Linxiang Wang ◽  
Roderick Melnik
Keyword(s):  
Shape Memory Alloys ◽  
Single Crystal ◽  
Shape Memory ◽  
Phenomenological Model ◽  
Landau Theory ◽  
Thermally Induced ◽  
First Order ◽  
Proposed Model ◽  
Crystal Model ◽  
Hysteretic Response

In the current study, a 1-D phenomenological model is constructed to capture the temperature-induced hysteretic response in polycrystalline shape memory alloys (SMAs). The martensitic and austenitic transformations are regarded as the first-order transitions. A differential single-crystal model is formulated on the basis of Landau theory. It is assumed that the transformation temperatures follow the normal distribution among the grains due to the anisotropic stress field developed in the material. The polycrystalline hysteretic response is expressed as the integration of single-crystal responses. Besides, the prediction strategy for incomplete transitions is presented, and the first-order reversal curves are obtained via density reassignment. The proposed model is numerically implemented for validation. Comparisons between the modeling results and the experimental ones demonstrate the capability of the proposed model in addressing the hysteresis in thermally-induced phase transformations.

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.

A three-dimensional phenomenological model for shape memory alloys including two-way shape memory effect and plasticity

2019 ◽  
Vol 136 ◽  
pp. 103085 ◽  
Author(s):  
Giulia Scalet ◽  
Fabrizio Niccoli ◽  
Cedric Garion ◽  
Paolo Chiggiato ◽  
Carmine Maletta ◽  
...  
Keyword(s):  
Shape Memory Alloys ◽  
Shape Memory ◽  
Shape Memory Effect ◽  
Memory Effect ◽  
Phenomenological Model ◽  
Three Dimensional
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