scholarly journals Parallel projection—An improved return mapping algorithm for finite element modeling of shape memory alloys

2022 ◽  
Vol 389 ◽  
pp. 114364
Author(s):  
Ziliang Kang ◽  
Daniel A. Tortorelli ◽  
Kai A. James
Keyword(s):  
Finite Element ◽  
Shape Memory Alloys ◽  
Finite Element Modeling ◽  
Shape Memory ◽  
Parallel Projection ◽  
Mapping Algorithm ◽  
Element Modeling ◽  
Return Mapping ◽  
Return Mapping Algorithm

Corrugated structures reinforced by shape memory alloy sheets: Analytical modeling and finite element modeling

2018 ◽  
Vol 233 (7) ◽  
pp. 2445-2454 ◽  
Author(s):  
Maryam Koudzari ◽  
Mohammad-Reza Zakerzadeh ◽  
Mostafa Baghani
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory Alloys ◽  
Finite Element Modeling ◽  
Shape Memory ◽  
Smart Structure ◽  
Design Parameters ◽  
Asymmetric Mode ◽  
Element Modeling ◽  
Structure Changes

In this study, an analytical solution is presented for a trapezoidal corrugated beam, which is reinforced by shape memory alloy sheets on both sides. Formulas are presented for shape memory alloys in states of compression and tension. According to the modified Brinson model, shape memory alloys have different thermomechanical behavior in compression and tension, and also these alloys would behave differently in different temperatures. The developed formulation is based on Euler–Bernoulli theory. Deflection of the smart structure and the effect of asymmetric response in shape memory alloys are studied. Results found from the semi-analytic modeling are compared to and validated through a finite element modeling, and there is more than [Formula: see text] agreement between two solutions. With regard to the results, the neutral axis of the smart structure changes in each section. The maximum deflection ratio of asymmetric mode to symmetric one mode is 1.7. Additionally, the effect of design parameters on deflection is studied in detail.

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.

Displacement Back Analysis Based on Return Mapping Algorithm and Differential Evolution Algorithm

2011 ◽  
Vol 301-303 ◽  
pp. 564-568
Author(s):  
Jun Xiang Wang ◽  
An Nan Jiang
Keyword(s):  
Finite Element ◽  
Differential Evolution ◽  
Differential Evolution Algorithm ◽  
Implicit Integration ◽  
Integration Algorithm ◽  
Mapping Algorithm ◽  
Return Mapping ◽  
Return Mapping Algorithm ◽  
Calculation Step ◽  
Evolution Algorithm

Differential evolution algorithm is a new global optimization algorithm. DE does not require an initial value, and it has rapid convergence, strong adaptability to a nonlinear function, the features of parallelcalculation, especially in adoption to the complex problem of multivariable optimization. The constitutive integration algorithm affecting the incremental calculation step, and convergence and accuracy of the results is a key of finite element analysis. It is usually divided into an explicit and implicit integration. Return mapping algorithm is an implicit integration to avoid solving the equivalent plastic strain directly so that we achieve a fast and accurate solution for the constitutive equations. Making use of DE and return mapping algorithm to program, the elasticplastic finite element simulation and parameter inversion, the inversion and simulation results are verificated, the results show that it is closed to the actual situation, indicating usefulness and correctness of the program.

scholarly journals Finite element modeling of shape memory polyurethane foams for treatment of cerebral aneurysms

2021 ◽  
Author(s):  
H. R. Jarrah ◽  
A. Zolfagharian ◽  
M. Bodaghi
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Shape Memory ◽  
Cerebral Aneurysms ◽  
Element Model ◽  
Polyurethane Foams ◽  
Patient Specific ◽  
Structural Cell ◽  
Element Modeling ◽  
Shape Memory Polyurethane

AbstractIn this paper, a thermo-mechanical analysis of shape memory polyurethane foams (SMPUFs) with aiding of a finite element model (FEM) for treating cerebral aneurysms (CAs) is introduced. Since the deformation of foam cells is extremely difficult to observe experimentally due to their small size, a structural cell-assembly model is established in this work via finite element modeling to examine all-level deformation details. Representative volume elements of random equilateral Kelvin open-cell microstructures are adopted for the cell foam. Also, a user-defined material subroutine (UMAT) is developed based on a thermo-visco-elastic constitutive model for SMPUFs, and implemented in the ABAQUS software package. The model is able to capture thermo-mechanical responses of SMPUFs for a full shape memory thermodynamic cycle. One of the latest treatments of CAs is filling the inside of aneurysms with SMPUFs. The developed FEM is conducted on patient-specific basilar aneurysms treated by SMPUFs. Three sizes of foams are selected for the filling inside of the aneurysm and then governing boundary conditions and loadings are applied to the foams. The results of the distribution of stress and displacement in the absence and presence of the foam are compared. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem and provide pertinent results that are instrumental in the design of SMPUFs for treating CAs.

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