Nonlinear bending analysis of shape memory alloy beam considering both material and geometric nonlinearity effects

2018 ◽  
Vol 30 (6) ◽  
pp. 823-843 ◽  
Author(s):  
Rasool Zamani Alavije ◽  
Mohsen Botshekanan Dehkordi
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Geometric Nonlinearity ◽  
Volume Fraction ◽  
Virtual Work ◽  
Kinetic Equations ◽  
Weighted Residual Method ◽  
Material And Geometric Nonlinearity

This study examined the nonlinear super-elastic bending of shape memory alloy beam considering the material and geometric nonlinearity effects that coupled together. Shape memory alloy properties change instantaneously at different points in the beam, while they are unknown at the same time. In other words, coupling of the governing and kinetic equations of the shape memory alloy beams together results in a more complicated analysis. In this study, the governing equations were extracted through using the Timoshenko beam theory and applying the principle of virtual work. For achieving this goal, von Karman strains were applied to consider large deflections. The Boyd–Lagoudas three-dimensional constitutive model and return mapping algorithm were also used for shape memory alloy modeling. Furthermore, in order to obtain the characteristics of finite element beam, the Galerkin weighted-residual method was used by developing the iterative nonlinear finite element model. Considering the different supporting conditions and forces for the shape memory alloy beam, this study examined their effects on the distribution of martensitic volume fraction, stress distribution, and changes in the location of the neutral axis. The obtained results revealed that as loading increases, the magnitude of martensitic volume fraction and the level of hysteresis increase, which in turn would result in reduction of the modulus of elasticity and the strength of the material and consequently increases the deflection of shape memory alloy beam. The findings suggested the necessity of nonlinear strain field in this modeling by which the stress distribution and volume fraction become asymmetric along the beam thickness. The results were presented in the forms of loading and unloading diagrams for different support and force conditions, and the martensitic volume fraction along the length and through the thickness of the shape memory alloy beam were also shown. To validate the proposed formulation, the results were compared with other experimental findings in this regard suggesting that there is an acceptable and satisfying level of agreement between them.

Micromechanics of stress transfer in shape memory alloy reinforced three-phase composites

2018 ◽  
Vol 29 (15) ◽  
pp. 3151-3164 ◽  
Author(s):  
Fathollah Taheri-Behrooz ◽  
Mohammad Javad Mahdavizade ◽  
Alireza Ostadrahimi
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Thermal Loading ◽  
Hybrid Composites ◽  
Stress Transfer ◽  
Shape Memory Alloy Wire ◽  
Alloy Wire ◽  
Pull Out

Due to the weak interface in shape memory alloy wire–reinforced composites, the influence of interphase on the mechanical properties and stress distribution of hybrid composites is of considerable importance. In this article, a three-cylinder axisymmetric model using a pull-out test is developed to predict stress transfer and interfacial behavior between shape memory alloy wire, interphase, and matrix. In this article, only superelasticity behavior of the shape memory alloy wire is considered. Based on the stress function method and the principle of minimum complementary energy, stress distribution is derived for three different cases in terms of loading and boundary conditions (thermal loading model, intact model, and partially debonded model). Inhomogeneous interphase and different radial and hoop stress components in each phase are considered to achieve deeper physical understanding. Finite element analysis also performed to simulate stress transfer from the wire to the matrix through the interphase. To evaluate the accuracy of this model, the results of the work are compared with the results of the two-cylinder model proposed by Wang et al. and finite element results.

scholarly journals The Instability Improvement of the Symmetric Angle-Ply and Cross-Ply Composite Plates with Shape Memory Alloy Using Finite Element Method

2014 ◽  
Vol 6 ◽  
pp. 632825 ◽  
Author(s):  
Zainudin A. Rasid ◽  
Rizal Zahari ◽  
Amran Ayob
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Element Formulation ◽  
Recovery Stress ◽  
Buckling Behavior ◽  
Post Buckling

Shape memory alloy (SMA) wires were embedded within laminated composite plates to take advantage of the shape memory effect property of the SMA in improving post-buckling behavior of composite plates. A nonlinear finite element formulation was developed for this study. The plate-bending formulation used in this study was developed based on the first order shear deformation theory, where the von Karman's nonlinear moderate strain terms were added to the strain equations. The effect of the SMA was captured by adding recovery stress term in the constitutive equation of the SMA composite plates. Values of the recovery stress of the SMA were determined using Brinson's model. Using the principle of virtual work and the total Lagrangian approach, the final finite element nonlinear governing equation for the post-buckling of SMA composite plates was derived. Buckling and post-buckling analyses were then conducted on the symmetric angle-ply and cross-ply SMA composite plates. The effect of several parameters such as the activation temperature, volume fraction, and the initial strain of the SMA on the post-buckling behavior of the SMA composite plates were studied. It was found that significant improvements in the post-buckling behavior for composite plates can be attained.

scholarly journals Finite Element Modeling of A phenomenological Constitutive Model for Super-elastic Shape Memory Alloy and its Application for Preload Process Analysis of Bolted Joint

2018 ◽  
Author(s):  
Xiangjun Jiang ◽  
Jin Huang ◽  
Yongkun Wang ◽  
Fengqun Pan ◽  
Baotong Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Constitutive Model ◽  
Shape Memory ◽  
Volume Fraction ◽  
Process Analysis ◽  
Bolted Joint ◽  
Integration Algorithm ◽  
Applied Loading ◽  
Proposed Model

A phenomenological constitutive model is developed to describe the uniaxial transformation ratcheting behaviors of super–elastic shape memory alloy (SMA) by employing a cosine–type phase transformation equation with the initial martensite evolution coefficient that can capture the feature of the predictive residual martensite accumulation evolution and the nonlinear hysteresis loop on a finite element (FE) analysis framework. The effect of the applied loading level on transformation ratcheting are considered in the proposed model. The evolutions of transformation ratcheting and transformation stresses are constructed as the function of the accumulated residual martensite volume fraction. The FE implementation of the proposed model is carried out for the numerical analysis of transformation ratcheting of the SMA bar element. The integration algorithm and the expression of consistent tangent modulus are deduced in a new form for the forward and reverse transformation. The numerical results are compared with those of existing model and the experimental results to show the validity of the proposed model and its FE implementation in transformation ratcheting. Finally, a FE modeling is established for a repeated preload analysis of SMA bolted joint

Nonlinear two-dimensional finite element model for transient and damping analysis of cylindrical sandwich panels with pseudoelastic shape memory alloy composite face sheets

2017 ◽  
Vol 21 (1) ◽  
pp. 19-76 ◽  
Author(s):  
Maryam Khanjani ◽  
Mahmoud Shakeri ◽  
Mojtaba Sadighi
Keyword(s):  
Finite Element ◽  
Phase Transformation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Volume Fraction ◽  
Element Model ◽  
Martensite Phase ◽  
Governing Equations ◽  
Time Step ◽  
Composite Face

A new nonlinear finite element model is proposed for the dynamic analysis of cylindrical sandwich panels with shape memory alloy hybrid composite face sheets and flexible core. In order to present a realistic transient vibration analysis, all the material complexities arising from the instantaneous and spatial martensite phase transformation of the shape memory alloy wires are taken into consideration. The one-dimensional constitutive equation proposed by Boyd and Lagoudas is used for modeling the pseudoelastic behavior of the shape memory alloy wires. Since the martensite volume fraction at each point depends on the stress at that point, the phase transformation kinetic equations and the governing equations are coupled together. Therefore, at each time step, an iterative method should be used to solve the highly nonlinear equations. Moreover, considering that the stress resultants generated by the martensite phase transformation in the wires are path-dependent values, an incremental method is used to estimate the increment of the stress resultants at each time step. The governing equations are derived based on the energy method and Newmark time integration method is used to solve the discretized finite element equations. Finally, several numerical examples are presented to examine the effect of various parameters such as intensity of applied pressure load, operating temperature, location of shape memory alloy wires, volume fraction of the shape memory alloy wires, and also boundary conditions upon the loss factor for panels with different aspect ratios.

scholarly journals Galerkin Weighted Residual Method for Axially Functionally Graded Shape Memory Alloy Beams

2019 ◽  
Vol 36 (3) ◽  
pp. 331-345
Author(s):  
Z. T. Kang ◽  
Z. Y. Wang ◽  
B. Zhou ◽  
S. F. Xue
Keyword(s):  
Elastic Modulus ◽  
Martensitic Transformation ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Geometrical Shape ◽  
Weighted Residual Method ◽  
Concentrated Load ◽  
Residual Method

ABSTRACTThis paper focus on the mechanical and martensitic transformation behaviors of axially functionally graded shape memory alloy (AFG SMA) beams. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus, critical transformation stresses and maximum transformation strain vary continuously along the longitudinal direction. According to the simplified linear SMA constitutive equations and Bernoulli-Euler beam theory, the formulations of stress, strain, martensitic volume fraction and governing equations of the deflection, height and length of transformed layers are derived. Employing the Galerkin’s weighted residual method, the governing differential equation of the deflection is solved. As an example, the bending behaviors of an AFG SMA cantilever beam subjected to an end concentrated load are numerically analyzed using the developed model. Results show that the mechanical and martensitic transformation behaviors of the AFG SMA beam are complex after the martensitic transformation of SMA occurs. The influences of FG parameter on the mechanical behaviors and geometrical shape of transformed regions are obvious, and should be considered in the design and analysis of AFG SMA beams in the related regions.

Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method

2010 ◽  
Vol 224 (4) ◽  
pp. 757-769 ◽  
Author(s):  
S K Panda ◽  
B N Singh
Keyword(s):  
Finite Element ◽  
Shape Memory Alloy ◽  
Spherical Shell ◽  
Shape Memory ◽  
Volume Fraction ◽  
Laminated Composite ◽  
Linear Finite Element ◽  
Non Linear ◽  
Post Buckling ◽  
Shell Panel

In this article, the buckling and post-buckling behaviours of a laminated composite spherical shallow shell panel embedded with shape memory alloy (SMA) fibres are studied under a thermal environment. System equations for a laminated composite spherical shell panel embedded with SMA fibres are for the first time derived by modelling the geometric non-linearity in the Green—Lagrange sense and the material non-linearity in SMA fibres in the framework of the higher-order shear deformation theory. The shell panel model is discretized by using a non-linear finite-element approach. The governing algebraic equations are then derived by the variational approach and solved using a direct iterative technique. Influences of the thickness ratio, boundary condition, aspect ratio, curvature ratio, lamination scheme, SMA volume fraction, percentage of prestrain, and amplitude ratio on the buckling and post-buckling temperatures of a laminated composite shell panel with and without SMA have been examined in detail. The results are computed using the present model and compared with those available in the literature.

A constitutive model for Fe-based shape memory alloy considering martensitic transformation and plastic sliding coupling: Application to a finite element structural analysis

2012 ◽  
Vol 23 (10) ◽  
pp. 1143-1160 ◽  
Author(s):  
Walid Khalil ◽  
Alain Mikolajczak ◽  
Céline Bouby ◽  
Tarak Ben Zineb
Keyword(s):  
Finite Element ◽  
Phase Transformation ◽  
Structural Analysis ◽  
Shape Memory Alloy ◽  
Constitutive Model ◽  
Shape Memory ◽  
Internal Variables ◽  
Thermomechanical Loading ◽  
Proposed Model ◽  
Numerical Tool

In this article, we propose a finite element numerical tool adapted to a Fe-based shape memory alloy structural analysis, based on a developed constitutive model that describes the effect of phase transformation, plastic sliding, and their interactions on the thermomechanical behavior. This model was derived from an assumed expression of the Gibbs free energy taking into account nonlinear interaction quantities related to inter- and intragranular incompatibilities as well as mechanical and chemical quantities. Two scalar internal variables were considered to describe the phase transformation and plastic sliding effects. The hysteretic and specific behavior patterns of Fe-based shape memory alloy during reverse transformation were studied by assuming a dissipation expression. The proposed model effectively describes the complex thermomechanical loading paths. The numerical tool derived from the implicit resolution of the nonlinear partial derivative constitutive equations was implemented into the Abaqus® finite element code via the User MATerial (UMAT) subroutine. After tests to verify the model for homogeneous and heterogeneous thermomechanical loadings, an example of Fe-based shape memory alloy application was studied, which corresponds to a tightening system made up of fishplates for crane rails. The results we obtained were compared to experimental ones.

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