Wael Zaki
KUSTAR, Mechanical Engineering, Faculty Member
- ---edit
Shape memory alloys (SMAs) are often used in applications involving time-varying loads. Under such conditions, fatigue leading to possible fracture is a paramount cause of failure, which has been extensively investigated since the 1960s.... more
Shape memory alloys (SMAs) are often used in applications involving time-varying loads. Under such conditions, fatigue leading to possible fracture is a paramount cause of failure, which has been extensively investigated since the 1960s. This work reviews developments in this field with emphasis on recent results related to additively manufactured SMAs. Multiple factors influencing structural and functional degradation in presence of cyclic loading are considered, including microstructural and surface features, thermal loading history, and heat treatment. For completeness, select modeling approaches proposed in the literature to predict SMA fatigue are briefly overviewed and a discussion is provided on the statistical relevance and uncertainty of published data. Conclusions are then formulated to guide subsequent research.
Research Interests:
Research Interests:
Based on the ZM model for shape memory alloys, an analytical model is derived for a functionally graded material (FGM)/shape memory alloy (SMA) laminated composite cantilever beam subjected to concentrated force at the tip. The beam... more
Based on the ZM model for shape memory alloys, an analytical model is derived for a functionally graded material (FGM)/shape memory alloy (SMA) laminated composite cantilever beam subjected to concentrated force at the tip. The beam consists of a SMA core layer bonded to identical FGM layers on both sides. The FGM layer is considered to be elastic with an equivalent Young’s modulus related to those of the constituents by means of a power law. Phase transformation within the SMA layer is accounted for in deriving the analytical relations, which are validated against finite element analysis results.
Research Interests:
Research Interests:
This paper intends to describe the process of derivation of loading surfaces with respect to phase transformation, when a structure is subjected to cyclic loading. This structure is realized as a Schwarz Primitive unit cell, for which... more
This paper intends to describe the process of derivation of loading surfaces with respect to phase transformation, when a structure is subjected to cyclic loading. This structure is realized as a Schwarz Primitive unit cell, for which only 1/16th part is considered, due to the symmetry conditions. Displacement boundary conditions are applied to realize the periodicity of the unit cell, thus simulating the presence of adjacent unit cells. A homogenization of the stress fields is done, so as to obtain volume-averaged values that represent the whole domain. One limitation of the employed constitutive model is not considering plasticity. The large stresses observed in the results would be alleviate in a real application by plastic deformation. Another limitation of the model is not considering a thermomechanical coupling. Therefore, the heat that would be generated depending on the frequency employed is not taken into account. Thus, the frequency of the applied displacements only plays ...
Research Interests:
All in-text references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Research Interests:
Research Interests:
A novel theoretical model for a laminate cantilever beam consisting of numerous superelastic shape memory alloy (SMA) layers, based on the ZM model and Timoshenko theory is introduced. The mathematical equations are first developed to... more
A novel theoretical model for a laminate cantilever beam consisting of numerous superelastic shape memory alloy (SMA) layers, based on the ZM model and Timoshenko theory is introduced. The mathematical equations are first developed to predict and describe the internal material structure of laminated beam, according to the solid phase transformation in SMA layers. Then, the theoretical expression of the moment and shear force for a superelastic SMA composite cantilever beam is derived. The proposed model is validated against a 3D finite element analysis model (FEA), giving very good agreement in each case. The moment-curvature response, and distribution of martensite volume fraction and axial stress along the beam length are investigated.
Research Interests:
This work develops a novel torsional theory for a radially functionally graded (FG) porous shape memory alloy (SMA) circular bar. Prior to the theoretical development, the effective three-dimensional (3D) phenomenological constitutive... more
This work develops a novel torsional theory for a radially functionally graded (FG) porous shape memory alloy (SMA) circular bar. Prior to the theoretical development, the effective three-dimensional (3D) phenomenological constitutive model for SMAs with high porosity is proposed. To help derive successfully the theory, the pure shear-driven material parameters in the effective model are expressed in the cubic polynomial. Subsequently, the torsional theory for radially FG porous SMA circular bar is derived considering the evolution of effective phase evolution in the bar. This phase evolution consideration guarantees the accuracy of the developed theory. Indeed, the soundness of effective constitutive model is confirmed by 3D finite element method (FEM) simulation of porous SMA structure in Abaqus using the well-established ZM’s model for dense SMAs. Specifically, the simulating results in terms of the shear stress-shear strain response obtained from two prediction methods consideri...
Research Interests:
The paper presents results of finite element analysis of architectured iron-based shape memory alloy (SMA) samples consisting of bulk SMA and void combined to different proportions and according to different geometric patterns. The finite... more
The paper presents results of finite element analysis of architectured iron-based shape memory alloy (SMA) samples consisting of bulk SMA and void combined to different proportions and according to different geometric patterns. The finite element simulation uses a constitutive model for iron-based SMAs that was recently developed by the authors in order to account for the behavior of the bulk material. The simulation of the architectured SMA is then carried out using a unit cell method to simplify calculations and reduce computation time. For each unit cell, periodic boundary conditions are assumed and enforced. The validity of this assumption is demonstrated by comparing the average behavior of one unit cell to that of a considerably larger sample comprising multiple such cells. The averaging procedure used is implemented numerically, by calculating volume averages of mechanical fields such as stress and strain over each finite element model considered as a combination of mesh elem...
Research Interests: Materials Science and Sma
Abstract In this study, we propose a novel and simple exact semi-analytical model for superelastic Shape Memory Alloy (SMA) wire reinforced composites subjected to bending loads. In order to study the mechanical response of the composite... more
Abstract In this study, we propose a novel and simple exact semi-analytical model for superelastic Shape Memory Alloy (SMA) wire reinforced composites subjected to bending loads. In order to study the mechanical response of the composite during loading/unloading, a Representative Volume Element (RVE) is extracted to examine the bending response of the composite. Analytical moment-curvature, and shear force-shear strain relations are derived based on a 3-Dimensional (3D) thermomechanical SMA model and Timoshenko beam theory. The composite Simpson’s rule is adopted to numerically solve the exact analytical moment-curvature and shear force-shear strain relationships. Results including the moment-curvature response, axial stress distribution along the vertical and longitudinal directions, martensite volume fraction, and the tip deflection are reported and validated against 3D finite element simulations. The influence of temperature, martensite volume fraction distribution, and matrix stiffness on the mechanical performance of the composite is also investigated. In particular, the composite is found to behave superelastically under certain conditions of temperature, SMA volume fraction, and elastic stiffness of the matrix. Such behavior is advantageous in applications requiring large recoverable strains or high energy dissipation density.
Research Interests:
Research Interests:
A new model is proposed to describe the response of laminated composite beams consisting of one shape memory alloy layer and one functionally graded material layer. The model accounts for asymmetry in tension and compression of the shape... more
A new model is proposed to describe the response of laminated composite beams consisting of one shape memory alloy layer and one functionally graded material layer. The model accounts for asymmetry in tension and compression of the shape memory alloy behavior and successfully describes the dependence of the position of the neutral surface on phase transformation within the shape memory alloy and on the load direction. Moreover, the model is capable of describing the response of the composite beam to both loading and unloading cases. In particular, the derivation of the equations governing the behavior of the beam during unloading is presented for the first time. The effect of the functionally graded material gradient index and of temperature on the neutral axis deviation and on the overall behavior of the beam is also discussed. The results obtained using the model are shown to fit three-dimensional finite element simulations of the same beam.
Research Interests:
In this article, a new analytical model is proposed for laminated composite cantilever beams consisting of multiple alternating superelastic shape memory alloy and elastic layers. The model is based on the Zaki–Moumni model for shape... more
In this article, a new analytical model is proposed for laminated composite cantilever beams consisting of multiple alternating superelastic shape memory alloy and elastic layers. The model is based on the Zaki–Moumni model for shape memory alloys combined with Timoshenko’s beam theory. The Zaki–Moumni model accounts for solid phase transformation as well as detwinning and reorientation of martensite under multiaxial thermomechanical loading conditions. Mathematical formulas are first derived to characterize the evolution of the solid phase structure within the beam with a prescribed load at the tip during loading and unloading. Analytical moment–curvature and shear force–shear strain relations are then obtained following the strength of materials approach. The present work is the first to fully develop the nonlinear expressions of the axial stress in terms of the distance from the neutral plane and to allow the description of the phase distribution in both the longitudinal and the ...
Research Interests:
We propose a new analytical model for a superelastic shape memory alloy prismatic cantilever beam subjected to a concentrated force at the tip. The force is gradually increased and then removed and the corresponding distribution of phase... more
We propose a new analytical model for a superelastic shape memory alloy prismatic cantilever beam subjected to a concentrated force at the tip. The force is gradually increased and then removed and the corresponding distribution of phase transformation fields in the beam is determined, analytically, in both the transverse and longitudinal directions. Analytical moment–curvature and shear force–shear strain relations are also derived during loading and unloading of the beam. The proposed model is validated against an exact numerical beam model as well as a three-dimensional finite element analysis model for the same beam, with very good agreement in each case. Moreover, an experiment is proposed and carried out to characterize the load–deflection response of a shape memory alloy beam under the same boundary conditions as those considered in deriving the model. The obtained response is in good agreement with the analytical model as well as three-dimensional finite element analysis sim...
Research Interests:
Research Interests:
In this review paper, the influence of heat transfer on the thermomechanical behavior of Shape Memory Alloys (SMA) is discussed. Both experimental and theoretical results in the literature associated with this issue are presented and... more
In this review paper, the influence of heat transfer on the thermomechanical behavior of Shape Memory Alloys (SMA) is discussed. Both experimental and theoretical results in the literature associated with this issue are presented and discussed. Moreover, the impact of thermomechanical coupling on the fatigue lifetime of an SMA structure is considered. A novel approach to take into account the seemingly dependence of the fatigue lifetime on the temperature and frequency is proposed.
Research Interests:
Research Interests:
A new macro-scale model of shape memory alloys is developed within the framework of generalized standard materials with internal constraints [Moumni, Z., 1995. Sur la modélisation du changement de phase à l'état... more
A new macro-scale model of shape memory alloys is developed within the framework of generalized standard materials with internal constraints [Moumni, Z., 1995. Sur la modélisation du changement de phase à l'état solide. Ph. D. Thesis, École Nationale ...
Research Interests:
The model in the first part of this paper is extended to account for SMA behavior under cyclic loading. To this end, three new state variables are introduced: internal stress B, residual strain ɛr and cumulated martensite volume fraction... more
The model in the first part of this paper is extended to account for SMA behavior under cyclic loading. To this end, three new state variables are introduced: internal stress B, residual strain ɛr and cumulated martensite volume fraction ze. Several parameters of the ...
Research Interests:
The non-linear dynamic thermomechanical behaviour of superelastic shape memory alloys is investigated. To this end, the Zaki–Moumni model, initially developed for quasi-static loading cases, is extended to simulate the uniaxial forced... more
The non-linear dynamic thermomechanical behaviour of superelastic shape memory alloys is investigated. To this end, the Zaki–Moumni model, initially developed for quasi-static loading cases, is extended to simulate the uniaxial forced oscillations of a shape memory alloy device. First, the influence of loading rate is accounted for by considering the thermomechanical coupling in the behaviour of NiTi shape memory alloy. Comparisons between simulations and experimental results show good agreement. Then, the forced response of a shape memory alloy device is investigated at resonance. Both isothermal and non-isothermal conditions are studied, as well as non-symmetric tensile-compressive restoring force. In the case of large values of forcing amplitudes, simulation results show that the dynamic response is prone to jumps, bifurcations and chaotic solutions.
Research Interests:
... avenue John F. Kennedy, L-1855 Kirchberg, Luxembourg. 2 Materials and Structures Laboratory, École Nationale Supérieure de Techniques Avancées, F-91761 Palaiseau Cedex, France. E-mail: wael.zaki@tudor.lu Abstract. ...
Research Interests:
Research Interests:
Research Interests:
Ce papier présente une extension de la loi Moumni-Son [1] permettant la prise en compte de l'effet superthermique, ainsi qu'une amélioration de la modélisation de la pseudoélasticité et de la réorientation de la... more
Ce papier présente une extension de la loi Moumni-Son [1] permettant la prise en compte de l'effet superthermique, ainsi qu'une amélioration de la modélisation de la pseudoélasticité et de la réorientation de la martensite à basse température.
Research Interests:
In this paper, the effective behavior of shape memory alloy (SMA) triply periodic minimal surface (TPMS) structures is investigated by means of finite element analysis and numerical homogenization. For this purpose, the onset and... more
In this paper, the effective behavior of shape memory alloy (SMA) triply periodic minimal surface (TPMS) structures is investigated by means of finite element analysis and numerical homogenization. For this purpose, the onset and subsequent thresholds of phase transformation are determined considering TPMS primitive, gyroid, and diamond unit cells subjected to different loading conditions. At all relative densities studied, the initial phase transformation loading surfaces corresponding to the different geometries considered are found to be reasonably well represented by the anisotropic Hill’s and von Misses yield criterions. The observed surfaces, either shrink or expand as the effective martensite volume fraction increases, depending on TPMS geometry. The determination of subsequent loading surfaces as a function of the effective volume fraction of martensite shows a nonlinear hardening behavior, which seems to follow a unique trend for the different geometries considered. Ultimat...
Research Interests:
The study deals with a development of a novel analytical model based on extended ZM’s model together with Timoshenko beam theory for a superelastic shape memory alloy (SMA) cantilever beam taking into account the tension-compression... more
The study deals with a development of a novel analytical model based on extended ZM’s model together with Timoshenko beam theory for a superelastic shape memory alloy (SMA) cantilever beam taking into account the tension-compression asymmetry stress effect during loading/unloading process. The beam structure evolution is first identified by the trial method based on the geometric relation and force equilibrium. Subsequently, an analytical moment-curvature-neutral axis deviation and shear force-shear strain relations are derived for the identified beam structure. The moment-curvature response from theoretical model based on asymmetric effect, and theory and 3D FEM based on symmetric effect are shown to reveal the difference between them. Subsequently, the neutral axis deviation-tip load response and distribution of mertensite volume fraction along the beam length obtained from theory and 3D FEM based on asymmetric effect is demonstrated.
Research Interests:
Abstract This paper presents a new thermomechanically coupled constitutive model for polycrystalline shape memory alloys (SMAs) undergoing finite deformation. Three important characteristics of SMA behavior are considered in the... more
Abstract This paper presents a new thermomechanically coupled constitutive model for polycrystalline shape memory alloys (SMAs) undergoing finite deformation. Three important characteristics of SMA behavior are considered in the development of the model, namely the effect of coexistence between austenite and two martensite variants, the variation of hysteresis size with temperature, and the smooth material response at initiation and completion of phase transformation. The formulation of the model is based on a multi-tier decomposition of the deformation kinematics comprising, a multiplicative decomposition of the deformation gradient into thermal, elastic and transformation parts, an additive decomposition of the Hencky strain into spherical and deviatoric parts, and an additive decomposition of the transformation stretching tensor into phase transformation and martensite reorientation parts. A thermodynamically consistent framework is developed, and a Helmholtz free energy function consisting of elastic, thermal, interaction and constraint components is introduced. Constitutive and heat equations are then derived from this energy in compliance with thermodynamic principles. Time-discrete formulations of the constitutive equations and a Hencky-strain return-mapping integration algorithm are presented. The algorithm is then implemented in Abaqus/Explicit by means of a user-defined material subroutine (VUMAT). Numerical results are validated against experimental data obtained under various thermomechanical loading conditions. The robustness and efficiency of the proposed framework are illustrated by simulating a SMA helical spring actuator.
Research Interests:
A new analytical model is proposed for superelastic helical SMA springs subjected to axial loading. The model is derived based on the ZM constitutive model for SMAs and is applicable to springs with index greater than 4 and pitch angle... more
A new analytical model is proposed for superelastic helical SMA springs subjected to axial loading. The model is derived based on the ZM constitutive model for SMAs and is applicable to springs with index greater than 4 and pitch angle greater than 15°, which are common specifications in engineering applications. The analytical axial force-deformation relation for the helical spring is derived taking into account phase transformation within the SMA and the model is validated against 3D finite element analysis results.
Research Interests:
Au cours de ce memoire, nous avons presente un modele complet et unifie de comportement des materiaux a memoire de forme et un critere energetique applicable au calcul a la fatigue de structures fonctionnant dans le domaine pseudo... more
Au cours de ce memoire, nous avons presente un modele complet et unifie de comportement des materiaux a memoire de forme et un critere energetique applicable au calcul a la fatigue de structures fonctionnant dans le domaine pseudo elastique. Le modele et le critere sont valides en comparant leurs predictions a des resultats experimentaux. Notre modelisation presente les avantages suivants : – elle est complete, c'est-a-dire qu'elle permet de simuler tous les principaux phenomenes caracteristiques du comportement des MMF. La simulation s'appuie sur une meme loi de comportement et sur un meme ensemble de lois complementaires, ce qui lui confere un caractere unifie ; – les parametres sont simples a identifier ; – l'accord des predictions avec les resultats experimentaux disponibles est satisfaisant ; – etant donne la prise en compte des chargements non proportionnels, il est possible d'effectuer des calculs de structures en MMF soumises a des chargements complexes ; – ...
The ability of shape memory alloys (SMAs) to recover inelastic strains larger than any other metallic alloy has prompted their use in a wide range of applications. However, for the most common SMAs, including NiTi and Cu-based systems,... more
The ability of shape memory alloys (SMAs) to recover inelastic strains larger than any other metallic alloy has prompted their use in a wide range of applications. However, for the most common SMAs, including NiTi and Cu-based systems, fabrication using conventional means raises important challenges, including poor workability and potentially high tool wear. Additive manufacturing offers a direct answer to these challenges by eliminating the need for tooling and allowing the production of samples of complex geometries directly from computer-aided designs. The present work provides a comprehensive review of additive manufacturing applied to various SMA systems, with focus on the influence of process parameters and heat-treatment on the microstructure, printability, and the structural and functional behavior of additively fabricated samples.
A new analytical model is derived for cantilever beams made from superelastic shape memory alloy and subjected to tip load. The deformation of the beam is described based on Timoshenko beam theory using constitutive relations that account... more
A new analytical model is derived for cantilever beams made from superelastic shape memory alloy and subjected to tip load. The deformation of the beam is described based on Timoshenko beam theory using constitutive relations that account for asymmetric shape memory alloy response in tension and compression. Analytical moment and shear force equations are developed and the position of the neutral axis and the different solid phase regions in the beam are tracked throughout a full loading–unloading cycle. Validation of the proposed model is carried out against data from the literature and from the finite element analysis considering tensile–compressive asymmetry in shape memory alloy behavior.
Research Interests:
Abstract A new model is proposed for a composite laminated beam comprising multiple alternating shape memory alloy (SMA) and elastic layers. The model fully considers asymmetry in SMA behavior, which is found to significantly influence... more
Abstract A new model is proposed for a composite laminated beam comprising multiple alternating shape memory alloy (SMA) and elastic layers. The model fully considers asymmetry in SMA behavior, which is found to significantly influence the behavior of the laminates. Moreover, the equations governing the response of the SMA-reinforced beams are derived for a complete loading-unloading cycle considering a Timoshenko beam deformation model combined with well-established constitutive relations for SMAs. The derivation procedure involves first identifying the solid phase structure of the beam for a given applied load, followed by integration of the stress and strain in a cross section to obtain moment and shear force equations. The influence of temperature, as well as of layer thickness and material properties on the bending response of the beam is investigated. The results obtained using the proposed model are found to agree with finite element simulations.
Research Interests:
Abstract A new model is proposed for the behavior of superelastic shape memory alloy (SMA) helical springs with large index. The derived governing equations consider the response of the spring to monotonic loading followed by complete... more
Abstract A new model is proposed for the behavior of superelastic shape memory alloy (SMA) helical springs with large index. The derived governing equations consider the response of the spring to monotonic loading followed by complete unloading. In particular, the relation between axial force and axial deformation and the distribution of shear stress in a cross section of the spring wire are determined analytically for the entire loading-unloading cycle. Special attention is given to modeling the unloading stage, for which the proposed solution improves upon existing literature. The model is validated by comparison to 3D finite element simulations and the governing equations are used to investigate the influence of temperature, wire radius and mean radius on the superelastic behavior of a sample SMA spring.
Research Interests:
Abstract A new analytical model is developed for concrete composite beams reinforced with multiple superelastic shape memory alloy (SMA) circular bars and subjected to bending. The model is derived based on the three-dimensional (3D) ZM... more
Abstract A new analytical model is developed for concrete composite beams reinforced with multiple superelastic shape memory alloy (SMA) circular bars and subjected to bending. The model is derived based on the three-dimensional (3D) ZM model for SMAs combined with Timoshenko beam theory. Mathematic formulas are first developed to predict and describe the internal material structure of the composite taking into account solid phase transformation in the SMA bars. Analytical expressions are then obtained for the moment-curvature and shear force-shear strain relations. The present work is the first to derive nonlinear expressions for the axial stress and elastic moduli of regions experiencing phase transformation within SMA in the vertical y - coordinate and the evolution of phase transformation along the axial and transverse directions in the SMA bars during unloading. The proposed model is validated against 3D finite element analysis (FEA) results for the same beam. It is found that the superelasticity of the beam is further enhanced with temperature closer to austenitic finish temperature, higher SMA volume percentage, higher number of SMA bars, and location of SMA bars further away from the neutral plane. In contrast, the magnitude of the austenitic and martensitic moduli were found to have negligible influence on superelasticity.
Research Interests:
Research Interests:
Research Interests:
The mechanical behavior of a solid capable of undergoing internal phase change is considered. Reversible and dissipative constitutive equations are established within the framework of generalized standard materials with internal... more
The mechanical behavior of a solid capable of undergoing internal phase change is considered. Reversible and dissipative constitutive equations are established within the framework of generalized standard materials with internal constraints. These constraints ...
Research Interests: Materials Engineering, Mechanical Engineering, Civil Engineering, Plasticity, Chaos Theory Evolution Equation, and 14 moreShape Memory Alloys, Phase Change, Shape Memory Alloy, Dissipation, Phase Transformation, Strain Energy, Numerical Model, Lagrange Multiplier, Shape Memory Effect, Experimental Data, Constitutive Equation, Superelasticity, Energy function, and Evolution Equation
Research Interests:
Research Interests:
Research Interests:
Research Interests: Materials Engineering, Mechanical Engineering, Civil Engineering, Plasticity, Modeling, and 15 moreHeat Transfer, Finite element method, Finite Elements, Finite Element, Shape Memory Alloys, High strain rate testing, Shape Memory Alloy, Free Energy, Constitutive model, Boundary Value Problem, Experimental Data, Constitutive Equation, Heat Equation, Hysteresis Loop, and Latent Heat
Research Interests:
The article focuses on the numerical simulation of the thermomechanical behavior of steel T-stubs connected by iron-based shape memory alloys bolts. The three-dimensional macroscopic model used in this work was previously developed by the... more
The article focuses on the numerical simulation of the thermomechanical behavior of steel T-stubs connected by iron-based shape memory alloys bolts. The three-dimensional macroscopic model used in this work was previously developed by the authors considering different thermomechanical properties between austenite and martensite, and coupling between phase transformation and plasticity. The model is implemented in a UMAT code using an implicit time-discrete integration scheme that follows a “multisurface plasticity”-like approach. The numerical results show that the shape memory effect can be used to preload the bolt if the initial length of its shank is less than the total thickness of the flanges. For an initial shank length of 21.38 mm and a total flange thickness of 21.4 mm, the shape memory effect produced average contact forces of 101 N between the bolt head and the flange, and 37 N between the two flanges. The resulting average contact pressures were 210 and 25 MPa, respective...