Thermomechanical Behavior Of Shape Memory Alloys Research Articles

Nonlinear Mechanics of a Smart Biotensegrity Human Foot Prosthesis

This work deals with the nonlinear mechanics of smart bioinspired tensegrity structures. A minimal regular tensegrity prism actuated by shape memory alloy (SMA) elements is investigated to represent a human foot. A formulation considering the force density matrix approach is used to model the equilibrium equations of the tensegrity structure based on node mapping. Lagrange multipliers are employed to represent constraints. The SMA thermomechanical behavior is described by considering a modified polynomial constitutive model. Numerical simulations are developed from an optimization procedure employing the Levenberg–Marquardt method. An investigation of the tensegrity capability to model a human foot is carried out analyzing either mechanical or physiological aspects of the tensegrity prosthesis. The mechanical performance is compared with high performance prostheses available on the market, showing that it is an interesting alternative with respect to mechanical resistance. Regarding physiology, foot movements are properly mimicked from SMA actuation.

Analysis of One-Dimensional Ivshin-Pence Shape Memory Alloy Constitutive Model for Sensitivity and Uncertainty.

Shape memory alloys (SMAs) are classified as smart materials due to their capacity to display shape memory effect and pseudoelasticity with changing temperature and loading conditions. The thermomechanical behavior of SMAs has been simulated by several constitutive models that adopted microscopic thermodynamic or macroscopic phenomenological approaches. The Ivshin–Pence model is one of the most popular SMA macroscopic phenomenological constitutive models. The construction of the model requires involvement of parameters that possess inherent uncertainty. Under varying operating temperatures and loading conditions, the uncertainty in these parameters propagates and, therefore, affects the predictive power of the model. The propagation of uncertainty while using this model in real-life applications can result in performance discrepancies or failure at extreme conditions. In this study, we employed a probabilistic approach to perform the sensitivity and uncertainty analysis of the Ivshin–Pence model. Sobol and extended Fourier Amplitude Sensitivity Testing (eFAST) methods were used to perform the sensitivity analysis for simulated isothermal loading/unloading at various operating temperatures. It is evident that the model’s prediction of the SMA stress–strain curves varies due to the change in operating temperature and loading condition. The average and stress-dependent sensitivity indices present the most influential parameters at several temperatures.

Numerical Analysis of Growing the Ductile Damage in Structures Reinforced by SMA Using Continuum Damage Mechanics Approach

In this paper, the numerical study on mechanical behavior of materials reinforced with shape memory alloys (SMAs) in framework of continuum damage mechanics has been investigated. The investigated structure is an aluminum notched piece reinforced with SMA under tension loading. Simulation of the structure has been conducted with nonlinear finite element method. In numerical simulations, the SMA is embedded in the aluminum material and it is assumed that there is no slip between the aluminum and SMAs. To properly account for the mechanical behavior with damage effects, Lemaitre constitutive model via UMAT code have been developed. Simulation results were verified by experimental results. The Brinson model is used to consider the thermomechanical behavior of SMA. The simulation results showed that the mechanical behavior of aluminum with reinforced aluminum is rather different. Also, the presence of SMAs in the notched piece leads to increasing the energy absorption, piece fracture in higher loadings and a decreasing in the damage growth rate.

Nonlinear dynamics of an adaptive origami-stent system

Origami is an ancient art of the paper folding that has been the source of inspiration in many engineering designs due to its intrinsic ability of changing shape and volume. Self-expandable devices have been created based on origami concept together with smart materials. Shape memory alloys belong to this class of materials and provide high forces and large displacements by varying their temperature. This work deals with the nonlinear dynamics of an origami-stent, a cylindrical shaped origami structure, which has the capacity of changing its radius. The actuation is provided by antagonistic torsional shape memory alloy wires placed in the origami creases. The mathematical model assumes a polynomial constitutive model to describe the shape memory alloy thermomechanical behavior. Geometric assumptions establish a one-degree of freedom model with constitutive and geometric nonlinearities. Numerical simulations are carried out considering different thermomechanical loadings that represent operational conditions. The system presents complex responses including chaos.

A three-dimensional description of shape memory alloy thermomechanical behavior including plasticity

This paper introduces a novel three-dimensional constitutive model that describes the thermomechanical behavior of shape memory alloys (SMAs). The model is developed within the framework of continuum mechanics and the standard generalized materials. Four macrocospic phases are considered associated with austenite and three variants of martensite. Phase transformations can be induced by temperature, volumetric and deviatoric strains. The description of plasticity is also of concern assuming kinematic and isotropic hardening. Numerical simulations are carried out showing that the proposed model is able to capture the general thermomechanical behavior of SMAs for uniaxial and multiaxial tests, even in situations with complex thermomechanical loading paths.

UNCERTAINTY ANALYSIS OF A ONE-DIMENSIONAL CONSTITUTIVE MODEL FOR SHAPE MEMORY ALLOY THERMOMECHANICAL DESCRIPTION

The use of shape memory alloys (SMAs) in engineering applications has increased the interest of the accuracy analysis of their thermomechanical description. This work presents an uncertainty analysis related to experimental tensile tests conducted with shape memory alloy wires. Experimental data are compared with numerical simulations obtained from a constitutive model with internal constraints employed to describe the thermomechanical behavior of SMAs. The idea is to evaluate if the numerical simulations are within the uncertainty range of the experimental data. Parametric analysis is also developed showing the most sensitive constitutive parameters that contribute to the uncertainty. This analysis provides the contribution of each parameter establishing the accuracy of the constitutive equations.

Analysis of Thermo-Mechanical Behavior of Shape Memory Alloys

Shape Memory Alloy (SMA) is widely used and plays an important role in various engineering fields due to its special characteristics of shape memory effect and super-elasticity. In this paper the phase transformation behavior and thermo-mechanics behavior of 50.0at%Ni-Ti SMA are investigated though differential scanning colorimeter (DSC) and tensional tests respectively. Optical micrographs show the transformation of austenite and twinned martensite. The comparing numerical calculation result with tensional test result shows the new macro-mechanical constitutive equation can express the thermo-mechanical behavior of SMA effectively.

Tensile-compressive asymmetry influence on shape memory alloy system dynamics

The remarkable properties of shape memory alloys (SMAs) are attracting much technological interest in several science and engineering fields, varying from medical to aerospace applications. Hysteretic response of these systems is one of their essential characteristics being related to the martensitic phase transformation. The dynamical response of systems with SMA actuators presents a rich behavior due to their intrinsic nonlinear characteristic. Since experimental results show that SMAs present an asymmetric behavior when subjected to tensile or compressive loads, it is important to evaluate the influence of this kind of behavior in the nonlinear dynamics of mechanical systems with SMA devices. This article discusses the nonlinear dynamics of shape memory alloy systems, considering the influence of tensile-compressive asymmetry in the thermomechanical behavior of SMAs. An iterative numerical procedure based on the operator split technique, the orthogonal projection algorithm and the fourth-order Runge–Kutta method is developed to deal with nonlinearities in the formulation. A numerical investigation is carried out showing some qualitative results such as chaotic-like response and multi-stability behavior for a single degree of freedom SMA oscillator.

Meshfree modelling and simulation of the thermomechanical behaviour of shape memoryalloys

This paper presents the numerical modelling and simulation of the nonlinearthermomechanical behaviour of shape memory alloys via a meshfree technique. To describethe martensitic phase transformation and related shape memory effect efficiently,a finite strain constitutive model is formulated similar to that from plasticitytheory. The model takes into account the stress and temperature induced phasetransformation in the alloy. Simplified to be a thermoelastic phase transformationproblem, a constitutive integration algorithm developed in plasticity theory isapplied and numerically implemented in the present model. A nonlinear meshfreeprocedure is developed to numerically simulate the shape memory alloy materialbehaviour. The advantage of the present meshfree procedure lies in its ability forlarge deformation analysis, point-based approximation coinciding with point-wisephase transformation, and continuous stress/strain solution benefitting the phasetransformation determination as well as the convergence of the Newton iterationprocedure. Several numerical tests are presented to illustrate the potential of thepresent shape memory alloy constitutive model, the algorithm and the meshfreeprocedure. The process of stress and thermally induced phase transformationcan be captured. Hysteresis loops in the loading and unloading procedure areproduced.

A constitutive model for shape memory alloys considering tensile–compressive asymmetry and plasticity

Shape memory alloys (SMAs) are materials that present, among other characteristics, the capacity to undergo large permanent strains, and then, after a proper increase on the temperature, recover its original shape. Constitutive models consider phenomenological aspects of thermomechanical behavior of these alloys. The present contribution proposes a constitutive model to consider both the tensile–compressive asymmetry and plastic strains that occur in the thermomechanical behavior of SMAs. A numerical procedure is proposed in order to deal with nonlinearities of the formulation. Comparisons between experimental and numerical results predicted by the proposed model show that they are in close agreement. Moreover, numerical simulations show that the model is capable to capture the general behavior of SMAs, allowing the description of important characteristics of these alloys as pseudo-elasticity, one-way and two-way shape memory effect, phase transformation due to temperature variations, internal sub-loops due to incomplete phase transformations and tensile–compressive asymmetry.

Hysteresis in shape-memory alloys

We present an overview of hysteresis phenomena in the martensitic transformation, and their relevance in the thermomechanical behaviour of shape-memory alloys. The first part of the paper introduces the concept of hysteresis, and the related phenomena of branching, dissipation and memory. The second part deals with revising some aspects of the thermomechanical behaviour of shape-memory alloys, emphasizing the hysteretic behaviour of single crystals and polycrystals under different driving conditions. The last part of the work is dedicated to the problem of modelling hysteresis phenomena in shape-memory alloys. Our focus is on phenomenological approaches which, as shown in the paper, account for the memory properties observed in hysteretic trajectories and open the possibility of deriving a generic energy balance for systems with hysteresis.

Description of an Fe-based shape memory alloy thermomechanical behavior in terms of the synthetic model

The phenomenological two-level synthetic model of the non-linear deformation has been used for reflection of the interaction of deformational processes of principally different origin (martensitic, dislocational): the yield stress of a material in the two-phase state depends on the respective amount of the martensite. In the martensite deformation investigation the residual oriented microstresses action is taken into account. The principle advantages of the synthetic model – such as mathematical simplicity – are considered. The approach leads to the reliable description of the cyclic shape memory effect taking place under complex modes of temperature-stress investigations. Applicability of the model for description of deformational behavior of the modern Fe-based SME alloy has been demonstrated.

Characterization of NiTi Materials Using a Novel Aces Methodology

AbstractEffective use of Shape Memory Alloys (SMAs) depends upon detailed knowledge of their thermiomechanical behavior. In this paper, thermomechanical behavior of SMAs is studied using a novel ACES methodology. More specifically, variation of modulus of elasticity of equiatomic NiTi is studied, as a function of temperature. The results show that the modulus of elasticity of the NiTi studied herein varies from 38 GPa to 72 GPa as the temperature changes from –15 °C to 190°C, corresponding to phase transition from martensite to austenite. Comparison of Analytical, Computational, and Experimental Solutions (ACES) results showed good correlation.

Quantitative description of physicomechanical processes in shape-memory materials

We propose a model for a quantitative description of the thermomechanical behavior of shape-memory alloys based on methods of the thermodynamics of irreversible processes and continuum mechanics. We deduce equations of state, formulate balance relations of the model, and present necessary and sufficient conditions for direct and reverse martensite transformations under thermal and mechanical loading.