A review of constitutive models and modeling techniques for shape memory alloys (original) (raw)

An overview of constitutive models for shape memory alloys

Mathematical Problems in Engineering, 2006

The remarkable properties of shape memory alloys have facilitated their applications in many areas of technology. The purpose of this paper is to present an overview of thermomechanical behavior of these alloys, discussing the main constitutive models for their mathematical description. Metallurgical features and engineering applications are addressed as an introduction. Afterwards, five phenomenological theories are presented. In general, these models capture the general thermomechanical behavior of shape memory alloys, characterized by pseudoelasticity, shape memory effect, phase transformation phenomenon due to temperature variation, and internal subloops due to incomplete phase transformations.

A three-dimensional constitutive model for shape memory alloys

Archive of Applied Mechanics, 2010

Shape memory alloys (SMAs) are materials that, among other characteristics, have the ability to present high deformation levels when subjected to mechanical loading, returning to their original form after a temperature change. Literature presents numerous constitutive models that describe the phenomenological features of the thermomechanical behavior of SMAs. The present paper introduces a novel three-dimensional constitutive model that describes the martensitic phase transformations within the scope of standard generalized materials. The model is capable of describing the main features of the thermomechanical behavior of SMAs by considering four macroscopic phases associated with austenitic phase and three variants of martensite. A numerical procedure is proposed to deal with the nonlinearities of the model. Numerical simulations are carried out dealing with uniaxial and multiaxial single-point tests showing the capability of the introduced model to describe the general behavior of SMAs. Specifically, uniaxial tests show pseudoelasticity, shape memory effect, phase transformation due to temperature change and internal subloops due to incomplete phase transformations. Concerning multiaxial tests, the pure shear stress and hydrostatic tests are discussed showing qualitatively coherent results. Moreover, other tensile-shear tests are conducted modeling the general three-dimensional behavior of SMAs. It is shown that the multiaxial results are qualitative coherent with the related data presented in the literature.

Some Remarks on the Modelling of the Thermomechanical Behaviour of Shape Memory Alloys

Le Journal de Physique IV, 1991

Our aim is to examine from the continuum thermodynamic point of view, some models predicting the pseudoelastic behaviour of shape memory alloys. We investigate the choice of states variables, the structure of free energy and complementary laws. A special emphasis is made on generalized standard models. In the state of art, there is a lot of progress to do for modelling the behaviour of shape memory alloys.

On the thermomechanical modeling of shape memory alloys

International Journal of Non-Linear Mechanics, 2004

In this work, a general inelastic framework for the derivation of general three-dimensional thermomechanical constitutive laws for materials undergoing phase transformations is proposed. The proposed framework is based on the generalized plasticity theory and on some basic elements from the theory of continuum damage mechanics. More speciÿcally, a new elaborate formulation of generalized plasticity theory capable of accommodating the multiple and interacting loading mechanisms, which occur during the phase transformations, is developed. Furthermore, the sti ness variations occurring during phase transformations are taken into account by the proposed framework. For this purpose, the free energy is decomposed into elastic and inelastic parts, not in a conventional way, but in one which resembles the elastic-damage cases. Also, a rate-dependent version of the theory is provided. The concepts presented are applied for the derivation of a three-dimensional thermomechanical constitutive model for Shape Memory Alloy materials. Numerical simulations to show qualitatively the ability of the model to capture the behavior of the shape memory alloys are also presented. Furthermore, the model has been ÿtted to actual experimental results from the literature. ?

On the Fremond’s constitutive model for shape memory alloys

Mechanics Research Communications, 2004

The remarkable properties of shape memory alloys have increasing the interest in applications in different areas varying from biomedical to aerospace hardware. Despite the large number of applications, the modeling of SMA is the objective of many researches developed in order to describe all details of its thermomechanical behavior. The present contribution revisits a constitutive model presented by , which is built up on the classical FremondÕs model, in order to contemplate the horizontal enlargement of the stress-strain hysteresis loop. Numerical simulations present qualitative agreement with experimental data, showing pseudoelastic, one-way and two-way shape memory effects.

A macro-mechanical constitutive model of shape memory alloys

Science China-physics Mechanics & Astronomy, 2009

It is of practical interest to establish a precise constitutive model which includes the equations describing the phase transformation behaviors and thermo-mechanical processes of shape memory alloy (SMA). The microscopic mechanism of super elasticity and shape memory effect of SMA is explained based on the concept of shape memory factor defined by the author of this paper. The conventional super elasticity and shape memory effect of SMA are further unified as shape memory effect. Shape memory factor is redefined in order to make clear its physical meaning. A new shape memory evolution equation is developed to predict the phase transformation behaviors of SMA based on the differential relationship between martensitic volume fraction and phase transformation free energy and the results of DSC test. It overcomes the limitations that the previous shape memory evolution equations or phase transformation equations fail to express the influences of the phase transformation peak temperatures on the phase transformation behaviors and the transformation from twinned martensite to detwinned martensite occurring in SMA. A new macro-mechanical constitutive equation is established to predict the thermo-mechanical processes realizing the shape memory effect of SMA from the expression of Gibbs free energy. It is expanded from one-dimension to three-dimension with assuming SMA as isotropic material. All material constants in the new constitutive equation can be determined from macroscopic experiments, which makes it more easily used in practical applications.

Thermomechanical couplings in shape memory alloy materials

Continuum Mechanics and Thermodynamics

In this work, we address several theoretical and computational issues which are related to the thermomechanical modeling of shape memory alloy materials. More specifically, in this paper we revisit a nonisothermal version of the theory of large deformation generalized plasticity which is suitable for describing the multiple and complex mechanisms occurring in these materials during phase transformations. We also discuss the computational implementation of a generalized plasticity-based constitutive model, and we demonstrate the ability of the theory in simulating the basic patterns of the experimentally observed behavior by a set of representative numerical examples.

An experimentally-fitted thermodynamical constitutive model for polycrystalline shape memory alloys

Discrete and Continuous Dynamical Systems - Series S, 2021

A phenomenological model for polycrystalline NiTi shape-memory alloys with a refined dissipation function is here enhanced by a thermomechanical coupling and rigorously analyzed as far as existence of weak solutions and numerical stability and convergence of the numerical approximation performed by a staggered time discretization. Moreover, the model is verified on one-dimensional computational simulations compared with real laboratory experiments on a NiTi wire.