One-dimensional Shape Memory Alloy Model Research Articles

Mesoscopic free energy as a framework for modeling shape memory alloys

This article presents a reinterpretation of the one-dimensional shape memory alloy model by Müller, Achenbach, and Seelecke (M-A-S) that offers extended capabilities and a simpler formulation. The cornerstone of this model is a continuous, multi-well free energy that governs phase change at a mesoscopic material scale. The free energy has been reformulated to allow asymmetric tensile and compressive behavior as well as temperature-dependent hysteresis while maintaining the necessary smoothness conditions. The free energy is then used to derive expressions for latent heat coefficients that include the influence of stress, the difference in stiffness between the phases, and irreversibility. Special attention is devoted to the role of irreversibility and latent heat predictions, which are compared to experimental measurements. The new model also includes an updated set of kinetics equations that operate on the convexity of the energy wells instead of the height of the energy barriers. This modification eliminates several sets of equations from the overall formulation without any compromises in performance and also bypasses limitations of the barrier-based equations.

A shape memory alloy rod element based on the co-rotational formulation for nonlinear static analysis of tensegrity structures

In this article, a shape memory alloy rod element is derived based on the co-rotational formulation. In the co-rotational approach, the rigid body modes are removed from the total deformations by employing a local coordinate system at element level, and hence, the major part of geometric nonlinearity is isolated. The linear shape memory alloy rod element is developed using a shape memory alloy constitutive model together with the small strain framework employed by the co-rotational approach. The one-dimensional shape memory alloy model is adopted to calculate both the pseudo-elastic response and the shape memory effects. The new formulation is exploited to perform static analysis of tensegrity structures in order to study the accuracy and robustness of the proposed element and its capability to describe the structural response of shape memory alloy devices.

Active shape/stress control of shape memory alloy laminated beams

This paper deals with a study of the modeling and active shape/stress control of laminated beams subjected to the static loading with integrated/embedded shape memory alloy (SMA) layer. A one-dimensional shape memory alloy model is proposed which is able to simulate main aspects of SMAs including martensite transformation/reorientation, shape memory effect and pseudo-elasticity. In particular, the model includes a ferro-elasticity effect which is essential for accurate prediction of behavior of pre-stained SMA layers. Euler–Bernoulli beam theory and von Karman geometrically non-linearity are utilized to describe displacement and strain fields of laminated beams consist of SMA and elastic layers. A finite element method along with an iterative incremental approach is developed to treat material and geometrical non-linearities of the governing equations of equilibrium. To validate the proposed SMA model, numerical results of partial uniaxial tension tests are compared with experimental data in the literature which show excellent correlations. Influence of pre-strain, temperature and location of SMA layer on the active shape/stress control of SMA laminated beams subjected to different thermo-mechanical loading paths are put into evidence via a parametric study, and pertinent conclusions are outlined.

On a one-dimensional shape-memory alloy model in its fast-temperature-activation limit

We study a one-dimensional model describing the motion of a shape-memory alloy spring at a small characteristic time scale, called here fast-temperature-activation limit. At this level, the standard Falk's model reduces to a nonlinear elliptic partial differential equation (PDE) with Newton boundary condition. We show existence and uniqueness of a bounded weak solution and approximate this numerically. Interestingly, in spite of the nonlinearity of the model, the approximate solution exhibits nearly a linear profile. Finally, we extend the reduced model to the simplest PDE system for shape memory alloys that can capture oscillations and then damp out these oscillations numerically. The numerical results for both limiting cases show excellent agreement. The graphs show that the valve opens in an instant, which is realistic behavior of the free boundary.

Constitutive modeling of SMA SMP multifunctional high performance smart adaptiveshape memory composite

Materials design involving the thermomechanical constitutive modeling of shape memoryalloy (SMA) and shape memory polymer (SMP) composites is a key topic in thedevelopment of smart adaptive shape memory composites (SASMC). In this work, aconstitutive model for SASMC is developed. First, a one-dimensional SMA model, whichcan simulate the pseudoelastic (PE) and shape memory effects (SME) is presented.Subsequently, a one-dimensional SMP model able to reproduce the SME is addressed. BothSMA and SMP models are based on a single internal state variable, namely themartensite fraction and the frozen fraction, which can be expressed as a function oftemperature. A consistent form of the analytical solution for the SMP model is obtainedusing the fourth-order Runge–Kutta method. Finally, the SASMC constitutivemodel is proposed, following two analytical homogenization approaches. Oneapproach is based on an equivalent inclusion method and the other approachis the rule of mixtures. The SMA and SMP constitutive models are validatedindependently with experimental results. However, the validation of the composite modelis performed using the two homogenization approaches and a close agreementin results is observed. Results regarding the isothermal and thermomechanicalstress–strain responses are analyzed as a function of SMA volume fraction. Further, it isconcluded that the proposed composite model is able to reproduce consistentlythe overall composite response by taking into consideration not only the phasetransformations, variable modulus and transformation stresses in SMA but alsothe variable modulus, the evolution of stored strain and thermal strain in theSMP.

One-Dimensional Shape Memory Alloy Model Applicable to Any Status of Stress and Temperature

The transformation kinetics formulation is the principal factor underlying the constitutive model of shape memory alloys. Therefore, the transformation kinetics formulation, which is applicable to any status of stress and temperature, is essential for predicting the material behavior of SMAs. In this work, we show that the transformation kinetics of the Brinson model, which is the most widely used 1-dimensional model, has shortcomings under certain stress and temperature histories. In addition, we propose a modified transformation kinetics model that can be used for any stress or temperature conditions. The martensite transformation kinetics is modified so that the transformation from austenite into temperature-induced martensite, due to the decrement of temperature, is coupled with a transformation from austenite or temperature-induced martensite into stress-induced martensite, due to the increment of the stress. Through this modification, the suggested model can simulate the behavior of shape memory alloy materials under arbitrarily changed circumstances at every stress-temperature region.