Marcelo A. Savi

An overview of constitutive models for shape memory alloys

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.

Experimental and numerical investigations of shape memory alloy helical springs

Shape memory alloys (SMAs) belong to the class of smart materials and have been used in numerous applications. Solid phase transformations induced either by stress or temperature are behind the remarkable properties of SMAs that motivate the concept of innovative smart actuators for different purposes. The SMA element used in these actuators can assume different forms and a spring is an element usually employed for this aim. This contribution deals with the modeling, simulation and experimental analysis of SMA helical springs. Basically, a one-dimensional constitutive model is assumed to describe the SMA thermomechanical shear behavior and, afterwards, helical springs are modeled by considering a classical approach for linear-elastic springs. A numerical method based on the operator split technique is developed. SMA helical spring thermomechanical behavior is investigated through experimental tests performed with different thermomechanical loadings. Shape memory and pseudoelastic effects are treated. Numerical simulations show that the model results are in close agreement with those obtained by experimental tests, revealing that the proposed model captures the general thermomechanical behavior of SMA springs.

Nonlinear dynamics and chaos in coupled shape memory oscillators

Shape memory and pseudoelastic effects are thermomechanical phenomena associated with martensitic phase transformations, presented by shape memory alloys. This contribution concerns with the dynamical response of coupled shape memory oscillators. Equations of motion are formulated by assuming a polynomial constitutive model to describe the restitution force of the oscillators and, since they are associated with a five-dimensional system, the analysis is performed by splitting the state space in subspaces. Free and forced vibrations are analyzed showing different kinds of responses. Periodic, quasi-periodic, chaos and hyperchaos are all possible in this system. Numerical investigations show interesting and complex behaviors. Dynamical jumps in free vibration and amplitude variation when temperature characteristics are changed are some examples. This article also shown some characteristics related to chaos–hyperchaos transition. � 2003 Elsevier Ltd. All rights reserved.

Numerical Investigation of an Adaptive Vibration Absorber Using Shape Memory Alloys

The tuned vibration absorber (TVA) is a well-established passive vibration control device for achieving vibration reduction of a primary system subjected to external excitation. This contribution deals with the non-linear dynamics of an adaptive tuned vibration absorber (ATVA) with a shape memory alloy (SMA) element. Initially, a single-degree of freedom oscillator with an SMA element is analyzed showing the general characteristics of its dynamical response. Then, the analysis of an ATVA with an SMA element is carried out. Initially, small amplitude vibrations are considered in such a way that the SMA element does not undergo a stress-induced phase transformation. Under this assumption, the SMA influence is only caused by stiffness changes corresponding to temperature-induced phase transformation. Afterwards, the influence of the hysteretic behavior due to stress-induced phase transformation is considered. A proper constitutive description is employed in order to capture the general thermomechanical aspects of the SMAs. The hysteretic behavior introduces complex characteristics to the system dynamics but also changes the absorber response allowing vibration reduction in different frequency ranges. Numerical simulations establish comparisons of the ATVA results with those obtained from the classical TVA.

Experimental investigation of vibration reduction using shape memory alloys

Smart materials have a growing technological importance due to their unique thermomechanical characteristics. Shape memory alloys belong to this class of materials being easy to manufacture, relatively lightweight, and able to produce high forces or displacements with low power consumption. These aspects could be exploited in different applications including vibration control. Nevertheless, literature presents only a few references concerning the experimental analysis of shape memory alloy dynamical systems. This contribution deals with the experimental analysis of shape memory alloy dynamical systems by considering an experimental apparatus consisted of low-friction cars free to move in a rail. A shaker that provides harmonic forcing excites the system. The vibration analysis reveals that shape memory alloy elements introduce complex behaviors to the system and that different thermomechanical loadings are of concern showing the main aspects of the shape memory alloy dynamical response. Special attention is dedicated to the analysis of vibration reduction that can be achieved by considering different approaches exploiting either temperature variations promoted by electric current changes or vibration absorber techniques. The results establish that adaptability due to temperature variations is defined by a competition between stiffness and hysteretic behavior changes.

Chaos and order in biomedical rhythms

Nature is full of nonlinearities, responsible for a great variety of responses in natural systems. Physiological rhythms constitute a central characteristic of life, which is motivating the analysis of dynamical aspects related to natural systems. Natural rhythms could be either periodic or irregular over time and space and, each kind of dynamical behavior may be related to both normal and pathological physiological functioning. This review article presents an overview of nonlinear dynamics and chaos concepts useful for the analysis of biomedical system. After that, it is presented an overview of dynamical aspects related to different biomedical systems. Cardiovascular rhythms, brain rhythms, cellular and molecular rhythms are discussed from a dynamical approach pointing some characteristics of normal and pathological responses.

BIFURCATION CONTROL OF A PARAMETRIC PENDULUM

In this paper, we apply chaos control methods to modify bifurcations in a parametric pendulum-shaker system. Specifically, the extended time-delayed feedback control method is employed to maintain stable rotational solutions of the system avoiding period doubling bifurcation and bifurcation to chaos. First, the classical chaos control is realized, where some unstable periodic orbits embedded in chaotic attractor are stabilized. Then period doubling bifurcation is prevented in order to extend the frequency range where a period-1 rotating orbit is observed. Finally, bifurcation to chaos is avoided and a stable rotating solution is obtained. In all cases, the continuous method is used for successive control. The bifurcation control method proposed here allows the system to maintain the desired rotational solutions over an extended range of excitation frequency and amplitude.

Bifurcations and Crises in a Shape Memory Oscillator

The remarkable properties of shape memory alloys have been motivating the interest in applications in different areas varying from biomedical to aerospace hardware. The dynamical response of systems composed by shape memory actuators presents nonlinear characteristics and a very rich behavior, showing periodic, quasi-periodic and chaotic responses. This contribution analyses some aspects related to bifurcation phenomenon in a shape memory oscillator where the restitution force is described by a polynomial constitutive model. The term bifurcation is used to describe qualitative changes that occur in the orbit structure of a system, as a consequence of parameter changes, being related to chaos. Numerical simulations show that the response of the shape memory oscillator presents period doubling cascades, direct and reverse, and crises.

A Phenomenological Description of the Thermomechanical Coupling and the Rate-dependent Behavior of Shape Memory Alloys

Shape memory alloys (SMAs) present a rate-dependent behavior, which means that the thermomechanical response depends on the loading rate. Therefore, although martensitic transformation can be considered as a non-diffusive process, the phase transformation critical stresses are temperature dependent and, since heat transfer process is time dependent, it affects the thermomechanical behavior of SMAs. This article deals with the rate dependence of SMAs, proposing a 1D constitutive model to describe this effect. The proposed model is formulated within the framework of continuum mechanics and thermomechanical coupling terms of the energy equation are incorporated in the formulation in order to describe the rate-dependent behavior. Numerical simulations are carried out comparing results with experimental data available in literature for different loading rates and environmental media, presenting a close agreement. Afterwards, numerical tests are performed in order to evaluate the model capabilities showing that it is capable to capture the general thermomechanical behavior of SMAs.

Chaos control in mechanical systems

Chaos has an intrinsically richness related to its structure and, because of that, there are benefits for a natural system of adopting chaotic regimes with their wide range of potential behaviors. Under this condition, the system may quickly react to some new situation, changing conditions and their response. Therefore, chaos and many regulatory mechanisms control the dynamics of living systems, conferring a great flexibility to the system. Inspired by nature, the idea that chaotic behavior may be controlled by small perturbations of some physical parameter is making this kind of behavior to be desirable in different applications. Mechanical systems constitute a class of system where it is possible to exploit these ideas. Chaos control usually involves two steps. In the first, unstable periodic orbits (UPOs) that are embedded in the chaotic set are identified. After that, a control technique is employed in order to stabilize a desirable orbit. This contribution employs the close-return method to identify UPOs and a semi-continuous control method, which is built up on the OGY method, to stabilize some desirable UPO. As an application to a mechanical system, a nonlinear pendulum is considered and, based on parameters obtained from an experimental setup, analyses are carried out. Signals are generated by numerical integration of the mathematical model and two different situations are treated. Firstly, it is assumed that all state variables are available. After that, the analysis is done from scalar time series and therefore, it is important to evaluate the effect of state space reconstruction. Delay coordinates method and extended state observers are employed with this aim. Results show situations where these techniques may be used to control chaos in mechanical systems.