Estudo teórico e numérico de modelos constitutivos de ligas com memória de forma e associação com sistemas vibratórios

Abstract

In recent times, much research effort has been undertaken aiming at the development of the so-called smart materials, understood as those that exhibit coupling between two or more physical domains in such a way that, when stimulated externally, they undergo controlled variations of some of their properties, such as viscosity, stiffness, volume or electrical conductivity. The degree of maturity of the technology of smart materials and structures is confirmed by numerous examples of applications found in industrial products. The present work is dedicated to the study of shape memory alloys, which are considered as being some of the most promising smart materials in terms of potentiality for industrial innovation. Those materials present the capacity of, once submitted to external loads, recovering their original form and dimensions through the application of thermal cycles or by removing the load. This behavior is due to two effects exhibited by those materials: shape memory and pseudoelasticity. The present dissertation reports the study carried-out by the author concerning some of the most relevant constitutive models intended for the description of the thermomechanical behavior of shape memory alloys, based on assumed transformation kinetics and on internal variables with constraints. The understanding of such models is considered to be essential for the development of modeling procedures of intelligent devices. After the description of the potentiality of applications of the shape memory alloys in the context of the smart material and structures technology and the assessment of the most relevant phenomenological aspects, specially the underlying phase transformations, the formulations of some constitutive models, chosen among those considered to be the most representative ones, are described, namely: models with assumed transformation kinetics (Tanaka, Liang-Rogers, Brinson, and Boyd-Lagoudas models) and models based on internal variables with constraints (modified Fremond and Savi and coauthors models). Numerical simulations are carried-out with the aim of evaluating the main features of the models considered and validating the numerical implementations by comparisons with results extracted from the literature. Afterwards, the analytical developments and numerical simulations regarding the incorporation of the Liang- Rogers model in a single-degree-of-freedom vibrating system are presented, enabling to evaluate the interest in using shape memory alloys for the purpose of vibration control. The study reported herein has been developed in the context of the National Institute of Science and Technology of Smart Structures in Engineering, leaded by the Structural Mechanics Laboratory Prof. J.E.T. Reis, of the School of Mechanical Engineering of the Federal University of Uberlândia, which is dedicated to the study of the foundations and applications of intelligent materials to various problems of engineering as well as to multidisciplinary problems.