Dynamics of Thermoelastic Media: Shape Memory Alloys

Abstract

Layered elastic structures are usually subject to a variety of dynamic loads, including changes in temperature. Because the layers may possess varying thermo-mechanical properties, temperature changes would induce non-uniform stresses within the structure. Thus, the study of the thermoelasticity of such structures is of paramount importance. It is not enough to understand the influence of temperature changes on the state of stress in the structure, it is also essential to understand how the changes in the state of stress influence the temperature distributions within the structure. To be able to systematically model the constitutive relationships, it is essential to revisit the basic thermodynamic concepts (Vedantam, 2000) to establish the foundations of linear thermoelasticity. Basic Thermodynamic ConceptsThe first law of thermodynamics is essentially the statement of the principle of conservation of energy applied to thermodynamic systems. Thus, the variation in the internal energy of a thermodynamic system due to transformation of the state of the system U can be expressed in terms of the work W performed during the transformation and the amount of energy Q received by the system in forms other than work, as U = Q − W .The first law arose primarily to state the impossibility of constructing a machine that could create energy. It places no limitations on the possibility of transforming heat into work or work into heat, as they are different forms of energy. However, the second law explicitly places certain limitations on how much heat can be transformed to useful work. Thus, the second law of thermodynamics states that 'A transformation whose only final result is to transform into work, heat extracted from a source which is the same temperature throughout is impossible'. Alternatively, the second law may be stated as 'A transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible'. This implies that only part of the heat that is absorbed by the system from the source at a higher temperature can be transformed to useful work and that the rest of the heat must be surrendered to the source at lower temperature. This leads naturally to the concept of entropy, and the second law could be stated as 'For any transformation occurring in an isolated system the entropy of the final state can never be less than that of the initial state'. Thus, if an isolated system is Dynamics of Smart StructuresRanjan Vepa