Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

The non-linear field theories of mechanics

This paper deals with thermoelastic material behavior without energy dissipation; it deals with both nonlinear and linear theories, although emphasis is placed on the latter. In particular, the linearized theory of thermoelasticity discussed possesses the following properties: (a) the heat flow, in contrast to that in classical thermoelasticity characterized by the Fourier law, does not involve energy dissipation; (b) a constitutive equation for an entropy flux vector is determined by the same potential function which also determines the stress; and (c) it permits the transmission of heat as thermal waves at finite speed. Also, a general uniqueness theorem is proved which is appropriate for linear thermoelasticity without energy dissipation.

Thermoelasticity without energy dissipation

Summary) The abstract should follow the structure of the article (relevance, degree of exploration of the problem, the goal, the main results, conclusion) and characterize the theoretical and practical significance of the study results. The abstract should not contain wording echoing the title, cumbersome grammatical structures and abbreviations. The text should be written in scientific style. The volume of abstracts (summaries) depends on the content of the article, but should not be less than 250 words. All abbreviations must be disclosed in the summary (in spite of the fact that they will be disclosed in the main text of the article), references to the numbers of publications from reference list should not be made. The sentences of the abstract should constitute an integral text, which can be made by use of the words “consequently”, “for example”, “as a result”. Avoid the use of unnecessary introductory phrases (eg, “the author of the article considers...”, “The article presents...” and so on.)

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Ministry of Education and Science of the Russian Federation

This paper is concerned with thermoelastic material behavior whose constitutive response functions possess thermal features that are more general than in the usual classical thermoelasticity. After a general development of the constitutive equations in the context of both nonlinear and linear theories, attention is focused on the latter. In particular, the one-dimensional version of the equation for the determination of temperature in the linearized theory provides an easy comparative basis of its predictive capability: In one special case where the Fourier conductivity is dominant, the temperature equation reduces to the classical Fourier law of heat conduction, which does not permit the possibility of undamped thermal waves; however,'in another special case in which the effect of conductivity is negligible, the equation has undamped thermal wave solutions without energy dissipation.

On undamped heat waves in an elastic solid

This paper is mainly concerned with a re-examination of the basic postulates and the consequent procedure for the construction of the constitutive equations of material behaviour in thermomechanics. However, the implication of the basic postulates and the significance of the related procedure for the development of the constitutive equations is also illustrated in some detail in the context of flow of heat in a rigid solid with particular reference to the propagation of thermal waves at finite speed. More specifically, after briefly examining the nature of the basic equations of motion for a system of particles within the scope of the classical newtonian mechanics, the basic postulates of the purely mechanical theory for a continuum (including its specialization for a rigid body) is re-examined. This includes some differences from the usual procedure on the subject. Next, thermal variables are introduced and after observing a useful analogy between the thermal and mechanical variables, a discussion of a theory of heat (or a purely thermal theory) is provided which differs from the usual development in the classical thermodynamics. A detailed application of the latter development is then made to the problem of heat flow in a stationary rigid solid using several different and well-motivated constitutive equations. Special cases of these include linearized theories of the classical heat flow by conduction and of heat flow transmitted as thermal waves. The remainder of the paper is concerned with thermal mechanical theory of deformable media along with discussions of a number of related issues on the subject.

A Re-Examination of the Basic Postulates of Thermomechanics

On the entropy production inequality

The contents of this paper represent a new approach to continuum thermo­dynamics and are chiefly concerned with ( a ) a procedure for obtaining restrictions on constitutive equations, ( b ) an appropriate mathematical statement of the second law and ( c ) the nature of restrictions placed by the latter on thermo-mechanical behaviour of single phase continua. Our point of departure is the introduction of a balance of entropy and the use of the energy equation as an identity for all motions and all temperature distributions after the elimination of the external fields. This is in contrast to the approach adopted in most of the current literature on continuum ther­modynamics based on the use of the Clausius-Duhem inequality. In order to gain some insight into the nature of our procedure we first study the case of an elastic material, which includes that of an ideal fluid as a special case, before the consideration of the second law. We then go on to postu­late an inequality which reflects the fact that for every process associated with a dissipative material, a part of the mechanical work is always con­verted into heat and this cannot be withdrawn from the medium as mech­anical work. The restriction on the heat conduction vector is considered separately and is confined to equilibrium cases in which heat flow is steady. A restriction is also obtained for the internal energy when the body is in mechanical equilibrium subjected to spatially homogeneous temperature fields. Using the above approach, next we study the nature of thermodynamic restrictions on the thermo-mechanical response of a viscous fluid and simple materials with fading memory. A drawback to the Clausius-Duhem inequality is discussed by means of an example. For a class of rigid heat conductors in thermal equilibrium, the Clausius-Duhem inequality requires that if heat is added to the medium, the resulting spatially homogeneous temperature of the conductor decreases . Moreover, the in­-equality denies the possibility of propagation of heat in the conductor as a thermal wave with finite speed. The inequalities proposed in this paper do not suffer from these shortcomings.

Albert Edward Green

Papers

Thermoelasticity without energy dissipation

On undamped heat waves in an elastic solid

A Re-Examination of the Basic Postulates of Thermomechanics

On the entropy production inequality

On thermodynamics and the nature of the second law