Classical Thermodynamics Of Irreversible Processes Research Articles

Constitutive Theory of fiber suspensions

We will demonstrate, that in fiber suspensions the stress tensor has a skew-symmetric part, i.e. fiber suspensions are micropolar fluids with non-zero couple stresses. Consequently, a continuum mechanical description of fiber suspensions requires the consideration of the balance of angular momentum in addition to the balance equations of mass, momentum and energy. An antisymmetric stress tensor is found for an isotropic orientation distribution of deformable fibers as well as for an anisotropic distribution of fiber orientations.Mainly, the method of classical Thermodynamics of Irreversible Processes with internal variables is applied. The internal variables are fiber deformation variables and an orientation tensor in the case of a non-isotropic distribution of fiber orientations. In addition to the result on couple stresses, relaxation equations for the bend and twist deformation variables are derived.Finally a mesoscopic background theory is discussed. In this approach a distribution of different fiber orientations and fiber deformations is assumed. The fiber orientation and deformation are additional variables in the domain of field quantities. The usual macroscopic fields of continuum mechanics are averages of mesoscopic fields over the different orientations and deformations. Macroscopic quantities characterizing the orientational order, the alignment tensors, and quantities characterizing fiber deformation, are defined by the help of the distribution function. They are internal variables in the macroscopic theory. The mesoscopic theory also demonstrates, that there is a skew symmetric part of the stress tensor in fiber suspensions.

Thermodynamic potential of free energy for thermo-elastic-plastic body

The procedure of derivation of thermodynamic potential of free energy (Helmholtz free energy) for a thermo-elastic-plastic body is presented. This procedure concerns a special thermodynamic model of a thermo-elastic-plastic body with isotropic hardening characteristics. The classical thermodynamics of irreversible processes for material characterized by macroscopic internal parameters is used in the derivation. Thermodynamic potential of free energy may be used for practical determination of the level of stored energy accumulated in material during plastic processing applied, e.g., for industry components and other machinery parts received by plastic deformation processing. In this paper the stored energy for the simple stretching of austenitic steel will be presented.

The Holographic Quantum

We present a map of standard quantum mechanics onto a dual theory, that of the classical thermodynamics of irreversible processes. While no gravity is present in our construction, our map exhibits features that are reminiscent of the holographic principle of quantum gravity.

Constraints in nonequilibrium thermodynamics: General framework and application to multicomponent diffusion

We elaborate how holonomic constraints can be incorporated into the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework of nonequilibrium thermodynamics. Dirac's ideas for constructing constrained Poisson brackets are extended to dissipative brackets. The construction is presented such that it can be put into practice most readily. We illustrate the procedure by developing a symmetric thermodynamic description of diffusion in multicomponent systems and, as a further example, we impose an incompressibility constraint. As a consequence of its more elaborate and restrictive structure, GENERIC removes the ambiguities occurring in the classical thermodynamics of irreversible processes when one works with redundant variables.

Thermal Exchanges and Thermomechanical Couplings in Amorphous Polymers

During mechanical loading, the strain process can be accompanied by thermal effects generated by thermomechanical couplings. The aim of this work was the determination of energy (heat sources, mechanical energy, internal dissipated energy) during a mechanical test on polymer materials by observing strain and thermal data fields. Heat sources were calculated by establishing the heat equation using concepts of the classical thermodynamics of irreversible processes and applied to polymer materials. With a simple experimental set-up, we show that the thermal exchanges and the thermal losses in polymer samples are mainly induced by conduction and convective. The temperature at the surface was assumed to be equal to the average temperature in the thickness. We show that it is possible to obtain heat source values quantitatively without knowing their position and dimension along the thickness. It can also be difficult to calculate heat sources correctly because of lack of knowledge of the polymer property values involved in the heat equation (thermal conductivity, specific heat and heat transfer coefficient). So we present a procedure to determine these thermal parameters easily in our environmental conditions of work without making a mechanical hypothesis, and without knowing the heat source distribution because we analyse thermal data as soon as the heat source is switched off. In conclusion, we show an application involving a large strain mechanical test on a specimen of PC. The strain field is obtained by a mark tracking method. The energy balance has been calculated and associated with the volumetric deformation, showing the macroscopic and microscopic behaviour.

Thermal and Mechanical Couplings in Plain and Wood Fibre Reinforced Polypropylene during Tensile and Fracture Tests

The aim of this work was to show the influence of spruce fibres on polypropylene, by way of an experimental thermo-mechanical approach. These studies were performed by the simultaneous measurement of the strain field and the thermal field. A digital image correlation method was used for the strain measurements. The thermal field was obtained with the help of an infrared camera. The heat equation established in the context of classical thermodynamics of irreversible processes allowed us to evaluate the heat sources. The main difference between the plain resin and the composite material was that the heat sources dissipated by the composite were locally lower. In tensile tests the plain material allowed the creation of a neck zone with very high strain values. In fracture tests, it also generated very high strains localised at the crack tip. For the composite, the results of tensile tests showed that the presence of wood fibres led to a quasi-brittle failure of the specimen. In fracture tests, a better overstress accommodation was observed near the crack tip by distributing the strains in a wider zone.

Ilya Priogogine and the classical thermodynamics of irreversible processes

Ilya Priogogine and the classical thermodynamics of irreversible processes

A Comparative Study of the Coupling of Flow with Non-Fickean Thermodiffusion. Part III: Internal Variables

Classical thermodynamics of irreversible processes is easily extended to describe non-equilibrium processes which are not directly involved in the conservation laws of mass, momentum and energy. These non-equilibrium processes can be understood as the evolution in time of some internal variables. Thermodynamics with internal variables is here used to describe unusual transport phenomena taking place in binary fluid mixtures and suspensions of particles. We also revisit the unusual heat transport of superfluids. A comparison is made with the description of these unusual phenomena given by Extended Irreversible Thermodynamics (Part I) and the GENERIC framework (Part II).

Internal variables and the non-equilibrium thermodynamics of colloidal suspensions

Classical thermodynamics of irreversible processes is a valuable tool for the study of suspensions, provided due care is devoted to the selection of internal variables. As a first example, the flow-induced anisotropic microstructure appearing in many a suspension is usually depicted by a vector, the orientation and length of which are submitted to a statistical distribution. We show how irreversible thermodynamics imposes restrictions on the time evolution of that structural internal variable (and consequently on the time evolution of its statistical distribution), and how this evolution is related to the elastic stress of the suspension. As a second example, we consider the possibility of a mean relative motion between the particles and the suspending fluid. Upgrading that relative velocity to the status of an internal variable, we analyse the consequences concerning the transport of mass, momentum and energy, providing a link with the two-fluid model of suspensions, as well as with the well-known description of molecular mixtures.

Thermodynamic formulation of constitutive equations and application to the viscoplasticity and viscoelasticity of metals and polymers

Elastoviscoplasticity for metallic materials and viscoelasticity for polymers are generally treated as completely independent processes. In the present paper we intend to discuss some possible bridges between the two kind of constitutive theories. Two aspects are more specifically addressed: (i) the classical thermodynamics of irreversible processes, using material state variables, is further extended in order to incorporate more easily dynamic and static recovery effects in the kinematic hardening evolutionary equations; (ii) the qualitative and quantitative equivalence between elasto-viscoplasticity and viscoelasticity is discussed both in terms of the simplest linear model and for a more complicated non-linear situation. In fact, it is demonstrated that superposing several non-linear kinematic hardening and static recovery rules allows to model a viscoelastic behavior. One of the advantages of the approach is to describe easily the cyclic loading situations, as shown by comparison with experiments made on a glass-epoxy composite.

Constrained equilibrium in network-like polymer systems: A concept of irreversible thermodynamics

Network-like polymer systems are considered to be composed of thermodynamically equivalent subsystems. On deformation up to large strains, the shape of these subsystems is believed to be transformed according to the law of affinity. The thermodynamics of such systems is presented. This description is then extended so as to be able to describe relaxation processes. Special attention is directed to a discussion of constrained equilibrium states because of their being representative of many polymer systems. The methods of classical thermodynamics of irreversible processes are shown to be appropriate for describing large deformations of many different network-like systems such as polymer glasses and semicrystalline polymers. For the deformation experiments discussed here, the whole energy balance during deformation is known from stretching calorimetric measurements. This is a significant presumption for obtaining clear, fundamental conclusions; they would be difficult to achieve otherwise.

Principles of the van der Waals network concept: Time‐dependent processes

AbstractThe leading ideas behind the van der Waals modification of the Gaussian network are explained including a discussion of the meaning of the van der Waals parameters. The utility of approach is demonstrated in terms of a representation of deformations, of networks under different strains and of the heat exchanged during extension. The interpretation of stress‐strain experiments carried out on bimodal end‐linked model networks leads to a characterization of the width of the chain‐length distribution in rubbers. Finally, it is shown that the non‐linear visco‐elastic response in stress‐strain cycles of natural rubber can be understood within the framework of the classical thermodynamics of irreversible processes. The time dependent stress‐strain behaviour is fairly well described in the temperature regime of rubber‐elasticity by using a discrete small‐strain shear‐relaxation spectrum.

Irreversible deformation of semicrystalline PUR-elastomers —a novel concept

A description of irreversible quasi-isothermal deformation of PUR-elastomers to large strains is developed on the basis of the classical thermodynamics of irreversible processes. This approach is shown by representing stress-strain cycles at different constant strain rates and at two temperatures.

Ein beitrag zur thermodynamik fluider systeme. I

Two different versions of the entropy-free thermodynamics of irreversible processes developed by J. Meixner are given and compared with each other. Each formulation of the theory includes the classical thermodynamics of irreversible processes as a special case.

On the validity of the Clausius-Duhem inequality

The author discusses the applicability of various theories for describing processes in continuous matter and deals in some detail with the entropy-free thermodynamics of irreversible processes, basing his discourse on the work of J. Meixner in this field. Today there are essentially three different phenomenological theories available for describing processes in continuous matter: (1) The classical Thermodynamics of Irreversible Processes (TIP)1. (2) The Non-linear Field-Theories of Mechanics and their thermodynamic extensions (NFT)2. (3) The Entropy-free Thermodynamics of Processes (ETIP)3' . These theories have in common the conservation laws of continuous matter and the laws of thermostatics. They differ essentially in the arguments on which the constitutive equations (CE) are based. Classical TIP starts from a generalized Clausius—Duhem Inequality (CDI) for the well-known (specific) thermostatic entropy s p5+divJ8O (1) The quantity is well defined by the second law of thermodynamics and is a function = s5(u, p) for fluids and a function = s(u, F) for solid systems. Here u means the (specific) internal energy, p... density, Ff1... deformation gradient, substantial time derivative of and J... current of s. In the case of thermodynamic systems without diffusion one has

Thermodynamik der Vorgänge in einfachen fluiden Medien und die Charakterisierung der Thermodynamik irreversibler Prozesse

Thermodynamics of processes in continuous matter has found several treatments: (1) classical thermodynamics of irreversible processes, (2) the nonlinear field theory of mechanics with the incorporation of thermodynamic aspects, (3) the new entropyfree thermodynamics of processes. An important feature of the last theory is the fundamental inequality. It provides a basis for the formulation of constitutive equations, which are discussed for simple thermodynamic fluid materials. Classical thermodynamics of irreversible processes results as a well defined special case with a modification that has been overlooked previously. It is shown by an example that this modification which differentiates between a dynamic and a thermostatic temperature is necessary in order to make classical thermodynamics of irreversible processes consistent.