Our aim is to propose a theory which goes beyond the classical formulation of thermodynamics. This is achieved by enlarging the space of basic independent variables, through the introduction of non-equilibrium variables, such as the dissipative fluxes appearing in the balance equations. The next step is to find evolution equations for the dissipative fluxes. Whereas the evolution equations for the classical variables are given by the usual balance laws, no general criteria exist concerning the evolution equations of the dissipative fluxes, with the exception of the restrictions imposed on them by the second law of thermodynamics.

https://iopscience.iop.org/article/10.1088/0034-4885/51/8/002/pdf

Extended irreversible thermodynamics

Some constitutive equations for liquid crystals

The use of the thermoelastic martensitic transformation and its reverse transformation has recently been proposed and demonstrated for several active control ap plications. However, the present constitutive models have lacked several important funda mental concepts that are essential for many of the proposed intelligent material system ap plications such as shape memory hybrid composites.A complete, unified, one-dimensional constitutive model of shape memory materials is developed and presented in this paper. The thermomechanical model formulation herein will investigate important material characteristics involved with the internal phase transformation of shape memory alloys. These characteristics include energy dissipation in the material that governs the damping behavior, stress-strain-temperature relations for pseudoelasticity, and the shape memory effect. Some numerical examples using the model are also presented.

One-Dimensional Thermomechanical Constitutive Relations for Shape Memory Materials

Nonstationary irreversible thermodynamics: A Causal relativistic theory

When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. Unless fission due to rotation, the radiation of mass, or the blowing off of mass by radiation, reduce the star's mass to the order of that of the sun, this contraction will continue indefinitely. In the present paper we study the solutions of the gravitational field equations which describe this process. In I, general and qualitative arguments are given on the behavior of the metrical tensor as the contraction progresses: the radius of the star approaches asymptotically its gravitational radius; light from the surface of the star is progressively reddened, and can escape over a progressively narrower range of angles. In II, an analytic solution of the field equations confirming these general arguments is obtained for the case that the pressure within the star can be neglected. The total time of collapse for an observer comoving with the stellar matter is finite, and for this idealized case and typical stellar masses, of the order of a day; an external observer sees the star asymptotically shrinking to its gravitational radius.

On Continued Gravitational Contraction

1 Tour d'Horizon 2 Early Version of Extended Thermodynamics 1 Paradox of Heat Conduction and Shear Diffusion 1.1 Heuristic Derivation of the Laws of Fourier and Navier-Stokes 1.2 Parabolic Laws of Heat Conduction and Shear Diffusion 2 Paradox Removed 2.1 The Cattaneo Equation 2.2 Extended TIP 2.3 Finite Pulse Speeds in Extended TIP 2.4 Conclusion and Criticism 3 Kinetic Theory of Mon-atomic Gases 3.1 Boltzmann-Equation and Moments 3.2 Equations of Balance for Moments 3.3 Balance of Entropy and Possible Equilibria 3.4 The Grad Distribution 3.5 Entropy and Entropy Flux in Grad's 13-Moment Theory 3.6 Phenomenological Equations derived from the Kinetic Theory 3.7 Pulse Speeds 3.8 Conclusions 3 Formal Structure of Extended Thermodynamics 1 Field Equations 1.1 Thermodynamic Processes and Principles of the Constitutive Theory 1.2 Universal Principles of the Constitutive Theory 2 Entropy Inequality, Symmetric Hyperbolicity 2.1 Exploitation of the Entropy Inequality 2.2 Symmetric Hyperbolic Field Equations 2.3 Discussion 2.4 Characeristic Speeds 3 Main Subsystems 3.1 Constraints on the Main Field 3.2 A Main.

Rational extended thermodynamics

A thermodynamic theory of mixtures of fluids

The coldness, a universal function in thermoelastic bodies

It is often considered that in solids a non-monotone load-deformation characteristic of the “van der Waals type” may give rise to hysteretic behaviour in a phase transition. Here we consider a pseudo-elastic hysteresis that occurs in the austenitic-martensitic phase transition of shape memory alloys. For demonstrative purposes we let the non-monotone characteristic first be defined by the Landau-Devonshire model, later we even use straight lines. We ask the following questions: (i) How wide is the hysteresis loop? (ii) How does the width of the hysteresis loop change with temperature? (iii) What are the possible processes inside the hysteresis loop? Answers are provided for all three questions, viz. On (i) The width is determined by the interfacial energy of the phases. On (ii) There is no significant dependence on temperature. On (iii) The hysteresis loop contains metastable states that loose their (meta-)stability on a line defining phase equilibrium. The theoretical predictions are qualitative results. They are supported by tensile experiments on a CuZnAl single crystal.

Ingo Müller

Papers

Rational extended thermodynamics

A thermodynamic theory of mixtures of fluids

The coldness, a universal function in thermoelastic bodies

On the pseudo-elastic hysteresis

On the entropy inequality