Thermodynamics Of Continuous Media Research Articles

An Example of a One-Parameter Family of Rank-One Convex Stored Energies for Isotropic Compressible Solids

Applying the theorem proved by the authors in Ndanou et al. (J. Elast. 115:1–15, 2014), we established the hyperbolicity of non-stationary equations of hyperelastic isotropic solids for a one-parameter family of equations of state containing, in particular, generalized neo-Hookean solids. The hyperbolicity is equivalent to the rank-one convexity of the corresponding stored energy (Dafermos, Hyperbolic Conservation Laws in Continuum Mechanics, Springer, Berlin, 2000; Silhavý, The Mechanics and Thermodynamics of Continuous Media, Springer, Berlin, 1996). The influence of the parameter on the solution properties is shown in the case of a strong shear test.

Thermodynamics of continuous media with intrinsic rotation and magnetoelectric coupling

The thermodynamics of an electrically charged, multicomponent continuous medium with intrinsic rotation is analysed in the presence of electromagnetic fields with a weak linear magnetoelectric coupling in the non-relativistic limit. Taking into account the chemical composition of the current densities and stress tensors yields scalar dissipation terms accounting for chemical reactivities and vectorial dissipation terms accounting for transport. Three equations characterising the continuous medium are derived: a thermostatic equilibrium equation, a reversible and an irreversible thermodynamic evolution equation. Explicit expressions for the temperature and the chemical potentials are derived in terms of the electromagnetic fields and the magnetoelectric coupling. The transport equations contain electromagnetic terms normally not included in a standard thermodynamic phenomenology.

Thermo-mechanical processes

The theory of thermo-mechanical processes, as an apparatus in the development of equations of state and thermodynamics of continuous media, includes all the main sections of the fundamental mechanics of deformable solids. The paper considers two aspects of the overall problem: 1) non-monotonic processes in visco-plastic flows; 2) panel flutter of viscoelastic plates. In the first case there is released a fundamentally new problem - the definition of the functional of contact friction and the construction of the theory of plasticity under complex loading of bodies with non-uniform initial stress-strain state. The solution is supposed to look by using the SN-EVM (CH-ЭВМ) method together with forming a data bank. In the second case there is risen the problem of definitive explaination of the well-known paradox of the definition of the critical parameters in the problem of flutter of viscoelastic plate. The article also addresses the issues of scientific ethics and morality; driving force behind this were the publications appeared in which subjective and biased historical facts relating to the development of the science of thermo-mechanical processes are interpreted subjective and interestedly.

Quasi-linear versus potential-based formulations of force–flux relations and the GENERIC for irreversible processes: comparisons and examples

An essential part in modeling out-of-equilibrium dynamics is the formulation of irreversible dynamics. In the latter, the major task consists in specifying the relations between thermodynamic forces and fluxes. In the literature, mainly two distinct approaches are used for the specification of force–flux relations. On the one hand, quasi-linear relations are employed, which are based on the physics of transport processes and fluctuation–dissipation theorems (de Groot and Mazur in Non-equilibrium thermodynamics, North Holland, Amsterdam, 1962, Lifshitz and Pitaevskii in Physical kinetics. Volume 10, Landau and Lifshitz series on theoretical physics, Pergamon Press, Oxford, 1981). On the other hand, force–flux relations are also often represented in potential form with the help of a dissipation potential (Silhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997). We address the question of how these two approaches are related. The main result of this presentation states that the class of models formulated by quasi-linear relations is larger than what can be described in a potential-based formulation. While the relation between the two methods is shown in general terms, it is demonstrated also with the help of three examples. The finding that quasi-linear force–flux relations are more general than dissipation-based ones also has ramifications for the general equation for non-equilibrium reversible–irreversible coupling (GENERIC: e.g., Grmela and Ottinger in Phys Rev E 56:6620–6632, 6633–6655, 1997, Ottinger in Beyond equilibrium thermodynamics, Wiley Interscience Publishers, Hoboken, 2005). This framework has been formulated and used in two different forms, namely a quasi-linear (Ottinger and Grmela in Phys Rev E 56:6633–6655, 1997, Ottinger in Beyond equilibrium thermodynamics, Wiley Interscience Publishers, Hoboken, 2005) and a dissipation potential–based (Grmela in Adv Chem Eng 39:75–129, 2010, Grmela in J Non-Newton Fluid Mech 165:980–986, 2010, Mielke in Continuum Mech Therm 23:233–256, 2011) form, respectively, relating the irreversible evolution to the entropy gradient. It is found that also in the case of GENERIC, the quasi-linear representation encompasses a wider class of phenomena as compared to the dissipation-based formulation. Furthermore, it is found that a potential exists for the irreversible part of the GENERIC if and only if one does for the underlying force–flux relations.

Thermodynamics of continuous media with electromagnetic fields

The thermodynamics of an electrically charged, multicomponent continuous medium with electromagnetic fields is analysed in the non-relativistic limit. Applying locally the first and second law of thermodynamics and Maxwell’s equations for a linear theory of electromagnetism, three equations characterising the continuous medium are derived: a thermostatic equilibrium equation, a reversible and an irreversible thermodynamic evolution equation. For a local thermodynamic equilibrium, explicit expressions for the temperature and the chemical potentials in terms of the electromagnetic fields are obtained. The linear phenomenological relations describe novel effects of non-uniform electromagnetic fields on the transport equations and account also for magnetoresistance and optical tweezers.

On the Formulation of Continuum Thermodynamic Models for Solids as General Equations for Non-equilibrium Reversible-Irreversible Coupling

The purpose of this work is the comparison of some aspects of the formulation of material models in the context of continuum thermodynamics (e.g., Silhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997) with their formulation in the form of a General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC: e.g., Grmela and Ottinger in Phys. Rev. E 56: 6620–6632, 1997; Ottinger and Grmela in Phys. Rev. E 56: 6633–6655, 1997; Ottinger in Beyond equilibrium thermodynamics, Wiley, New York, 2005; Grmela in J. Non-Newton. Fluid Mech. 165: 980–998, 2010). A GENERIC represents a generalization of the Ginzburg-Landau model for the approach of non-equilibrium systems to thermodynamic equilibrium. Originally developed to formulate non-equilibrium thermodynamic models for complex fluids, it has recently been applied to anisotropic inelastic solids in a Eulerian setting (Hutter and Tervoort in J. Non-Newton. Fluid Mech. 152: 45–52, 2008; 53–65, 2008; Adv. Appl. Mech. 42: 254–317, 2009) as well as to damage mechanics (Hutter and Tervoort in Acta Mech. 201: 297–312, 2008). In the current work, attention is focused for simplicity on the case of thermoelastic solids with heat conduction and viscosity in a Lagrangian setting (e.g., Silhavý in The mechanics and thermodynamics of continuous media, Springer, Berlin, 1997, Chaps. 9–12). In the process, the relation of the two formulations to each other is investigated in detail. A particular point in this regard is the concept of dissipation and its model representation in both contexts.

A primeira lei da termodinâmica dos processos homogêneos

Thermodynamics of homogeneous processes, which corresponds to the very special situation in thermodynamics of continuous media, is used to discuss the first law. An important part of this work is the exposition of some typical mathematical errors, frequently found in the traditional presentation of thermodynamics. The concepts of state and process functions are discussed, as well as reverse and reversible processes, temporality and its implications on thermodynamics, energy reservoirs and symmetry. Our proposal is to present the first law by using a time dependent viewpoint coherent with mechanics and the foundations of that viewpoint.

Thermodynamic Formulation of Endochronic Cyclic Viscoplasticity With Damage- Application to Eutectic Sn/Pb Solder Alloy

AbstractIn this paper, an endochronic theory of cyclic viscoplasticy with damage is established based on the irreversible thermodynamics of continuous media with internal state variables containing an isotropic damage parameter. The constitutive equations derived have the same mathematical form as those of convectional endochronic theory without damage, except the effective stress with damage is used. This result coincides with the Lemaitre's statements of stain equivalence principle.Using the experimental cyclic stress-strain curves of 63Sn/37Pb solder bars, corrected from the uniaxially constant displacement amplitude cyclic tests under MTS Tytron microtester, the computational results of cyclic stess-strain curves with several degrees of damage can reproduce the experimental data quite well. Based on compressive buckling appeared in the vicinity of the compressive end parts of the hysteresis loop, the critical values of damage are determined between 0.3 and 0.4.The evolution equation of damage proposed in terms of the intrinsic damage time scale and its results in the modified Coffin-Manson LCF law can be extended in the future research for a statistical theory of life distribution under low cycle fatigue tests.

Deformation Kinetics of Steady Creep in Sn/Pb Solder Alloys With Applications

AbstractIn this paper, a constitutive equation of steady creep rates:is derived based on a liaison of the theory of irreversible thermodynamics of continuous media with internal state variables (ISV); and the deformation kinetics. In steady creep, only one ISV is used, whose evolution equation is derived by the concepts of deformation kinetics, in which micromotions are generated by a group of atoms climbing over a tilted potential barrier of the highest height ε0.Applications of the constitutive equation in the cases of some Sn/Pb solder alloys-63Sn/37Pb, 60Sn/40Pb and 97.5Pb/2.5Sn under shear creep tests; and 98Pb/2Sn under tensile creep tests, show that the theoretical results can describe the experimental data quite well. These results pave the way for future research in the comparisons of creep resistance among solders with various Sn/Pb compositions and in the generalization of three-dimensional constitutive equation.

The Mechanics and Thermodynamics of Continuous Media, Miroslav Šilhavý

The Mechanics and Thermodynamics of Continuous Media, Miroslav Šilhavý

A constitutive relation for microcracked materials including the effects of microcrack opening-closing

In the general framework of the thermodynamics of continuous media (TCM) an elastic damageable model with a microcrack opening-closing threshold is proposed to describe the nonlinear constitutive behavior of ceramic-matrix composite. The assumptions currently made (based on physical considerations) are in fact a direct consequence of the implementation of TCM for these materials that have an internal constraint. When the applied stress is lower than the threshold stress the microcracks are inactive and the material has the behavior of the virgin one. But as soon as the stress level exceeds the threshold, the microcracks are active and the material has an elastic damaged behavior.

Reversible Processes in the Thermodynamics of Continuous Media

Reversible Processes in the Thermodynamics of Continuous Media

Non-Equilibrium Thermodynamics of Continuous Media

Non-Equilibrium Thermodynamics of Continuous Media

Thermodynamic formulation of finite linear viscoelasticity for anisotropic media

The theory of irreversible thermodynamics of continuous media with fading memory is used to formulate general constitutive equations of finite linear viscoelasticity. Specific forms for transversely isotropic and orthotropic media based on both the mechanical and thermodynamic theories are found.

On some special problems of thermodynamics of continuous media

On some special problems of thermodynamics of continuous media