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On rheology and thermodynamics of irreversible processes
No full textBy generalizing the thermodynamical theory for elasticity and plasticity, developed by the author in a previous paper, a general formalism is obtained in which such phenomena as elasticity, plasticity (Maxwell bodies), viscoelasticity (Kelvin bodies), and viscous fluid flow are included. The rheological equations for Jeffreys bodies (viscoanelastic media without memory) are derived. It is seen that (also in isotropic media) a cross-effect may exist between viscoelasticity and anelasticity (plasticity). We restrict ourselves to small elastic and inelastic deformations
On vectorial internal variables and dielectric and magnetic relaxation phenomena
No full textIn a previous paper it has been shown by the author that a vectorial internal variable may give rise to dielectric relaxation phenomena and that if such a variable occurs the polarization P may be written in the form P = P(0) + P(1), where changes in P(0) are reversible processes and changes in P(1) are irreversible.
In this paper we introduce a somewhat more general assumption concerning the entropy. This generalization leads to the possibility that both changes in P(0) and in P(1) are irreversible phenomena. In this way a formalism is obtained with two relaxation times for dielectric relaxation. In particular we investigate the linearized form of the theory. It is seen that in the linear case the relation between the electric field E and the polarization P has the form of a linear relation among E, P, the first derivatives with respect to time of E and P, and the second derivative with respect to time of P. Debye's equation for dielectric relaxation in polar liquids and the equation derived by De Groot and Mazur are special cases of the equation which has been obtained in this paper. Analogous results can be derived for magnetic relaxation phenomena. Snoek's equation and the equation obtained by De Groot and Mazur are special cases of the equation for magnetic relaxation which is derived in this paper
On the thermodynamics of viscosity and plasticity
No full textThe thermodynamic theory for viscosity and plasticity phenomena, given by the author in some previous papers, is further developed. A rather general Theological equation is derived from which the rheological equations for Poynting-Thomson, Jeffreys, Maxwell, Kelvin, Hooke, Newton, Prandtl-Reuss, and Bingham media may be considered as degeneracies. The physical meaning of these degeneracies is discussed. In particular it is seen that a Bingham medium may be considered as a special case of a Jeffreys medium. Explicit expressions are given for the free energy, the internal energy, and the entropy of the substances just mentioned. Temperature phenomena are taken into account. Some higher order effects (Poynting effect, structural viscosity, and thixotropy) are discussed from the point of view of the developed theory. A generalization of the Von Mises yield criterion is proposed. With the help of this criterion the Bauschinger effect may be explained as a consequence of memory phenomena. For media without memory this new criterion and the Von Mises criterion coalesce. It will be seen that for plastic media with memory a rheological equation holds, which may be considered as a generalization of the Poynting-Thomson equation. Both distortional and volumetric phenomena are considered. It is assumed that the deformations and rotations are small
On dielectric and magnetic relaxation phenomena and vectorial internal degrees
No full textIt has been shown by the author in a previous paper that thermodynamic vectorial internal degrees of freedom which influence the polarization or the magnetization of a medium may give rise to dielectric or magnetic relaxation phenomena. Snoek's equation for magnetic relaxation phenomena was derived and it was shown that Debye's theory for dielectric after-effects in polar liquids is a special case of the developed theory. In this paper it is shown that if Z is some vectorial internal degree of freedom which influences the polarization a new internal degree of freedom bip(int) may be defined which is a function of biZ, which may replace biZ as vectorial internal degree of freedom and which is a part of the total specific polarization. Furthermore, p(int) may be introduced in such a way that the remaining part of the polarization, p(el) (defined by p(el)=p- pint), where p is the total polarization per unit of mass), has the property that it vanishes for all values of p(int) if the medium is in a state where the electric field E and the mechanical elastic stresses vanish and the temperature of the medium equals some reference temperature. If the equations of state are linearized the latter result implies for an isotropic medium E=¿a(0,0)(bdp) p(el), where ¿ is the mass density and a(0,0)(P) a constant. On the other hand p(int) satifies a relaxation equation. It is seen that the use of p(int) as an internal degree of freedom is of great advantage. This is connected with the fact that p(int) is a measurable quantity in contradistinction to an arbitrary hidden vectorial internal degree of freedom. Analogous results may be obtained for magnetic after-effects
A note on the thermodynamics of Maxwell bodies, Kelvin bodies (Voigt bodies), and fluids
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Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
On heat dissipation due to irreversible mechanical phenomena in continuous media
No full textThe heat dissipation function is derived for media in which viscous and inelastic (plastic) flows occur. It is shown that the heat dissipation is a quadratic expression in the components of the stress tensor, the strain tensor, and the time derivative of the latter tensor, where the coefficients are simple algebraic functions of the coefficients which occur in the stress-strain relation. The heat dissipation functions for ordinary viscous fluids (with shear and volume viscosity), and for Maxwell, Kelvin (Voigt), Poynting-Thomson, Jeffreys, Prandtl-Reuss, Bingham, Saint Venant, and Hooke media are special cases of the more general expression which is derived. For Kelvin media (and for ordinary viscous fluids) the heat dissipation function reduces to the Rayleigh dissipation function. From the non-negative character of the entropy production and from stability considerations some inequalities are derived for the coefficients which occur in the theory
A thermodynamic discussion of the possibility of singular yield conditions in plasticity theory
No full textA generalization is given of the author's theory for plasticity phenomena. The generalization leads to the possibility that the yield surface has singularities. From the theory a formula may be derived which is analogous to a formula proposed by Koiter for plastic flow in media with singular yield surfaces. The possibility of elastic relaxation phenomena in the preplastic range is included in the developed formalism
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