Material indifference: A principle or a convenience

Edelen, Dominic G. B.; McLennan, James A.

doi:10.1016/0020-7225(73)90031-1

Cited by 72 publications

(25 citation statements)

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“…Said differently, any average ascribed to time t is performed over the time interval t À Á ( t in inertial frames, and then referred at time t to a general frame. Finally, resurrecting superscript F+_ (see footnote 21), material points can be associated bijectively with geometrical points in the region occupied by M þ at any time 22 in such a way that they trace out the trajectories of field v þ w;Á . REMARK 12.…”

Section: Time Averaging and Mass Balance For Time-dependent Systemsmentioning

confidence: 99%

Some Primitive Concepts in Continuum Mechanics Regarded in Terms of Objective Space-Time Molecular Averaging: The Key Rôle Played by Inertial Observers

Murdoch

2006

J Elasticity

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In Continuum Mechanics the notions of body, material point, and motion, are primitive. Here these concepts are derived for any (possibly time-dependent) material system via mass and momentum densities whose values are local spacetime averages of molecular quantities. The averaging procedure necessary to ensure molecular-based densities can be agreed upon by all observers (that is, are objective) has implications for constitutive relations. Specifically, such relations should first be expressed in terms of Galilean-invariant functions of the motion relative to an inertial frame. Thereafter such relations can be re-phrased for general observers, thereby yielding general-frame constitutive relations compatible with material frame-indifference. Two postulates concerning observer agreement (which together constitute a statement of material frameindifference) are shown to imply that any stress response function which is assumed to depend upon the motion in an inertial (general) frame must be Galilean-invariant (invariant under superposed rigid body motions). Accordingly, invariance under superposed rigid body motions is not a fundamental tenet of continuum physics, but rather a consequence of material frameindifference whenever constitutive dependence upon motion in a general observer frame is postulated. (2000): 70F, 74A. Mathematics Subject Classifications

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Section: Time Averaging and Mass Balance For Time-dependent Systemsmentioning

confidence: 99%

Some Primitive Concepts in Continuum Mechanics Regarded in Terms of Objective Space-Time Molecular Averaging: The Key Rôle Played by Inertial Observers

Murdoch

2006

J Elasticity

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“…Though a subject of controversy (Edelen and McLennan [1]; Wang [15]), the requirement of material frame indifference (MFI) plays a major role in constitutive theory (Noll [10]; Oldroyd [11]; Truesdell and Toupin [14]). Part of the disagreement lies in whether MFI should be adopted or a less restrictive requirement, the principle of Galilean invariance, should be used to formulate constitutive relations.…”

Section: Interfacial Jump Conditionsmentioning

confidence: 99%

“…Thus, we need to decide whether we will enforce the requirement of material frame indifference for this problem. We are aware of the controversy surrounding this topic (Edelen and McLennan [1]; Wang [15]) and we will not pursue a thorough discussion of it. We require Galilean invariance, instead of the more restrictive material frame indifference, within the framework of classical non-relativistic theory, for the sake of consistency to put the constitutive relations on the electromagnetic and the thermodynamic quantities on the same footing.…”

Section: Introductionmentioning

confidence: 99%

Modeling of the microwave drying process of aqueous dielectrics

Rajagopal

Tao

2002

Z. angew. Math. Phys.

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We propose a thermodynamic framework for describing the microwave drying process of aqueous dielectrics based on Maxwell-Lorentz field equations and mixture theory. Several issues are discussed such as the form of entropy equation; the constitutive relations for the macroscopic electric polarization vectors, Cauchy stresses, heat fluxes, internal momentum supplies, etc., for each component of the mixture: porous solid, water and gas in different regions; and the interfacial jump conditions between different regions in the mixture. A brief examination of the status of material frame indifference within the context of our framework is presented.

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“…The principle and also its formulation initiated a long and unfinished discussion among those who are interested in the fundamental aspects of continuum physics. Here we give an incomplete list of the most important looking related works [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43].…”

Section: Introductionmentioning

confidence: 99%

Galilean relativistic fluid mechanics

Ván

2017

Continuum Mech. Thermodyn.

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Abstract. Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given.The usual basic fields of mass, momentum, energy and their current densities, the heat flux, pressure tensor and diffusion flux are the time-and spacelike components of the third order mass-momentum-energy density-flux four-tensor. The corresponding Galilean transformation rules of the physical quantities are derived.It is proved, that the non-equilibrium thermodynamic frame theory, including the thermostatic Gibbs relation and extensivity condition and also the entropy production is independent of the reference frame and also the flow-frame of the fluid. The continuity-Fourier-Navier-Stokes equations are obtained almost in the traditional form if the flow of the fluid is fixed to the temperature. This choice of the flow-frame is the thermo-flow.A simple consequence of the theory is that the relation between the total, kinetic and internal energies is a Galilean transformation rule.

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Material indifference: A principle or a convenience

Cited by 72 publications

References 1 publication

Some Primitive Concepts in Continuum Mechanics Regarded in Terms of Objective Space-Time Molecular Averaging: The Key Rôle Played by Inertial Observers

Some Primitive Concepts in Continuum Mechanics Regarded in Terms of Objective Space-Time Molecular Averaging: The Key Rôle Played by Inertial Observers

Modeling of the microwave drying process of aqueous dielectrics

Galilean relativistic fluid mechanics

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