Abstract
In this paper objectivity and material frame-indifference are systematically discussed, because changing the observer and changing the motion of a material with respect to an observer independent standard frame of reference have to be distinguished carefully. Objectivity and observer invariance of the physical laws and of the constitutive mappings are introduced. Semi-objectivity and objectivity of different time derivative operators are investigated. As examples, changing the observer in liquid crystal theory and changing the motion in linear heat conducting materials is considered.
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References
Noll W. (1958). A mathematical theory of the mechanical behavior of continuous media. Arch. Rat. Mech. Anal. 2: 197
Truesdell, C., Toupin, R.A.: Encyclopedia of physics. In: Flügge, S. (ed.) The Classical Field Theories, vol. III/1, Sect. 157. Springer, Berlin (1960)
Truesdell, C., Noll, W.: Encyclopedia of physics. In: Flügge, S. (ed.) Non-Linear Field Theories of Mechanics, vol. III/3, Sect. 19. Springer, Berlin (1965)
Truesdell C. (1969). Rational Thermodynamics, Lecture 5. McGraw-Hill, New York
Bressan A. (1972). On the principles of material indifference and local equivalence. Meccanica 7: 3
Müller I. (1972). On the frame dependence of stress and heat flux. Arch. Rat. Mech. Anal. 45: 241
Edelen D.G.B. and McLennan J.A. (1973). Material indifference: a principle or a convenience. Int. J. Engng. Sci. 11: 813
Noll, W.: The foundations of classical mechanics in the light of recent advances in continuum mechanics. In: The axiomatic method, with special reference to geometry and physics (Symposium at Berkeley 1957). North-Holland, Amsterdam. In: Noll, W.: The foundations of mechanics and thermodynamics, Selected Papers, pp. 32–47. Springer, Berlin (1974)
Lianis G. and Papastavridis J.G. (1977). The proper rigid frame and the principle of objectivity. Nuovo Cim. 38B: 37
Muschik W. and Brunk G. (1977). Bemerkungen zur objektivität und zur materiellen indifferenz bei beliebigem Wechsel des Bezugssystems. ZAMM 57: T108
Bampi F. and Morro A. (1980). Objectivity and objective time derivatives in continuum physics. Found. Phys. 10: 905
Murdoch A.I. (1982). On material frame-indifference. Proc. R. Soc. Lond. A A380: 417
Muschik W. (1982). Prinzip der Objektivität, Rahmenforderung oder Naturgesetz. ZAMM 62: T143
Appleby P.G. and Kadianakis N. (1986). A frame-independent description of the principles of classical mechanics. Arch. Rat. Mech. Anal. 95: 1
Muschik W. (1990). Aspects of non-equilibrium thermodynamics, Sect. 1.2. World Scientific, Singapore
Muschik W. (1998). Objectivity and frame indifference, revisited. Arch. Mech. 50: 541
Svendsen B. and Bertram A. (1999). On frame-indifference and form-invariance in constitutive theory. Acta Mech. 132: 195
Muschik, W.: Covariance and objectivity in electrodynamics. In: Maruszewski, B. (ed.) Cia̧głe modele zjawisk mechanicznych w układach materialnych i środowisku, p. 71. Wydawnictwo Politechniki Poznanskiej, Poznan (1999)
Bertram A. and Svendsen B. (2001). On material objectivity and reduced constitutive equations. Arch. Mech. 53: 653
Muschik W. and Restuccia L. (2002). Changing the observer and moving materials in continuum physics: objectivity and frame-indifference. Tech. Mech. 22: 152
Hermann, H., Muschik, W., Rückner, G., Restuccia, L.: Constitutive mappings and the non-objective part of material frame indifference. In: Procs of The International Symposium on Trends in Continuum Physics (TRECOP’04), November 17–19, 2004, Poznan, Poland, p. 128
Ericksen J.L. (1960). Anisotropic fluids. Arch. Rat. Mech. Anal. 4: 231
Leslie F.M. (1968). Some constitutive equations for liquid crystals. Arch. Rat. Mech. Anal. 28: 265
Blenk S. and Muschik W. (1991). Orientational balances for nematic liquid crystals. J. Non-Equilib. Thermodyn. 16: 67
Blenk S., Ehrentraut H. and Muschik W. (1991). Statistical foundation of macroscopic balances for liquid crystals in alignment tensor formulation. Physica A 174: 119
Muschik W., Ehrentraut H. and Blenk S. (1995). Ericksen–Leslie liquid crystal theory revisited from a mesoscopic point of view. J. Non-Equilib. Thermodyn. 20: 92
Muschik W., Papenfuss C. and Ehrentraut H. (2004). Mesoscopic theory of liquid crystals. J. Non-Equilib. Thermodyn. 29: 75
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Muschik, W., Restuccia, L. Systematic remarks on objectivity and frame-indifference, liquid crystal theory as an example. Arch Appl Mech 78, 837–854 (2008). https://doi.org/10.1007/s00419-007-0193-2
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DOI: https://doi.org/10.1007/s00419-007-0193-2