Abstract
As I pointed out at the end of Sect. 4 in [6] of my booklet Five Contributions to Natural Philosophy, it should be possible to make the principle of material frame-indifference vacuously satisfied by using an intrinsic mathematical frame-work that does not use an external frame-space at all when describing the internal interactions of a physical system. Here I will do just that for the classical theory of elasticity and also for the theory of hyperelasticity, i.e., elasticity based on a strain-energy function. I will also comment on possible restrictions on the corresponding intrinsic response functions.
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References
W. Noll, Finite-Dimensional Spaces: Algebra, Geometry, and Analysis, Vol. I. Kluwer Academic (1987) 393 pages.
C. Truesdell and W. Noll, The Non-Linear Field Theories of Mechanics, 3rd edn. Springer (2004) 602 pages. (The first edition appeared in 1965.)
W. Noll, Five Contributions to Natural Pilosophy. Published electronically (2004) 73 pages. Posted on the website math.cmu.edu/~wn0g/noll.
W. Noll, Introduction to [3]
W. Noll, On the Principle of Material Frame-Indifference. Second paper in [3].
W. Noll, Updating the Non-Linear Field Theories of Mechanics. Third paper in [3].
W. Noll, The Theory of Surface Interactions (2005) 14 pages. Posted on the website math.cmu.edu/~wn0g/noll.
W. Noll, A new mathematical theory of simple materials. Arch. Ration. Mech. Anal. 52 (1972) 1–50.
W. Noll, Isocategories and Tensor Functors. Dept. of Mathematics, Carnegie Mellon University, Research Report No.92-142 (1992) 19 pages. Posted on the website math.cmu.edu/~wn0g/noll.
W. Noll and J.J. Schäffer, Orders, gauge, and distance in faceless linear cones; with examples relevant to continuum mechanics and relativity. Arch. Ration. Mech. Anal. 66 (1977) 345–377.
W. Noll and E. Virga, Fit regions and functions of bounded variation. Arch. Ration. Mech. Anal. 102 (1988) 1–21.
B.D. Coleman and W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13 (1963) 167–178.
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This paper is based, in part, on lectures that I gave on June 29, 2005 at the meeting in Reggio-Calabria in honor of the 65th birthday of Gianpietro Del Piero and on July 6, 2005, at the University of Messina.
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Noll, W. A Frame-Free Formulation of Elasticity. J Elasticity 83, 291–307 (2006). https://doi.org/10.1007/s10659-005-9046-9
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DOI: https://doi.org/10.1007/s10659-005-9046-9