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References

Published online by Cambridge University Press:  05 February 2012

Ellad B. Tadmor
Affiliation:
University of Minnesota
Ronald E. Miller
Affiliation:
Carleton University, Ottawa
Ryan S. Elliott
Affiliation:
University of Minnesota
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Continuum Mechanics and Thermodynamics
From Fundamental Concepts to Governing Equations
, pp. 334 - 342
Publisher: Cambridge University Press
Print publication year: 2011

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References

[Adk83] C. J., Adkins. Equilibrium Thermodynamics. Cambridge: Cambridge University Press, third edition, 1983.Google Scholar
[AF73] R. J., Atkin and N., Fox. On the frame-dependence of stress and heat flux in polar fluids. J. Appl. Math. Phys. (ZAMP), 24:853–860, 1973.Google Scholar
[AK86] P. G., Appleby and N., Kadianakis. A frame-independent description of the principles of classical mechanics. Arch. Ration. Mech. Anal., 95:1–22, 1986.Google Scholar
[Ale56] H. G., Alexander. The Leibniz–Clarke Correspondence. Manchester: Manchester University Press, 1956.Google Scholar
[Art95] R. T. W., Arthur. Newton's fluxions and equably flowing time. Stud. Hist. Phil. Sci., 26:323–351, 1995.Google Scholar
[AS02] S. N., Atluri and S. P., Shen. The meshless local Petrov–Galerkin (MLPG) method: A simple less-costly alternative to the finite element and boundary element methods. Comput. Model. Eng. Sci., 3(1):11–51, 2002.Google Scholar
[AT11] N. C., Admal and E. B., Tadmor. Stress and heat flux for arbitrary multi-body potentials: A unified framework. J. Chem. Phys., 134:184106, 2011.Google Scholar
[AW95] G. B., Arfken and H. J., Weber. Mathematical Methods of Physicists. San Diego: Academic Press, Inc., fourth edition, 1995.Google Scholar
[AZ00] S. N., Atluri and T., Zhu. New concepts in meshless methods. Int. J. Numer. Methods Eng., 47:537–556, 2000.Google Scholar
[Bal76] J. M., Ball. Convexity conditions and existence theorems in nonlinear elasticity. Arch. Ration. Mech. Anal., 63(4):337–403, 1976.Google Scholar
[Ban84] W., Band. Effect of rotation on radial heat flow in a gas. Phys. Rev. A, 29:2139–2144, 1984.Google Scholar
[BBS04] A. Bóna, I., Bucataru, and M. A., Slawinski. Material symmetries of elasticity tensors. Q. J. Mech. Appl. Math., 57(4):583–598, 2004.Google Scholar
[BdGH83] R. B., Bird, P. G., de Gennes, and W. G., Hoover. Discussion. Physica A, 118:43–47, 1983.Google Scholar
[Bea67] M. F., Beatty. On the foundation principles of general classical mechanics. Arch. Ration. Mech. Anal., 24:264–273, 1967.Google Scholar
[BG68] R. L., Bishop and S. I., Goldberg. Tensor Analysis on Manifolds. New York: Macmillan, 1968.Google Scholar
[Bil86] E. W., Billington. The Poynting effect. Acta Mech., 58:19–31, 1986.Google Scholar
[BJ96] G. I., Barenblatt and D. D., Joseph, editors. Collected Papers of R. S. Rivlin, volumes I & II. New York: Springer, 1996.Google Scholar
[BK62] P. J., Blatz and W. L., Ko. Application of finite elasticity to the deformation of rubbery materials. Trans. Soc. Rheol., 6:223–251, 1962.Google Scholar
[BKO+ 96] T., Belytschko, Y., Krongauz, D., Organ, M., Fleming, and P., Krysl. Meshless methods: An overview and recent developments. Comput. Meth. Appl. Mech. Eng., 139:3–47, 1996.Google Scholar
[BLM00] T., Belytschko, W. K., Liu, and B., Moran. Nonlinear Finite Elements for Continua and Structures. Chichester: Wiley, 2000.Google Scholar
[BM80] F., Bampi and A., Morro. Objectivity and objective time derivatives in continuum mechanics. Found. Phys., 10:905–920, 1980.Google Scholar
[BM97] I., Babuska and J. M., Melenk. The partition of unity method. Int. J. Numer. Methods Eng., 40(4):727–758, 1997.Google Scholar
[BSL60] R. B., Bird, W. E., Stewart, and E. N., Lightfoot. Transport Phenomena. New York: Wiley, 1960.Google Scholar
[BT03] B., Buffoni and J., Toland. Analytic Theory of Global Bifurcation: An Introduction. Princeton Series in Applied Mathematics. Princeton: Princeton University Press, first edition, 2003.Google Scholar
[Cal85] H. B., Callen. Thermodynamics and an Introduction to Thermostatics. New York: John Wiley and Sons, second edition, 1985.Google Scholar
[Car67] M. M., Carroll. Controllable deformations of incompressible simple materials. Int. J. Eng. Sci., 5:515–525, 1967.Google Scholar
[CG95] M., Como and A., Grimaldi. Theory of Stability of Continuous Elastic Structures. Boca Raton: CRC Press, 1995.Google Scholar
[CG01] P., Cermelli and M. E., Gurtin. On the characterization of geometrically necessary dislocations in finite plasticity. J. Mech. Phys. Solids, 49:1539–1568, 2001.Google Scholar
[Cha99] P., Chadwick. Continuum Mechanics: Concise Theory and Problems. Mineola: Dover, second edition, 1999.Google Scholar
[CJ93] C., Chu and R. D., James. Biaxial loading experiments on Cu–Al–Ni single crystals. In K. S., Kim, editor, Experiments in Smart Materials and Structures, volume 181, pages 61–69. New York: ASME-AMD, 1993.Google Scholar
[CM87] S. C., Cowin and M. M., Mehrabadi. On the identification of material symmetry for anisotropic elastic materials. Q. J. Mech. Appl. Math., 40:451–476, 1987.Google Scholar
[CN63] B. D., Coleman and W., Noll. The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal., 13:167–178, 1963.Google Scholar
[CR07] D., Capecchi and G. C., Ruta. Piola's contribution to continuum mechanics. Arch. Hist. Exact Sci., 61:303–342, 2007.Google Scholar
[CVC01] P., Chadwick, M., Vianello, and S. C., Cowin. A new proof that the number of linear elastic symmetries is eight. J. Mech. Phys. Solids, 49:2471–2492, 2001.Google Scholar
[dGM62] S. R., de Groot and P., Mazur. Non-Equilibrium Thermodynamics. Amsterdam: North-Holland Publishing Company, 1962.Google Scholar
[DiS91] R., DiSalle. Conventionalism and the origins of the inertial frame concept. In A., Fine, M., Forbes, and L., Wessels, editors, PSA 1990, volume 2 of PSA - Philosophy of Science Association Proceedings Series. Biennial Meeting of the Philosophy of Science Assoc, Minneapolis, MN, 1990, pages 139–147. Chicago: University of Chicago Press, 1991.Google Scholar
[DiS02] R., DiSalle. Space and time: Inertial frames. In E. N., Zalta, editor, The Stanford Encyclopedia of Philosophy. Stanford University, Summer 2002. http://plato.stanford.edu/archives/sum2002/entries/spacetime-iframesGoogle Scholar
[DiS06] R., DiSalle. Understanding Space-Time. Cambridge: Cambridge University Press, 2006.Google Scholar
[Duf84] J. W., Dufty. Viscoelastic and non-Newtonian effects in shear-flow. Phys. Rev. A, 30:622–623, 1984.Google Scholar
[Ear70] J., Earman. Who's afraid of absolute space? Australasian J. Philosophy, 48:287–319, 1970.Google Scholar
[EH89] M. W., Evans and D. M., Heyes. On the material frame indifference controversy: Some results from group theory and computer simulation. J. Mol. Liq., 40:297–304, 1989.Google Scholar
[Ein16] A., Einstein. Die Grundlage der allgemeinen Relativitätstheorie. Ann. der Phys., 49:769– 822, 1916.Google Scholar
[EM73] D. G. B., Edelen and J. A., McLennan. Material indifference: A principle or convenience. Int. J. Eng. Sci., 11:813–817, 1973.Google Scholar
[EM90a] A. C., Eringen and G. A., Maugin. Electrodynamics of Continua I: Foundations and Solid Media. New York: Springer, 1990.Google Scholar
[EM90b] A. C., Eringen and G. A., Maugin. Electrodynamics of Continua II: Fluids and Complex Media. New York: Springer, 1990.Google Scholar
[EM90c] D. J., Evans and G. P., Morriss. Statistical Mechanics of Nonequilibrium Liquids. London: Academic Press, 1990.Google Scholar
[Eri54] J. L., Ericksen. Deformations possible in every isotropic, incompressible, perfectly elastic body. J. Appl. Math. Phys. (ZAMP), 5:466–488, 1954.Google Scholar
[Eri55] J. L., Ericksen. Deformations possible in every isotropic compressible, perfectly elastic body. J. Math. Phys, 34:126–128, 1955.Google Scholar
[Eri77] J. L., Ericksen. Special topics in elastostatics. In C.-S., Yih, editor, Advances in Applied Mechanics, volume 17, pages 189–244. New York: Academic Press, 1977.Google Scholar
[Eri02] A. C., Eringen. Nonlocal Continuum Field Theories. New York: Springer, 2002.Google Scholar
[Eu85] B. C., Eu. On the corotating frame and evolution equations in kinetic theory. J. Chem. Phys., 82:3773–3778, 1985.Google Scholar
[Eu86] B. C., Eu. Reply to “comment on ‘on the corotating frame and evolution equations in kinetic theory’”. J. Chem. Phys., 86:2342–2343, 1986.Google Scholar
[FF77] R., Fletcher and T. L., Freeman. A modified Newtonmethod forminimization. J. Optimiz. Theory App., 23:357–372, 1977.Google Scholar
[FMAH94] N. A., Fleck, G. M., Muller, M. F., Ashby, and J. W., Hutchinson. Strain gradient plasticity: Theory and experiment. Acta Metall. Mater., 42:475–487, 1994.Google Scholar
[Fre09] M., Frewer. More clarity on the concept of material frame-indifference in classical continuum mechanics. Acta Mech., 202:213–246, 2009.Google Scholar
[FV89] R. L., Fosdick and E. G., Virga. A variational proof of the stress theorem of Cauchy. Arch. Ration. Mech. Anal., 105:95–103, 1989.Google Scholar
[FV96] S., Forte and M., Vianello. Symmetry classes for elasticity tensors. J. Elast., 43:81–108, 1996.Google Scholar
[Gen96] A. N., Gent. A new constitutive relation for rubber. Rubber Chemistry Tech., 69:59–61, 1996.Google Scholar
[GFA10] M. E., Gurtin, E., Fried, and L., Anand. The Mechanics and Thermodynamics of Continua. Cambridge: Cambridge University Press, 2010.Google Scholar
[GR64] A. E., Green and R. S., Rivlin. On Cauchy's equations of motion. J. Appl. Math. Phys. (ZAMP), 15:290–292, 1964.Google Scholar
[Gra91] H., Grandin. Fundamentals of the Finite Element Method. Prospect Heights: Waveland Press, 1991.Google Scholar
[Gre04] B., Greene. The Fabric of the Cosmos. New York: Vintage Books, 2004.Google Scholar
[Gur65] M. E., Gurtin. Thermodynamics and the possibility of spatial interaction in elastic materials. Arch. Ration. Mech. Anal., 19:339–352, 1965.Google Scholar
[Gur81] M. E., Gurtin. An Introduction to Continuum Mechanics, volume 158 of Mathematics in Science and Engineering. New York: Academic Press, 1981.Google Scholar
[Gur95] M. E., Gurtin. The nature of configurational forces. Arch. Ration. Mech. Anal., 131:67–100, 1995.Google Scholar
[GW66] M. E., Gurtin and W. O., Williams. On the Clausius–Duhem inequality. J. Appl. Math. Phys. (ZAMP), 17:626–633, 1966.Google Scholar
[HM83] M., Heckl and I., Müller. Frame dependence, entropy, entropy flux, and wave speeds in mixtures of gases. Acta Mech., 50:71–95, 1983.Google Scholar
[HMML81] W. G., Hoover, B., Moran, R. M., More, and A. J. C., Ladd. Heat conduction in a rotating disk via nonequilibrium molecular dynamics. Phys. Rev. B, 24:2109–2115, 1981.Google Scholar
[HO03] F. W., Hehl and Y. N., Obukhov. Foundations of Classical Electrodynamics. Boston: Birkhauser, 2003.Google Scholar
[Hol00] G. A., Holzapfel. Nonlinear Solid Mechanics. Chichester: Wiley, 2000.Google Scholar
[Hug87] T. J. R., Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Englewood Cliffs: Prentice-Hall, 1987.Google Scholar
[IK50] J. H., Irving and J. G., Kirkwood. The statistical mechanical theory of transport processes. IV. the equations of hydrodynamics. J. Chem. Phys., 18:817–829, 1950.Google Scholar
[IM02] K., Ikeda and K., Murota. Imperfect Bifurcation in Structures and Materials: Engineering Use of Group-Theoretic Bifurcation Theory, volume 149 of Applied Mathematical Sciences. New York: Springer, first edition, 2002.Google Scholar
[Jau67] W., Jaunzemis. Continuum Mechanics. New York: Macmillan, 1967.Google Scholar
[JB67] L., Jansen and M., Boon. Theory of Finite Groups. Applications in Physics. Amsterdam: North Holland, 1967.Google Scholar
[Kem89] L. J. T. M., Kempers. The principle of material frame indifference and the covariance principle. Il Nuovo Cimento B, 103:227–236, 1989.Google Scholar
[Kha02] H. K., Khalil. Nonlinear Systems. New York: Prentice-Hall, third edition, 2002.Google Scholar
[Kir52] G., Kirchhoff. Über die Gleichungen des Gleichgewichtes eines elastischen Körpers bei nicht unendlich kleinen Verscheibungen seiner Theile. Sitzungsberichte der Akademie der Wissenschaften Wien, 9:762–773, 1852.Google Scholar
[Koi63] W. T., Koiter. The concept of stability of equilibrium for continuous bodies. Proc. Koninkl. Nederl. Akademie van Wetenschappen, 66(4):173–177, 1963.Google Scholar
[Koi65a] W. T., Koiter. The energy criterion of stability for continuous elastic bodies. – I. Proc. of the Koninklijke Nederlandse Akademie Van Wetenschappen, Ser. B, 68(4):178–189, 1965.Google Scholar
[Koi65b] W. T., Koiter. The energy criterion of stability for continuous elastic bodies. – II. Proc. of the Koninklijke Nederlandse Akademie Van Wetenschappen, Ser. B, 68(4):190–202, 1965.Google Scholar
[Koi65c] W. T., Koiter. On the instability of equilibrium in the absence of a minimum of the potential energy. Proc. of the Koninklijke Nederlandse Akademie Van Wetenschappen, Ser. B, 68(3):107–113, 1965.Google Scholar
[Koi71] W. T., Koiter. Thermodynamics of elastic stability. In P. G., Glockner, editor, Proceedings [of the] Third Canadian Congress of Applied Mechanics May 17–21, 1971 at the University of Calgary, pages 29–37, Calgary: University of Calgary.
[Kov00] A., Kovetz. Electromagnetic Theory. New York: Oxford University Press, 2000.Google Scholar
[KW73] R., Knops and W., Wilkes. Theory of elastic stability. In C., Truesdell, editor, Handbook of Physics, volume VIa/3, pages 125–302. Berlin: Springer-Verlag, 1973.Google Scholar
[Lan70] C., Lanczos. The Variational Principles of Mechanics. Mineola: Dover, fourth edition, 1970.Google Scholar
[Lap51] Pierre, Simon Laplace. A Philosophical Essay on Probabilities [English translation by F. W., Truscott and F. L., Emery]. Dover, New York, 1951.Google Scholar
[LBCJ86] A. S., Lodge, R. B., Bird, C. F., Curtiss, and M. W., Johnson. A comment on “on the corotating frame and evolution equations in kinetic theory”. J. Chem. Phys., 85:2341–2342, 1986.Google Scholar
[Lei68] D. C., Leigh. Nonlinear Continuum Mechanics. New York: McGraw-Hill, 1968.Google Scholar
[Les74] A. M., Lesk. Do particles of an ideal gas collide? J. Chem. Educ., 51:141–141, 1974.Google Scholar
[Liu04] I.-S., Liu. On Euclidean objectivity and the principle of material frame-indifference. Continuum Mech. Thermodyn., 16:177–183, 2004.Google Scholar
[Liu05] I.-S., Liu. Further remarks on Euclidean objectivity and the principle of material frameindifference. Continuum Mech. Thermodyn., 17:125–133, 2005.Google Scholar
[LJCV08] G., Lebon, D., Jou, and J., Casas-Vázquez. Understanding Non-equilitrium Thermodynamics: Foundations, Applications, Frontiers. Berlin: Springer-Verlag, 2008.Google Scholar
[LL09] S., Lipschutz and M., Lipson. Schaum's Outline for Linear Algebra. New York:McGraw-Hill, fourth edition, 2009.Google Scholar
[LRK78] W. M., Lai, D., Rubin, and E., Krempl. Introduction to Continuum Mechanics. New York: Pergamon Press, 1978.Google Scholar
[Lub72] J., Lubliner. On the thermodynamic foundations of non-linear solid mechanics. Int. J. Nonlinear Mech., 7:237–254, 1972.Google Scholar
[Lum70] J. L., Lumley. Toward a turbulent constitutive relation. J. Fluid Mech., 41:413–434, 1970.Google Scholar
[Mac60] E., Mach. The Science of Mechanics: A Critical and Historical Account of its Development. Translated by Thomas J., McCormack. La Salle: Open Court, sixth edition, 1960.Google Scholar
[Mal69] L. E., Malvern. Introduction to the Mechanics of a Continuous Medium. Englewood Cliffs: Prentice-Hall, 1969.Google Scholar
[Mar90] E., Marquit. A plea for a correct translation of Newton's law of inertia. Am. J. Phys., 58:867–870, 1990.Google Scholar
[Mat86] T., Matolcsi. On material frame-indifference. Arch. Ration. Mech. Anal., 91:99–118, 1986.Google Scholar
[McW02] R., McWeeny. Symmetry: An Introduction to Group Theory and its Applications. Mineola: Dover, 2002.Google Scholar
[Mei03] L., Meirovitch. Methods of Analytical Dynamics. Mineola: Dover, 2003.Google Scholar
[MH94] J. E., Marsden and T. J. R., Hughes. Mathematical Foundations of Elasticity. New York: Dover, 1994.Google Scholar
[Mil72] W., Miller, Jr. Symmetry Groups and Their Applications, volume 50 of Pure and Applied Mathematics. New York: Academic Press, 1972. Available online at http://www.ima.umn.edu/∼miller/.Google Scholar
[MM98] P., Moin and K., Mahesh. Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech., 30:539–578, 1998.Google Scholar
[Moo90] D. M., Moody. Unsteady expansion of an ideal gas into a vacuum. J. Fluid Mech., 214:455–468, 1990.Google Scholar
[MR08] W., Muschik and L., Restuccia. Systematic remarks on objectivity and frame-indifference, liquid crystal theory as an example. Arch. Appl. Mech, 78:837–854, 2008.
[Mül72] I., Müller. On the frame dependence of stress and heat flux. Arch. Ration. Mech. Anal., 45:241–250, 1972.Google Scholar
[Mül76] I., Müller. Frame dependence of electric-current and heat flux in a metal. Acta Mech., 24:117–128, 1976.Google Scholar
[Mur82] A. I., Murdoch. On material frame-indifference. Proc. R. Soc. London, Ser. A, 380:417–426, 1982.Google Scholar
[Mur83] A. I., Murdoch. On material frame-indifference, intrinsic spin, and certain constitutive relations motivated by the kinetic theory of gases. Arch. Ration. Mech. Anal., 83:185–194, 1983.Google Scholar
[Mur03] A. I., Murdoch. Objectivity in classical continuum physics: a rationale for discarding the principle of invariance under superposed rigid body motions in favour of purely objective considerations. Continuum Mech. Thermodyn., 15:209–320, 2003.Google Scholar
[Mur05] A. I., Murdoch. On criticism of the nature of objectivity in classical continuum physics. Continuum Mech. Thermodyn., 17:135–148, 2005.Google Scholar
[Nan74] E. J., Nanson. Note on hydrodynamics. Messenger of Mathematics, 3:120–121, 1874.Google Scholar
[Nan78] E. J., Nanson. Note on hydrodynamics. Messenger of Mathematics, 7:182–183, 18771878.Google Scholar
[New62] I., Newton. Philosophiae Naturalis Principia Mathematica [translated by A. Motte revised by F. Gajori], volume I. Berkeley: University of California Press, 1962.Google Scholar
[Nio87] E. M. S., Niou. A note on Nanson's rule. Public Choice, 54:191–193, 1987.Google Scholar
[Nol55] W., Noll. Die Herleitung der Grundgleichungen der Thermomechanik der Kontinua aus der statischen Mechanik. J. Ration. Mech. Anal., 4:627–646, 1955.Google Scholar
[Nol58] W., Noll. A mathematical theory of the mechanical behaviour of continuous media. Arch. Ration. Mech. Anal., 2:197–226, 1958.Google Scholar
[Nol63] W., Noll. La mécanique classique, basée sur un axiome d'objectivité. In La Méthode Axiomatique dans les Mécaniques Classiques et Nouvelles, pages 47–56, Paris: Gauthier-Villars, 1963.Google Scholar
[Nol73] W., Noll. Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Ration. Mech. Anal., 52:62–92, 1973.Google Scholar
[Nol87] W., Noll. Finite-Dimensional Spaces: Algebra, Geometry and Analysis, volume I. Dordrecht: Kluwer, 1987. Available online at http://www.math.cmu.edu/∼wn0g/.Google Scholar
[Nol04] W., Noll. Five contributions to natural philosophy, 2004. Available online at http://www.math.cmu.edu/∼wn0g/noll.
[Nol06] W., Noll. A frame-free formulation of elasticity. J. Elast., 83:291–307, 2006.Google Scholar
[NW99] J., Nocedal and S. J., Wright. Numerical Optimization. New York: Springer Verlag, 1999.Google Scholar
[Nye85] J. F., Nye. Physical Properties of Crystals. Oxford: Clarendon Press, 1985.Google Scholar
[Ogd84] R. W., Ogden. Non-linear Elastic Deformations. Ellis Horwood, Chichester, 1984.Google Scholar
[OIZT96] E., Onate, S., Idelsohn, O. C., Zienkiewicz, and R. L., Taylor. A finite point method in computational mechanics. Applications to convective transport and fluid flow. Int. J. Numer. Methods Eng., 39(22):3839–3866, 1996.Google Scholar
[Old50] J. G., Oldroyd. On the formulation of rheological equations of state. Proc. R. Soc. London, Ser. A, 200:523–541, 1950.Google Scholar
[PC68] H. J., Petroski and D. E., Carlson. Controllable states of elastic heat conductors. Arch. Ration. Mech. Anal., 31(2):127–150, 1968.Google Scholar
[Pio32] G., Piola. La meccanica de' corpi naturalmente estesi trattata col calcolo delle variazioni. In Opuscoli Matematici e Fisici di Diversi Autori, volume 1, pages 201–236. Milano: Paolo Emilio Giusti, 1832.Google Scholar
[PM92] A. R., Plastino and J. C., Muzzio. On the use and abuse of Newton's second law for variable mass problems. Celestial Mech. and Dyn. Astron., 53:227–232, 1992.Google Scholar
[Pol71] E., Polak. Computational Methods in Optimization: A Unified Approach, volume 77 of Mathematics in Science and Engineering. New York: Academic Press, 1971.Google Scholar
[Poy09] J. H., Poynting. On pressure perpendicular to the shear-planes in finite pure shears, and on the lengthening of loaded wires when twisted. Proc. R. Soc. London, Ser. A, 82:546–559, 1909.Google Scholar
[PTVF92] W. H., Press, S. A., Teukolsky,W. T., Vetterling, and B. P., Flannery. Numerical Recipes in FORTRAN: The Art of Scientific Computing. Cambridge: Cambridge University Press, second edition, 1992.Google Scholar
[PTVF08] W. H., Press, S. A., Teukolsky, W. T., Vetterling, and B. P., Flannery. Numerical recipes: The art of scientific computing. http://www.nr.com, 2008.
[Rei45] M., Reiner. A mathematical theory of dilatancy. Am. J. Math., 67:350–362, 1945.Google Scholar
[Rei59] H., Reichenbach. Modern Philosophy of Science. New York: Routledge & Kegan Paul, 1959.Google Scholar
[Riv47] R. S., Rivlin. Hydrodynamics of non-newtonian fluids. Nature, 160:611–613, 1947.Google Scholar
[Riv48] R. S., Rivlin. Large elastic deformations of isotropic materials. II. Some uniqueness theorems for pure, homogeneous deformation. Philos. Trans. R. Soc. London, Ser. A, 240:491–508, 1948.Google Scholar
[Riv74] R. S., Rivlin. Stability of pure homogeneous deformations of an elastic cube under dead loading. Q. Appl. Math., 32:265–271, 1974.Google Scholar
[Ros08] J., Rosen. Symmetry Rules: How Science and Nature are Founded on Symmetry. The Frontiers Collection. Berlin: Springer, 2008.Google Scholar
[RS51] R. S., Rivlin and D. W., Saunders. Large elastic deformations of isotropic materials VII. experiments on the deformation of rubber. Philos. Trans. R. Soc. London, Ser. A, 243:251–288, 1951.Google Scholar
[Rub00] M. B., Rubin. Cosserat Theories: Shells, Rods and Points, volume 79 of Solid Mechanics and its Applications. Dordrecht: Kluwer, 2000.Google Scholar
[Rue99] D., Ruelle. Smooth dynamics and new theoretical ideas in nonequilibrium statistical mechanics. J. Stat. Phys., 95:393–468, 1999.Google Scholar
[Rus06] A., Ruszczyński. Nonlinear Optimization. Princeton: Princeton University Press, 2006.Google Scholar
[Rys85] G., Ryskin. Misconception which led to the “material frame-indifference” controversy. Phys. Rev. A, 32:1239–1240, 1985.Google Scholar
[SA04] S., Shen and S. N., Atluri. Multiscale simulation based on the meshless local Petrov–Galerkin (MLPG) method. Comput. Model. Eng. Sci., 5:235–255, 2004.Google Scholar
[Saa03] Y., Saad. Iterative Methods for Sparse Linear Systems. Philadelphia: Society for Industrial and Applied Mathematics, 2003.Google Scholar
[Sac01] Giuseppe, Saccomandi. Universal results in finite elasticity. In Y. B., Fu and R. W., Ogden, editors, Nonlinear Elasticity: Theory and Applications, number 283 in London Mathematical Society Lecture Note Series, chapter 3, pages 97–134. Cambridge: Cambridge University Press, 2001.Google Scholar
[Sal01] J., Salençon. Handbook of Continuum Mechanics: General Concepts, Thermoelasticity. Berlin: Springer, 2001.Google Scholar
[SB99] B., Svendsen and A., Bertram. On frame-indifference and form-invariance in constitutive theory. Acta Mech., 132:195–207, 1999.Google Scholar
[SG63] R. T., Shield and A. E., Green. On certain methods in the stability theory of continuous systems. Arch. Ration. Mech. Anal., 12(4):354–360, 1963.Google Scholar
[SH96] A., Sadiki and K., Hutter. On the frame dependence and form invariance of the transport equations for the Reynolds stress tensor and the turbulent heat flux vector: Its consequences on closure models in turbulence modelling. Continuum Mech. Thermodyn., 8:341–349, 1996.Google Scholar
[Shi71] R. T., Shield. Deformations possible in every compressible isotropic perfectly elastic material. J. Elast., 1:145–161, 1971.Google Scholar
[Sil02] S. A., Silling. The reformulation of elasiticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids, 48:175–209, 2002.Google Scholar
[SK95] F. M., Sharipov and G. M., Kremer. On the frame dependence of constitutive equations. I. Heat transfer through a rarefied gas between two rotating cylinders. Continuum Mech. Thermodyn., 7:57–71, 1995.Google Scholar
[SL09] R., Soutas-Little. History of continuum mechanics. In J., Merodio and G., Saccomandi, editors, Continuum Mechanics, EOLSS-UNESCO Encyclopedia, chapter 2. Paris: UNSECO, 2009. Available online at http://www.eolss.net.Google Scholar
[SMB98] N., Sukumar, B., Moran, and T., Belytschko. The natural element method in solid mechanics. Int. J. Numer. Methods Eng., 43(5):839+, 1998.Google Scholar
[Söd76] L. H., Söderholm. The principle of material frame-indifference and material equations of gases. Int. J. Eng. Sci., 14:523–528, 1976.Google Scholar
[Sok56] I. S., Sokolnikoff. Mathematical Theory of Elasticity. New York: McGraw-Hill, second edition, 1956.Google Scholar
[SP65] M., Singh and A. C., Pipkin. Note on Ericksen's problem. Z. angew. Math. Phys., 16:706–709, 1965.Google Scholar
[Spe81] C. G., Speziale. Some interesting properties of two-dimensional turbulence. Phys. Fluids, 24:1425–1427, 1981.Google Scholar
[Spe87] C. G., Speziale. Comments on the “material frame-indifference” controversy. Phys. Rev. A, 36:4522–4525, 1987.Google Scholar
[Ste54] E., Sternberg. On Saint-Venant's principle. Q. Appl. Math., 11(4):393–402, 1954.Google Scholar
[TA86] N., Triantafyllidis and E. C., Aifantis. A gradient approach to localization of deformation. 1. Hyperelastic materials. J. Elast., 16:225–237, 1986.Google Scholar
[TG51] S. P., Timoshenko and J. N., Goodier. Theory of Elasticity. New York: McGraw-Hill, 1951.Google Scholar
[TG61] S. P., Timoshenko and J., Gere. Theory of Elastic Stability. New York: McGraw-Hill, second edition, 1961. Note: A new Dover edition came out in 2009.Google Scholar
[TG06] Z., Tadmor and C. G., Gogos. Principles of Polymer Processing. Hoboken: Wiley, second edition, 2006.Google Scholar
[Tho82] J. M. T., Thompson. Instabilities and Catastrophes in Science and Engineering. Chichester: Wiley, 1982.Google Scholar
[TM04] P. A., Tipler and G., Mosca. Physics for Scientists and Engineers, volume 2. New York: W. H.|Freeman, fifth edition, 2004.Google Scholar
[TM11] E. B., Tadmor and R. E., Miller. Modeling Materials: Continuum, Atomistic and Multiscale Techniques. Cambridge: Cambridge University Press, 2011.Google Scholar
[TN65] C., Truesdell and W., Noll. The non-linear field theories of mechanics. In S., Flügge, editor, Handbuch der Physik, volume III/3, pages 1–603. Springer, 1965.Google Scholar
[TN04] C., Truesdell and W., Noll. In S. S., Antman, editor, The Non-linear Field Theories of Mechanics. Berlin: Springer-Verlag, third edition, 2004.Google Scholar
[Tre48] L. R. G., Treloar. Stress and birefringence in rubber subjected to general homogeneous strain. Proc. Phys. Soc. London, 60:135–144, 1948.Google Scholar
[Tru52] C., Truesdell. The mechanical foundations of elasticity and fluid dynamics. J. Ration. Mech. Anal., 1(1):125–300, 1952.Google Scholar
[Tru66a] C., Truesdell. The Elements of Continuum Mechanics. New York: Springer-Verlag, 1966.Google Scholar
[Tru66b] C., Truesdell. Thermodynamics of deformation. In S., Eskinazi, editor, Modern Developments in the Mechanics of Continua, pages 1–12, New York: Academic Press, 1966.Google Scholar
[Tru68] C., Truesdell. Essays in the History of Mechanics. New York: Springer-Verlag, 1968.Google Scholar
[Tru76] C., Truesdell. Correction of two errors in the kinetic theory of gaseswhich have been used to cast unfounded doubt upon the principle of material frame-indifference. Meccanica, 11:196–199, 1976.Google Scholar
[Tru77] C., Truesdell. A First Course in Rational Continuum Mechanics. New York: Academic Press, 1977.Google Scholar
[Tru84] C., Truesdell. Rational Thermodynamics. New York: Springer-Verlag, second edition, 1984.Google Scholar
[TT60] C., Truesdell and R., Toupin. The classical field theories. In S., Flügge, editor, Handbuch der Physik, volume III/1, pages 226–793. Berlin: Springer, 1960.Google Scholar
[Voi10] W., Voigt. Lehrbuch der Kristallphysik (mit Ausschluss der Kristalloptik). Leipzig: Teubner, 1910.Google Scholar
[Wal72] D. C., Wallace. Thermodynamics of Crystals. Mineola: Dover, 1972.Google Scholar
[Wal03] D. J., Wales. Energy Landscapes. Cambridge: Cambridge University Press, 2003.Google Scholar
[Wan75] C. C., Wang. On the concept of frame-indifference in continuum mechanics and in the kinetic theory of gases. Arch. Ration. Mech. Anal., 45:381–393, 1975.Google Scholar
[Wei11] E. W., Weisstein. Einstein summation. http://mathworld.wolfram.com/Einstein-Summation.html. Mathworld – A Wolfram Web Resource, 2011.
[Wik10] Wikipedia. Leopold, Kronecker – Wikipedia, the free encyclopedia. http://en.wikipedia.org/wiki/Leopold kronecker, 2010. Online; accessed 30 May 2010. Based on E. T. Bell, Men of Mathematics. New York: Simon and Schuster, 1968, p. 477.
[Woo83] L. C., Woods. Frame-indifferent kinetic theory. J. Fluid Mech., 136:423–433, 1983.Google Scholar
[ZM67] H., Ziegler and D., McVean. On the notion of an elastic solids. In B., Broberg, J., Hult, and F., Niordson, editors, Recent Progress in Applied Mechanics (The Folke Odquist Volume), pages 561–572. Stockholm: Almquist and Wiksell, 1967.Google Scholar
[ZT89] O. C., Zienkiewicz and R. L., Taylor. The Finite Element Method, volume I, Basic Formulations and Linear Problems. London: McGraw-Hill, 1989.Google Scholar
[ZT91] O. C., Zienkiewicz and R. L., Taylor. The Finite Element Method, volume II, Solid and Fluid Mechanics: Dynamics and Non-Linearity. London: McGraw-Hill, fourth edition, 1991.Google Scholar
[ZT05] O. C., Zienkiewicz and R. L., Taylor. The Finite Element Method. London: McGraw-Hill, sixth edition, 2005.Google Scholar

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  • References
  • Ellad B. Tadmor, University of Minnesota, Ronald E. Miller, Carleton University, Ottawa, Ryan S. Elliott, University of Minnesota
  • Book: Continuum Mechanics and Thermodynamics
  • Online publication: 05 February 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139017657.016
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  • References
  • Ellad B. Tadmor, University of Minnesota, Ronald E. Miller, Carleton University, Ottawa, Ryan S. Elliott, University of Minnesota
  • Book: Continuum Mechanics and Thermodynamics
  • Online publication: 05 February 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139017657.016
Available formats
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  • References
  • Ellad B. Tadmor, University of Minnesota, Ronald E. Miller, Carleton University, Ottawa, Ryan S. Elliott, University of Minnesota
  • Book: Continuum Mechanics and Thermodynamics
  • Online publication: 05 February 2012
  • Chapter DOI: https://doi.org/10.1017/CBO9781139017657.016
Available formats
×