On Implicit Constitutive Theories

Institute of Mathematics, Czech Academy of Sciences - Tập 48 Số 4 - Trang 279-319 - 2003
Κ. R. Rajagopal1
1Department of Mechanical Engineering, Texas A&M University, College Station, USA

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G. Amontons: De la résistance causée dans les machines. Mémoires de l' Académie Royale A (1699), 257–282.

E. C. Andrade: Viscosity of liquids. Nature 125 (1930), 309–310.

B. Bernstein: A unified theory of elasticity and plasticity. Internat. J. Engrg. Sci. 15 (1977), 645–660.

B. Bernstein: Hypo-elasticity and elasticity. Arch. Rational Mech. Anal. 6 (1960), 89–104.

P. Bridgman: The Physics of High Pressure. The MacMillan Company, New York, 1931.

C. A. Coulomb: Theories des machines simples, en ayant égard au frottement de leurs parties, et a la roider des cordages. Mém. Math. Phys. X (1785), 161–332.

J. d'Alembert: Traité de Dynamique. Paris, Chez David, Libraire, 1758.

C. Eckart: The thermodynamics of irreversible processes IV. The theory of elasticity and inelasticity. Physical Rev. 73 (1948), 373–382.

M. Franta, J. Málek and K. R. Rajagopal: On steady ows of uids and shear dependent viscosities. Proc. Roy. Soc. London Ser. A: Mathematical, Physical and Engineering Sciences (2003). Submitted.

C.F. Gauss: On a new general principle of mechanics; Translation of Ñber ein neues allgemeines Grundgesetz der Mechanik. J. Reine Angew. Math. 4 (1829), 232–235.

H. Goldstein: Classical Mechanics. Addison-Wesley, Boston, 1980.

J. Hron, J. Málek and K. R. Rajagopal: Simple flows of fluids with pressure dependent viscosities. Proc. Roy. Soc. London Ser. A: Mathematical, Physical and Engineering Sciences 457 (2001), 1603–1622.

K. Kannan, K. R. Rajagopal: A thermomechanical framework for the transition of a viscoelastic liquid to a viscoelastic solid. Mathematics and Mechanics of Solids. To appear.

K. Kannan, I. Rao and K. R. Rajagopal: A thermomechanical framework for the glass transition phenomenon in certain polymers and its application to the fiber spinning problems. J. of Rheology 46 (2002), 977–999.

J. L. Lagrange: Mécanique Analytique. Mme Ve Courcier, Paris, 1787, Translation (by A. Boissonnade, V. N. Vagliente), Kluwer Academic Publishers, Dordrecht, 1997.

M. Levy: Mémoire sur les équations générales des mouvements intérieurs des corps ductiles au delà des limites en élasticité pourrait les ramener à leur premier état. C. R. Acad. Sci. 70 (1870), 1323–1325.

J. Málek, J. Nečas and K. R. Rajagopal: Global analysis of the flows of fluids with pressure dependent viscosities. Arch. Rational Mech. Anal. 165 (2002), 243–269.

J. C. Maxwell: On the Dynamical Theory of Gases. Philosophical Transactions of the Royal Society of London, Series A (1866), 26–78.

A. J. A. Morgan: Some properties of media by constitutive equations in implicit form. Internat. J. Engrg. Sci. 4 (1966), 155–178.

J. Murali Krishnan, K. R. Rajagopal: A thermodynamic framework for the constitutive modeling of asphalt concrete: theory and aplications. ASCE Journal of Materials. Accepted for publication.

C. L. M. H. Navier: Mémoire sur les lois du mouvement des fluides. Mém. Acad. Re. Sci., Paris 6 (1823), 389–416.

W. Noll: A mathematical theory of the mechanical behavior of continuous media. Arch. Rational Mech. Anal. 2 (1958), 197–226.

W. Noll: A new mathematical theory of simple materials. Arch. Rational Mech. Anal. 48 (1972), 1–50.

S. D. Poisson: Mémoire sur les équations générales de l'équilibre et du mouvement des corps solides élastiques et des fluides. Journal de l'Ecole Polytechnique 13 (1831), 1–174.

L. Prandtl: Spannungsverteilung in plastischen Körpern. In: Proceeding of the 1st International Congress in Applied Mechanics. Delft, 1924.

K. R. Rajagopal, A. S. Wineman: On constitutive equations for branching of response with selectivity. Internat. J. Non-Linear Mech. 15 (1980), 83–91.

K. R. Rajagopal, A. S. Wineman: A constitutive equation for nonlinear solids which undergo deformation induced micro-structural changes. International Journal of Plasticity 8 (1992), 385–395.

K. R. Rajagopal: Multiple configurations in Continuum Mechanics. Report 6. Institute of Computational and Applied Mechanics, University of Pittsburgh, 1995.

K. R. Rajagopal, A. R. Srinivasa: On the inelastic behavior of solids—Part I: Twinning. International Journal of Plasticity 11 (1995), 653–678.

K. R. Rajagopal, A. R. Srinivasa: On the inelastic behavior of solids—Part II: Energetics associated with discontinuous deformation twinning. International Journal of Plasticity 13 (1997), 1–35.

K. R. Rajagopal, A. S. Wineman: A linearized theory for materials undergoing microstructural change. ARI 51 (1998), 160–168.

K. R. Rajagopal, A. R. Srinivasa: Mechanics of the inelastic behavior of materials—Part I: Theoretical underpinnings. International Journal of Plasticity 14 (1998), 945–967.

K. R. Rajagopal, A. R. Srinivasa: Mechanics of the inelastic behavior of materials—Part II: Inelastic response. International Journal of Plasticity 14 (1998), 969–995.

K. R. Rajagopal, A. R. Srinivasa: Thermomechanical modeling of shape memory alloys. ZAMP 50 (1999), 459–496.

K. R. Rajagopal, A. R. Srinivasa: A thermodynamic framework for rate type fluid models. Journal of Non-Newtonian Fluid Mechanics 88 (2000), 207–227.

K. R. Rajagopal, A. R. Srinivasa: Modeling anistropic fluids within the framework of bodies with multiple natural configurations. Journal of Non-Newtonian Fluid Mechanics (2001).

K. R. Rajagopal, L. Tao: Modeling of the microwave drying process of aqueous dielectrics. ZAMP 53 (2002), 923–948.

I. J. Rao, K. R. Rajagopal: A study of strain-induced crystallization of polymers. International Journal of Solids and Structures 38 (2001), 1149–1167.

I. J. Rao, J. D. Humphrey and K. R. Rajagopal: Growth and remodeling in a dynamically loaded axial tissue. Computational Method in Engineering Science. In press.

I. J. Rao, K. R. Rajagopal: Phenomenological modeling of polymer crystallization using the notion of multiple natural configurations. Interfaces and free boundaries 2 (2000), 73–94.

I. J. Rao, K. R. Rajagopal: A thermomechanical framework for crystallization of polymers. Z. Angew. Math. Phys. 53 (2002), 365–406.

E. Reuss: Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie. Z. Angew. Math. Mech. 10 (1939), 266–274.

A. J. C. B. Saint-Venant: Note à joindre au Mémoire sur la dynamique des fluides. C. R. Acad. Sci. 17 (1843), 1240–1243.

A. J. M. Spencer: Continuum Physics, Vol. 3 (A. C. Eringen, ed.). Academic Press, New York, 1975.

A. R. Srinivasa, K. R. Rajagopal and R. Armstrong: A phenomenological model of twinning based on dual reference structures. Acta. Metall. (1998), 1–14.

G. G. Stokes: On the theories of internal friction of fluids in motion, and of the equilibrium and motion of elastic solids. Transactions of the Cambridge Philosophical Society 8 (1845), 287–305.

H. E. Tresca: On the `flow of solids' with the practical application in some forgings. In: Proceedings of the Institution of Mechanical Engineers. London, 1867, pp. 114–150.

C. Truesdell: A First Course in Rational Continuum Mechanics. Academic Press, Boston-San Diego, 1991.

C. A. Truesdell: Hypo-elasticity. J. Rational Mechanics and Analysis 4 (1955), 323–425.

C. Truesdell, W. Noll: The Non-Linear Field Theories of Mechanics. Handbuch der Physik, III 3. Springer-Verlag, Berlin-Heidelberg-New York, 1965.

R. von Mises: Mechanik der festen Körpern im plastisch-deformablen Zustand. Nachrichten von der königlichen Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse (1913), 582–592.

A. S. Wineman, K. R. Rajagopal: On a constitutive theory for materials undergoing microstructural changes. Archives of Mechanics 42 (1990), 53–74.

H. Ziegler: Some extremum principles in irreversible thermodynamics. In: Progress in Solid Mechanics (I. Sneddon, R. Hill, eds.). North-Holland Publishing Company, Amsterdam, 1963.