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Balance Laws

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Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 174))

Abstract

Let us consider fundamental laws of continuum mechanics, and complement the set of Axioms1–3 (see Introduction) with new axioms.

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References

  1. Batra, R.C.: Elements of Continuum Mechanics. AIAA Education Series, Reston (2005)

    Google Scholar 

  2. Basar, Y., Weichert, D.: Nonlinear Continuum Mechanics of Solids. Springer, Berlin (2000)

    MATH  Google Scholar 

  3. Bonet, J., Wood, R.D.: Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  4. Borg, S.F.: Matrix Tensor Methods in Continuum Mechanics. World Scientific, London (1990)

    MATH  Google Scholar 

  5. Bowen, R.M.: Introduction to Continuum Mechanics for Engineers. Plenum Press, New York (1989)

    MATH  Google Scholar 

  6. Calcote, L.R.: Introduction to Continuum Mechanics. D. Van Nostrand, Princeton (1968)

    Google Scholar 

  7. Chadwick, P.: Continuum Mechanics: Concise Theory and Problems. Dover Publications (1999)

    Google Scholar 

  8. Chernykh, K.F.: An Introduction to Modern Anisotropic Elasticity, Moscow, Nauka, 1988 (in Russian). Begell Publishing House, New York (1998)

    Google Scholar 

  9. Coleman, B.D.: Thermodynamics of materials with memory. Arch. Ration. Mech. Anal. 17(1), 1–46 (1964)

    Article  Google Scholar 

  10. Cotter, B.A., Rivlin, R.S.: Tensors associated with time-dependent stress. Quart. Appl. Math. 13(2), 177–182 (1955)

    MATH  MathSciNet  Google Scholar 

  11. Dimitrienko, Yu.I.: Novel viscoelastic models for elastomers under finite strains. Eur. J. Mech. Solid. 21(2), 133–150 (2002)

    Article  MATH  Google Scholar 

  12. Dimitrienko, Yu.I.: Tensor Analysis and Nonlinear Tensor Functions. Kluwer Academic Publishers, Dordrecht-Boston-London (2002)

    MATH  Google Scholar 

  13. Ericksen, J.L., Rivlin, R.S.: Large elastic deformations of homogeneous anisotropic elastic materials. J. Ration. Mech. Anal. 3(3), 281-301 (1954)

    MathSciNet  Google Scholar 

  14. Eringen, A.C.: Nonlinear Theory of Continuous Media, McGraw–Hill, New York (1962)

    Google Scholar 

  15. Eringen, A.C.: Mechanics of Continuum. Wiley, New York (1967)

    Google Scholar 

  16. Ferrarese, G., Bini, D.: Introduction to Relativistic Continuum Mechanics (Lecture Notes in Physics). Springer, Berlin (2007)

    Google Scholar 

  17. Fung, Y.C.: A First Course in Continuum Mechanics. Prentice Hall, New Jersey (1977)

    Google Scholar 

  18. Gladwell, G.M.L.: Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff, 1980. Chinese Edition published (1991)

    Google Scholar 

  19. Green, A.E., Zerna, W.: Theoretical Elasticity. Oxford University Press (1954)

    Google Scholar 

  20. Godunov, S.K., Romenskii, E.I.: Elements of Continuum Mechanics and Conservation Laws. Springer, Berlin (2003)

    MATH  Google Scholar 

  21. Goldstein, R.V., Entov, V.M.: Qualitative Methods in Continuum Mechanics. Longman, London (1994)

    Google Scholar 

  22. Gonzalez, O., Stuart, A.M.: A First Course in Continuum Mechanics (Cambridge Texts in Applied Mathematics). Cambridge University Press (2007)

    Google Scholar 

  23. Gurtin, M.E.: Introduction to Continuum Mechanics (Mathematics in Science and Engineering). Academic Press, New York (1981)

    Google Scholar 

  24. Gurtin, M.E.: Configurational Forces as Basic Concepts of Continuum Physics. Springer, Berlin (1999)

    Google Scholar 

  25. Heinbockel, J.H.: Introduction to Tensor Calculus and Continuum Mechanics. Trafford Publishing, Canada (2001)

    Google Scholar 

  26. Hill, R.: Constitutive inequalities for isotropic elastic solids under finite strain. Proc. Roy. Soc. Lond. A 314, 1519 (1970)

    Google Scholar 

  27. Holzapfel, G.A.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Wiley, New York (2000)

    MATH  Google Scholar 

  28. Jaumann, G.: Grundlagen der Bewegungslehre. Springer, Leipzig (1905)

    MATH  Google Scholar 

  29. Jaunzemis, W.: Continuum Mechanics. The Macmillan Company, New York (1967)

    MATH  Google Scholar 

  30. Jog, C.S.: Continuum Mechanics. Alpha Science (2007)

    Google Scholar 

  31. Kolmogorov, A.N., Fomin, S.V.: Elements of the Theory of Functions and Functional Analysis, Moscow, Nauka, 1976 (in Russian). Dover Publications, New York (1999)

    Google Scholar 

  32. Lai, W.M., Rubin, D., Krempl, E.: Introduction to Continuum Mechanics. Butterworth–Heinemann, Pergamon, New York (1993)

    Google Scholar 

  33. Lebedev, L.P., Vorovich, I.I., Gladwell, G.M.L.: Functional Analysis: Applications in Mechanics and Inverse Problems. Kluwer Academic Publishers, Dordrecht-Boston-London (1996)

    MATH  Google Scholar 

  34. Leigh, D.C.: Nonlinear Continuum Mechanics. McGrawHill, New York (1968)

    Google Scholar 

  35. Liu, I-Shih: Continuum Mechanics. Springer, Berlin (2002)

    Google Scholar 

  36. Lurie, A.I.: Nonlinear Theory of Elasticity. Amsterdam, North–Holland (1990)

    Google Scholar 

  37. Lurie, A.I.: Theory of Elasticity. Springer, Berlin (2005)

    Book  Google Scholar 

  38. Malvern, L.E.: An Introduction to the Mechanics of a Continuous Media. Prentice–Hall, Englewood Cliffs (1970)

    Google Scholar 

  39. Mase, G.E.: Continuum Mechanics for Engineers. CRC Press, Boca Raton (1999)

    Book  MATH  Google Scholar 

  40. McDonald, P.H.: Continuum Mechanics (PWS Series in Engineering). PWS Publishing, Boston (1995)

    Google Scholar 

  41. Murnaghan, F.D.: Finite Deformation of an Elastic Solid. Wiley, New York (1951)

    MATH  Google Scholar 

  42. Nemat–Nasser, S.: On nonequilibrium thermodynamics of continua. Mechanics Today 2, 94–158 (1975)

    Google Scholar 

  43. Noll, W.: The Foundations of Mechanics and Thermodynamics, (Selected papers). Springer, Berlin (1974)

    MATH  Google Scholar 

  44. Oldroyd, J.G.: On the formulation of rheological equations of State. Proc. Roy. Soc. 200(1063), 523–541 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  45. Onsager, Lars.: Reciprocal relations in irreversible processes. Phys. Rev. 37(2), 405–426 (1931)

    Google Scholar 

  46. Onsager, Lars.: Reciprocal relations in irreversible processes. Phys. Rev. Second series 38(12), 2265–2279 (1931)

    Google Scholar 

  47. Reddy, J.N.: An Introduction to Continuum Mechanics. Cambridge University Press (2007)

    Google Scholar 

  48. Roberts, A.J.: A One-Dimensional Introduction to Continuum Mechanics. World Scientific, London (1994)

    MATH  Google Scholar 

  49. Roy, M.: Mecanique des millieux continus et deformables. Gauthier–Villars (1950)

    Google Scholar 

  50. Smith, D.R.: An Introduction to Continuum Mechanics (Solid Mechanics and Its Applications). Springer, Berlin (1999)

    Google Scholar 

  51. Spencer, A.J.M.: Continuum Mechanics. Dover Publications, New York (2004)

    MATH  Google Scholar 

  52. Talpaert, Y.R.: Tensor Analysis and Continuum Mechanics. Springer, Berlin (2003)

    Google Scholar 

  53. Temam, R., Miranville, A.: Mathematical Modeling in Continuum Mechanics. Cambridge University Press (2005)

    Google Scholar 

  54. Truesdell, C.A.: The Elements of Continuum Mechanics. Springer–Verlag, New York (1965)

    Google Scholar 

  55. Truesdell, C.A.: Rational Thermodynamics. McGrawHill, New York (1969)

    Google Scholar 

  56. Truesdell, C.A., Noll, W.: The Nonlinear–Field Theories of Mechanics. Springer, Berlin (2003)

    Google Scholar 

  57. Valanis, K.S.: Irreversible Thermodynamics of Continuous Media. Springer, New York (1971)

    Google Scholar 

  58. Vardoulakis, I., Eftaxiopoulos, D.: Engineering Continuum Mechanics: With Applications from Fluid Mechanics, Solid Mechanics, and Traffic Flow. Springer, Berlin (2007)

    Google Scholar 

  59. Wu Han-Chin: Continuum Mechanics and Plasticity (CRC Series–Modern Mechanics and Mathematics). Chapman & Hall/CRC, Boca Raton (2005)

    Google Scholar 

  60. Ziegler, H.: An Introduction to Thermodynamics. Amsterdam, North–Holland (1977)

    Google Scholar 

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Correspondence to Yuriy I. Dimitrienko .

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Dimitrienko, Y.I. (2011). Balance Laws. In: Nonlinear Continuum Mechanics and Large Inelastic Deformations. Solid Mechanics and Its Applications, vol 174. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0034-5_3

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  • DOI: https://doi.org/10.1007/978-94-007-0034-5_3

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