Advertisement

Elasticity and Thermoelasticity

  • Dallas N. LittleEmail author
  • David H. Allen
  • Amit Bhasin
Chapter

Abstract

This chapter presents an overview of the historical development of the three-dimensional theories of elasticity and thermoelasticity. While it is not an exhaustive coverage of this subject, the material presented herein is introduced as a means of preparing the reader for the subjects to come that deal with the inelastic deformations that occur in flexible pavements. As such, this material is an essential part of the knowledge necessary to design modern flexible road ways.

Keywords

Elasticity Thermoelasticity Linear elasticity Boundary conditions Boundary value problem Thermodynamic constraints Material symmetry Anisotropic material Orthotropic material Transversely isotropic material Isotropic material Material property characterization Analytic solution methods Computational solution methods Micromechanics Moisture effects 

References

  1. Allen, D., & Searcy, C. (2006). A model for predicting the evolution of multiple cracks on multiple length scales in viscoelastic composites. Journal Materials Science, 41, 6510.CrossRefGoogle Scholar
  2. Allen. D. (2013). Introduction to the mechanics of deformable solids: Bars and beams. Springer.Google Scholar
  3. Allen, D. (2014). How mechanics shaped the modern world. Springer.Google Scholar
  4. Amrouche, C., Ciarlet, P., Gratie, L., & Kesavan, S. (2006). On Saint Venant’s compatibility conditions and Poincaré’s lemma. Comptes Rendus de l’Académie des Sciences - Series I, 342, 887–891.zbMATHGoogle Scholar
  5. Boley, B., & Weiner, J. (1960). Theory of thermal stresses. Wiley.Google Scholar
  6. Boltzmann, L. (1874). Zur theorie der elastichen Nachwirkung. Sitz K u K Akad Wien, 70, 275.Google Scholar
  7. Boyd, J., Costanzo, F., & Allen, D. (1993). A micromechanics approach for constructing locally averaged damage dependent constitutive equations in inelastic composites. International Journal of Damage Mechanics, 2, 209.Google Scholar
  8. Cesaro, E. (1906). Sulle formole del Volterra, fondamentali nella teoria delle dostorsioni elastiche. Rendiconto dell’ Academia della Scienze Fisiche e Matematiche (Società Reale di Napoli).Google Scholar
  9. Coleman, B., & Noll, W. (1963). The thermodynamics of elastic materials with heat conduction and viscosity. Archive Rational Mechanics and Analysis, 13, 167.MathSciNetCrossRefzbMATHGoogle Scholar
  10. Duhamel, J. (1837), Second mémoire sur les phénomènes thermo-mécaniques. Journal de l’École Polytechnique.Google Scholar
  11. Euler, L. (1744). Methodus inveniendi lineas curvas. St. Petersburg.Google Scholar
  12. Fourier, J. (1822). Theorie analytique de la chaleur. Firmin Didot.Google Scholar
  13. Fung, Y. (1965). Foundations of solid mechanics. Prentice Hall.Google Scholar
  14. Galilei, G. (1638). Dialogues concerning two new sciences. University of Toronto Library.Google Scholar
  15. Hill, R. (1963). Elastic properties of reinforced solids: Some theoretical principles. Journal of the Mechanics and Physics of Solids, 13, 89.CrossRefzbMATHGoogle Scholar
  16. Love, A. (1906). A treatise on the mathematical theory of elasticity. University of Michigan library.Google Scholar
  17. Malvern, L. (1969). Introduction to the mechanics of a continuous medium. Prentice-Hall.Google Scholar
  18. Mandel, J. (1964). Proceedings of the 11th International Congress of Applied Mechanics (Vol. 502).Google Scholar
  19. Maugin, G. (2014). Continuum mechanics through the eighteenth and nineteenth centuries. Springer.Google Scholar
  20. Maxwell, J. (1860). Illustrations of the dynamical theory of gases, Parts I and II. Philosophical Magazine, 19, 9.Google Scholar
  21. Newton, I. (1687). Principia—Vol. 1—The motion of bodies. University of California Press.Google Scholar
  22. Saint-Venant, A. (1856). Mémoire sur la torsion des prismes, avec des considérations sur leur flexion ainsi que sur l’équilibre intérieur des solides élastiques en général, et des formules pratiques pour le calcul de leur résistance à divers efforts s’exercant simultanément. Mémoires Présentés par divers savants à l’Académie des sciences de l’Institut de France, 14, 233–560.Google Scholar
  23. Timoshenko, S. (1970). Theory of elasticity. McGraw-Hill.Google Scholar
  24. Todhunter, I., & Pearson, K. (1893). A history of the theory of elasticity and the strength of materials from Galilei to the present time. Cambridge University Press.Google Scholar
  25. Truesdell, C., Noll, W., & Antman, S. (2004). The non-linear field theories of mechanics. Springer.Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Dallas N. Little
    • 1
    Email author
  • David H. Allen
    • 1
  • Amit Bhasin
    • 2
  1. 1.Texas A&M UniversityCollege StationUSA
  2. 2.The University of Texas at AustinAustinUSA

Personalised recommendations