One-Dimensional Constitutive Theory

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


In this chapter, the concept of a thermomechanical constitutive model is introduced. Such a model is used to relate the kinematic variables to the kinetic variables in a solid subjected to thermomechanical loading. Because the constitutive behavior of real materials can be quite complicated, a series of constitutive models has been developed historically, and these models increase in mathematical complexity as more physically intricate behavior of materials is encompassed within the models. Because this mathematical complexity is quite challenging, the models to be developed in succeeding chapters in three dimensions are presented in this chapter in one-dimensional form as a means of introducing this subject in as mathematically and physically simple a form as possible. Accordingly, one-dimensional models are introduced for elastic, viscous, elasto-plastic, viscoelastic, and viscoplastic media. In addition, the effects of moisture and temperature on one-dimensional constitutive behavior are discussed. Finally, experimental techniques for obtaining material properties necessary for characterizing one-dimensional constitutive equations are detailed in this chapter.


Constitutive theory Constitutive experiments Elastic material model Viscous material model Viscoelastic material model Elasto-plastic material model Viscoplastic material model Thermo-material model Hygro-material model 


  1. Allen, D. (2014). How mechanics shaped the modern world. Springer.Google Scholar
  2. Allen, D., & Haisler, W. (1985). Introduction to aerospace structural analysis. Wiley.Google Scholar
  3. Da Vinci, L. (1972). I libri di meccanica. Reconstructed from the original notes by Arturo Uccelli, Kraus Reprint, Nendeln, Liechtenstein.Google Scholar
  4. Jardine, L. (2005). The curious life of Robert Hooke: The man who measured London. Harper Perennial.Google Scholar
  5. Leaderman, H. (1943). Elastic and creep properties of filamentous materials and other high polymers. Washington, D.C.: The Textile Foundation.Google Scholar
  6. Maxwell, J. (1867). On the dynamical theory of gases. London: Philosophical Transactions of the Royal Society.Google Scholar
  7. Parsons, W. (1939). Engineers and Engineering in the Renaissance. Cambridge, MA: MIT Press.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

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