Kinematic Constraints, Constitutive Equations and Failure Rules for Anisotropic Materials

  • A. J. M. Spencer
Part of the International Centre for Mechanical Sciences book series (CISM, volume 292)


It is common in many branches of continuum mechanics to treat material as though it is incompressible. Although no material is truly incompressible, there are many materials in which the ability to resist volume changes greatly exceeds the ability to resist shearing deformations; examples are liquids with low viscosity, like water, and some natural and artificial rubbers. For such materials, the assumption of incompressibility is a good approximation in many circumstances, and often greatly simplifies the solution of specific problems. It should be noted, though, that there are occasions when even a small degree of compressibility may produce a major effect; an example is the propagation of sound waves in water.


Constitutive Equation Yield Function Fibre Direction Kinematic Constraint Incompressible Material 
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  1. 1.
    SPENCER, A.J.M., Deformations of Fibre-reinforced Materials, Oxford University Press, 1972Google Scholar
  2. 2.
    PRAGER, W., A new method of analyzing stresses and strains in work-hardening plastic solids, J.Appl.Mech. 23 (1956): 493–496MATHMathSciNetGoogle Scholar
  3. 3.
    SPENCER, A.J.M., The formulation of constitutive equations for anisotropic solids, in Mechanical Behaviour of Anisotropie Solids (ed. J. P. Boehler ), Editions du CNRS, Paris and M. Nijhoff, The Hague, 1982: 2–26Google Scholar
  4. 4.
    SPENCER, A.J.M., Yield conditions and hardening rules for fibre-reinforced materials with plastic response, in Failure Criteria of Structured Media (ed. J. P. Boehler ), A. A. Balkema, 1986Google Scholar

Copyright information

© Springer-Verlag Wien 1987

Authors and Affiliations

  • A. J. M. Spencer
    • 1
  1. 1.The University of NottinghamEngland

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