On the Constitutive Theory of Power-Law Materials Containing Voids

  • C. Y. Hsu
  • B. J. Lee
  • M. E. Mear
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 114)


In the analysis of non-linear porous solids, it is commonplace to employ a spherical unit cell owing to the simplicity it affords. The macroscopic constitutive response is then predicted based upon either uniform traction or linear displacement/velocity boundary conditions applied on the outer surface of the cell. In this investigation we carry out a careful computational investigation of the effect of these two types of boundary conditions upon the predicted macroscopic response, and in particular, we explore the sensitivity of the predicted response to the macroscopic stress state and the degree of matrix non-linearity. In addition, we contrast the accurate numerical results obtained here with various approximate constitutive models in order to provide additional insight into the predictive capabilities of these models.

Key words

non-linear porous solids voids micromechanics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. L. Gurson, “Continuum theory of ductile rupture by void nucleation and growth: Part I-Yield criteria and flow rules for porous ductile media”, J. Eng. Materials Tech., vol. 99, p. 2, 1977.CrossRefGoogle Scholar
  2. [2]
    A. C. F. Cocks, “Inelastic deformation of porous materials”, J Mech. Phys. Solids, vol. 17, p. 693, 1989.CrossRefGoogle Scholar
  3. [3]
    J. M. Duva and P. D. Crow, “The densification of powders by power-law creep during hot isostatic pressing”, Acta. Metall. Mater., vol. 40, p. 31, 1992.CrossRefGoogle Scholar
  4. [4]
    P. Sofronis and R. M. McMeeking, “Creep of power-law material containing spherical voids”, J. Appl. Mech., vol. 59, p. 88, 1992.CrossRefGoogle Scholar
  5. [5]
    M. Haghi and L. Anand, “A constitutive model for isotropic, porous, elastic-viscoplastic metals”, Mech. Mater., vol. 13, p. 37, 1992.CrossRefGoogle Scholar
  6. [6]
    J. C. Michel and P. Suquet, “The constitutive law of nonlinear viscous and porous materials”, J. Mech. Phys. Solids, vol. 40, p. 783, 1992.CrossRefGoogle Scholar
  7. [7]
    A. A. Benzerga and J. Besson, “Plastic potentials for anisotropic porous solids”, Eur. J. Mech. A/Solids, vol. 20, p. 397, 2001.CrossRefGoogle Scholar
  8. [8]
    S. Nemat-Nasser and M. Hori, Micromechanics: overall properties of heterogeneous materials, Elsevier Science, 1993.Google Scholar
  9. [9]
    J. W. Hutchinson, Micromechanics of damage in deformation and fracture, Technical University of Denmark, Denmark, 1987.Google Scholar
  10. [10]
    R. Hill, “New horizons in the mechanics of solids”, J. Mech. Phys. Solids, vol. 5, p. 66, 1956.CrossRefGoogle Scholar
  11. [11]
    J. M. Duva, “A constitutive description of nonlinear materials containing voids”, Mech. Mater., vol. 5, p. 137, 1986.CrossRefGoogle Scholar
  12. [12]
    B. J. Lee and M. E. Mear, “Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids”, J. Mech. Phys. Solids, vol. 40, p. 1805, 1992.CrossRefGoogle Scholar
  13. [13]
    K. C. Yee and M. E. Mear, “Effect of void shape on the macroscopic response of nonlinear porous solids”, Int. J. of Plasticity, vol. 12, p. 45, 1996.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2004

Authors and Affiliations

  • C. Y. Hsu
    • 1
  • B. J. Lee
    • 2
  • M. E. Mear
    • 3
  1. 1.Department of Hydraulic EngineeringFeng Chia UniversityTaichungTaiwan, ROC
  2. 2.Department of Civil EngineeringFeng Chia UniversityTaichungTaiwan, ROC
  3. 3.Department of Aerospace Engineering and Engineering MechanicsThe University of Texas at AustinAustinUSA

Personalised recommendations