Skip to main content
Log in

A nonlinear theory of elastic materials with voids

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Goodman, M. A., & S. C. Cowin, “A Continuum Theory for Granular Materials,” Arch. Rational Mech. Anal. 44 (1972), 249–266.

    Google Scholar 

  2. Nunziato, J. W., & E. K. Walsh, “On the Influence of Void Compaction and Material Non-Uniformity on the Propagation of One-Dimensional Acceleration Waves in Granular Materials,” Arch. Rational Mech. Anal. 64 (1977), 299–316; Addendum, ibid., 67 (1978), 395–398.

    Google Scholar 

  3. Knowles, J. K., & M. T. Jakub, “Finite Dynamic Deformations of an Incompressible Elastic Medium Containing a Spherical Cavity,” Arch. Rational Mech. Anal. 18 (1965), 367–378.

    Google Scholar 

  4. Cowin, S. C., & F. Leslie, “On Kinetic Energy and Momenta in Cesserat Continua,” ZAMP (1979), to be published.

  5. Band, W., “Local Heating in Shocked Granular Materials,” Stanford Research Institute Internal Report 002-67, July 1967.

  6. Krizek, R. J., “Rheological Behavior of Cohesionless Soils Subjected to Dynamic Loads,” Trans. Soc. Rheol. 15 (1971), 491–540.

    Google Scholar 

  7. Butcher, B. M., “The Description of Strain-Rate Effects in Shocked Porous Materials,” Shock Waves and the Mechanical Properties of Solids, Syracuse University Press, 1971.

  8. Romano, M., “A Continuum Theory for Granular Media with a Critical State,” Arch. Mech. Stos. 26 (1974), 1011–1028.

    Google Scholar 

  9. Davis, R. O., “Undrained Simple Shearing of Rate Type Granular Medium,” Proc., Joint U.S.-Japan Seminar on the Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials, Sendai, Japan, 1978.

  10. Mullenger, G., “A Condition for a Continuum Model of Granular Structure,” ibid.

  11. Coleman, B. D., “Thermodynamics of Materials with Memory,” Arch. Rational Mech. Anal. 17 (1964), 1–46.

    Google Scholar 

  12. Nunziato, J. W., & E. K. Walsh, “Small-Amplitude Wave Behavior in One-Dimensional Granular Solids,” J. Appl. Mech. 44 (1977), 559–564.

    Google Scholar 

  13. Coleman, B. D., & M. E. Gurtin, “Waves in Materials with Memory, IV,” Arch. Rational Mech. Anal. 19 (1965), 317–338.

    Google Scholar 

  14. Atkin, R. J., S. C. Cowin, & N. Fox, “On Boundary Conditions for Polar Materials,” ZAMP 28 (1977), 1017–1026.

    Google Scholar 

  15. Protter, M. H., & H. F. Weinberger, Maximum Principles in Differential Equations, Prentice-Hall, 1967.

  16. Wang, C. C., & C. Truesdell, Introduction to Rational Elasticity, Noordhoff, 1973.

  17. Truesdell, C., & R. A. Toupin, “The Classical Field Theories,” Handbuch der Physik, III/1, Springer, 1960.

  18. Gurtin, M. E., “The Linear Theory of Elasticity,” Handbuch der Physik, VIa/2, Springer, 1972.

  19. Chen, P. J., ‘Growth and Decay of Waves in Solids,” Handbuch der Physik, VIa/3, Springer, 1973.

  20. Cowin, S. C., “Thermodynamic Model for Porous Materials with Vacuous Pores,” J. Appl. Phys. 43 (1972), 2495–2497.

    Google Scholar 

  21. Mindlin, R. D., “Microstructure in Linear Elasticity,” Arch. Rational Mech. Anal. 16 (1964), 51–78.

    Google Scholar 

  22. Toupin, R. A., “Theories of Elasticity with Couple Stress,” Arch. Rational Mech. Anal. 17 (1964), 85–112

    Google Scholar 

  23. Love, A. E. H., A Treatise on the Mathematical Theory of Elasticity, Cambridge, 1927.

  24. Eshelby, J. D., “The Force on an Elastic Singularity,” Phil. Trans. Roy. Soc. A244 (1951), 87–112.

    Google Scholar 

  25. MacKenzie, J. K., “The Elastic Constants of a Solid Containing Spherical Holes,” Proc. Phys. Soc. B63 (1950), 2–11.

    Google Scholar 

  26. Carroll, M. M., & A. C. Holt, “Static and Dynamic Pore-Collapse Relations for Ductile Porous Materials,” J. Appl. Phys. 43 (1972), 1626–1636.

    Google Scholar 

  27. Jenkins, J. T., “Static Equilibrium of Granular Materials,” J. Appl. Mech. 42 (1975), 603–606.

    Google Scholar 

  28. Truesdell, C., & W. Noll, “The Non-Linear Field Theories of Mechanics,” Handbuch der Physik III/3, Springer, 1965.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by C. Truesdell

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nunziato, J.W., Cowin, S.C. A nonlinear theory of elastic materials with voids. Arch. Rational Mech. Anal. 72, 175–201 (1979). https://doi.org/10.1007/BF00249363

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00249363

Keywords

Navigation