Skip to main content

Integral Representation for the Solution of a Crack Problem Under Stretching Pressure in Plane Asymmetric Elasticity

  • Chapter
Integral Methods in Science and Engineering

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aliabadi, M.H., Brebbia, C.A.: Advances in Boundary Element Methods for Fracture Mechanics. Computational Mechanics Publ., Southampton, Boston; Elsevier, London-New York (1993).

    Google Scholar 

  2. Atkinson, C., Leppington, F.G.: The effect of couple stresses on the tip of a crack. Internat. J. Solids Structures, 13, 1103–1122 (1977).

    Article  MATH  MathSciNet  Google Scholar 

  3. Bouyge, F., Jasiuk, I., Ostoja-Starzewski, M.: A micromechanically based couple-stress model of an elastic two-phase composite. Internat. J. Solids Structures, 38, 1721–1735 (2001).

    Article  MATH  Google Scholar 

  4. Brebbia, C.A.: The Boundary Element Method for Engineers. Pentech Press, London (1978).

    Google Scholar 

  5. Chudinovich, I., Constanda, C.: Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation. Chapman & Hall/CRC, Boca Raton-London-New York-Washington, DC (2000).

    MATH  Google Scholar 

  6. Eringen, A.C.: Linear theory of micropolar elasticity. J. Math. Mech., 15, 909–923 (1966).

    MATH  MathSciNet  Google Scholar 

  7. Gaul, L., Kögl, M., Wagner, M.: Boundary Element Methods for Engineers and Scientists. Springer, Berlin-Heidelberg-New York (2003).

    MATH  Google Scholar 

  8. Jasiuk, I., Ostoja-Starzewski, M.: Modeling of bone at a single lamella level. Biomech. Model. Mechanobiology, 3, 67–74 (2004).

    Article  Google Scholar 

  9. Lakes, R.: Dynamical study of couple stress effects in human compact bone. J. Biomedical Engng., 104, 6–11 (1982).

    Article  Google Scholar 

  10. Lakes, R.: Experimental methods for study of Cosserat elastic solids and other generalized elastic continua. In: Muhlhaus, H-B. (ed.), Continuum Models for Materials with Microstructure. Wiley, New York (1995), pp.1–22.

    Google Scholar 

  11. Lakes, R., Nakamura, S., Behiri, J., Bonfield, W.: Fracture mechanics of bone with short cracks. J. Biomech., 23, 967–975 (1990).

    Article  Google Scholar 

  12. Mühlhaus, H.-B., Pasternak, E.: Path independent integrals for Cosserat continua and application to crack problems. Internat. J. Fracture, 113, 21–26 (2002).

    Article  Google Scholar 

  13. Nakamura, S., Lakes, R.: Finite element analysis of stress concentration around a blunt crack in a Cosserat elastic solid. Comput. Methods Appl. Mech. Engng., 66, 257–266 (1988).

    Article  MATH  Google Scholar 

  14. Park, H., Lakes, R.: Cosserat micromechanics of human bone: strain redistribution by a hydration sensitive constituent. J. Biomechanics, 19, 385–397 (1986).

    Article  Google Scholar 

  15. Potapenko, S., Schiavone, P., Mioduchowski, A.: Generalized Fourier series solution of torsion of an elliptic beam with microstructure. Appl. Math. Lett., 17, 189–192 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  16. Schiavone, P.: Integral equation methods in plane asymmetric elasticity. J. Elasticity, 43, 31–43 (1996).

    MATH  MathSciNet  Google Scholar 

  17. Shmoylova, E., Potapenko, S., Rothenburg, L.: Weak solutions of the interior boundary value problems of plane Cosserat elasticity. Z. Angew. Math. Phys., 57, 506–522 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  18. Shmoylova, E., Potapenko, S., Rothenburg, L.: Weak solutions of the exterior boundary value problems of plane Cosserat elasticity. J. Integral Equations Appl. (in press).

    Google Scholar 

  19. Shmoylova, E., Potapenko, S., Rothenburg, L.: Stress distribution around a crack in plane micropolar elasticity. J. Elasticity (in press).

    Google Scholar 

  20. Sneddon, I.: Crack Problems in the Classical Theory of Elasticity. Wiley, New York (1969).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Birkhäuser Boston

About this chapter

Cite this chapter

Shmoylova, E., Potapenko, S., Rothenburg, L. (2008). Integral Representation for the Solution of a Crack Problem Under Stretching Pressure in Plane Asymmetric Elasticity. In: Constanda, C., Potapenko, S. (eds) Integral Methods in Science and Engineering. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4671-4_28

Download citation

Publish with us

Policies and ethics