Acta Mechanica

, Volume 13, Issue 3–4, pp 281–292 | Cite as

Stress concentration around a cylindrical cavity in a bone treated as a poroelastic body

  • J. L. Nowinski
Contributed Papers

Summary

Two-phase poroelastic material is taken as a model of a living bone in the sense that the osseous tissue is treated as a linear isotropic perfectly elastic solid, and the fluid substances filling the pores as a Newtonian viscous fluid. Using Biot equations, derived in his consolidation theory, and assuming a plane state of strain governing equations involving fluid excess pressure and the stress function are derived. Laplace transform technique enables one to find explicit solutions for stresses. It is found that under a constant external load the bone element starts to creep, so that the viscoelastic properties of the adopted bone model seem to be in agreement with the experimental findings ofSedlin.

Spannungserhöhung am Rande eines zylindrischen Loches in einem als porösen elastischen Körper betrachteten Knochen

Zusammenfassung

Ein zweiphasiges poröses elastisches Material wird als Model eimes lebenden Knochens genommen. Das knöcherne Gewebe wird als linearer isotroper und vollkommen elastischer Körper und die die Poren füllende Flüssigkeit als Newtonsche behandelt. Unter Verwendung der vonBiot hergeleiteten Gleichungen und unter der Annahme eines ebenen Verzerrungszustandes werden die den Flüssigkeitsüberdruck und die Spannungsfunktion beinhaltenden Grundgleichungen hergeleitet. Laplace-Transformation ermöglicht das Auffinden explizierter Lösungen für die Spannungen. Es zeigt sich, daß unter konstanter äußerer Belastung das Knochenelement zu kriechen beginnt, so daß die viskoelastischen Eigenschaften dieses Knochenmodells mit den experimentellen Ergebnissen vonSedlin übereinzustimmen scheint.

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References

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Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • J. L. Nowinski
    • 1
  1. 1.Mechanical and Aerospace EngineeringUniversity of DelawareNewarkUSA

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