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Meccanica

, Volume 4, Issue 4, pp 349–363 | Cite as

Limiting conditions of yielding for anisotropic materials

  • Ferdinando Stassi-D'Alia
Article

Summary

The known Limiting Conditions of Yielding presuppose homogeneity andisotropy of the material. Formulas for anisotropic materials have been proposed: but they cannot be applied to all practical applications. The Limiting Condition of Yielding already proposed by the A. for isotropic materials can easily be extended to materials with different mechanical properties in different directions: the formulas obtained confirm the particular cases and the particular formulas already known for isotropic materials. The various solutions proposed by the A. for anisotropic bodies are usually represented by paraboloids whose characteristics obviously depend on the experimental parameters.

Keywords

Mechanical Property Mechanical Engineer Civil Engineer Experimental Parameter Isotropic Material 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

σ1,σ2,σ3

principal normal stresses

σ01,σ02,σ03

limit stresses in pure tension along the three principal directions (positive)

σ0

limit stress in pure tension

σ01,σ02,σ03

limit stresses in pure compression along the three principal directions (positive)

σ0

limit stress in pure compression

x=σ1/σ01,y=σ2/σ02,z=σ3/σ03

non dimensional ratios between the principal normal stresses and the corresponding limit stresses in pure tension

σx,σy,σz

normal non principal stresses

τxy,τyz,τzx

shearing stresses

τ0

limit shearing stress

δ1=σ01/σ01;δ2=σ'02/σ02;δ3=σ'03/σ03

ratios between the limit stresses in pure compression and the corresponding limit stresses in pure tension (positive)

m=σ02/σ01;n=σ03/σ01

ratios of the second and the third limit stress in pure tensionvs. The first limit stress

m′=σ02/σ01;n′=σ03/σ01

ratios of the second and the third limit stress in pure compression vs. the first limit stress

σi

hydrostatic limit stress.

Sommario

Le condizioni di plastificazione che si conoscono presuppongono omogeneità eisotropia del materiale. Per corpi anisotropi sono state proposte espressioni che non possono essere applicate in casi riguardanti le pratiche applicazioni. La condizione di plastificazione proposta dall'A. per i corpi isotropi può essere con opportune trasformazioni adattata a materiali presentanti differenti proprietà meccaniche nelle tre direzioni principali: le formule che se ne ottengono confermano i casi particolari e le formule già note per i corpi isotropi. Le soluzioni proposte dall'A. per i corpi anisotropi sono rappresentate in genere da paraboloidi le cui caratteristiche dipendono ovviamente dai parametri sperimentali.

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References

  1. [1]
    R. Hill,The mathematical theory of Plasticity, Clarendon Press, Oxford, 1950.Google Scholar
  2. [2]
    F. Stassi,Sui criteri di resistenza dei corpi anisotropi, Atti dell'Accademia di Scienze Lettere e Arti, Palermo. Seduta del 28 Giugno 1968.Google Scholar
  3. [3]
    F. Stassi,Flow and fracture of materials according to a new limiting condition of yielding, Meccanica, Vol. 2, no. 3, 1967.Google Scholar
  4. [4]
    L. Rendulic,Eine Betrachtung zur Frage der plastischen Grenzzustande, Der Bauingenieur, 1938.Google Scholar
  5. [5]
    F. Stassi,Une fonction quadratique des tensions principales comme condition de plasticité des corps solides, Bulletin RILEM, no. 13, Décembre 1961.Google Scholar
  6. [6]
    F. Stassi,Interdépendance des caractéristiques de résistance des materiaux, Bulletin RILEM, no. 21, Décembre 1963.Google Scholar
  7. [7]
    F. Stassi,Ancora sui criteri di resistenza dei corpi anisotropi, Atti dell'Accademia di Scienze Lettere e Arti, Palermo, Seduta del 30 Novembre 1968.Google Scholar

Copyright information

© Tamburini Editore s.p.a. Milano 1966

Authors and Affiliations

  • Ferdinando Stassi-D'Alia
    • 1
  1. 1.Università di PalermoItaly

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