Calcul do champ de contrainte en pointe de fissure en elasticite plane en grandes deformations

Authors

  • Gilles Loppin Groupe de Mecanique des Materiaux et des Structures ( EA 1237) UFR Sciences, BP 347, 51062 Reims cedex

Keywords:

iterative procedure, finite element, elasticity, large strains, crack, interface, stress intensity factor

Abstract

An iterative procedure for the computation of the stress field near a crack tip within the frame of large strain plane elasticity is proposed. This numerical process, based on finite element method, has been already verified in linear elasticity context. It permits especially to obtain an estimation of some asymptotic coefficients associated with the local solution for rubberlike materials. One of them can be compared with a stress intensity factor of the linear theory and therefore is involved in a crack propagation criterium of non-linear Fracture Mechanics. Numerical tests are presented. The results obtained are in good agreement with known analytical solutions.

 

Downloads

Download data is not yet available.

References

[KNO 73] Knowles J. K. & Sternberg E. ,"An asymptotic finite-deformation

analysis of the elastic field near the tip of a crack", J. of Elasticity, 3, 67-107, 1973.

[KNO 83] Knowles J. K. & Sternberg E. ,"Large deformation near a tip of an

interface-crack between two neo-hookean sheets", J.ofElast., 13, 257-293, 1983.

[LE 93] Le K. C. & Stumpf H., "The singular elastostatic field due to a crack in

rubberlike materials", J. of Elasticity, 32, 183-222, 1993.

[LUN 90] Lund R. A. & Westmann R. A., "Finite element analysis ofhyperelastic

large deformation crack tip fields", Int. J. ofFracture, 43,257-270, 1990.

[LOP 92] LoppinG. & Rigolot A., "A numerical approximation for the analysis of

angular singularities in plane classical elasticity", Eur. J. ofMech./ Solids, 11, n°3,

-321, 1992.

[OGD 72] Ogden R. W., "Large deformation isotropic elasticity - on the

correlation of theory and experiment for incompressible rubberlike solids", Proc.

Roy. Soc. London, A.326, 565-584, 1972.

[R&S 68] Rice J. R. & Sih G. C., "Plane problems of cracks in dissimilar media",

J.of Appl. Mech., 32,418-423, 1968.

[RIC 68] Rice J. R., "A path independent integral and the approximate analysis of

strain concentration by notches and cracks", J. of Appl. Mech., 35, 379-386, 1968.

[STE 82] Stephenson R. A., "The equilibrium field near the tip of a crack for finite

plane strain of incompressible elastic material", J. ofElasticity, 12,65-99, 1982.

[WON 69] Wong F. S. & Shield R.T., "Large plane deformations of thin elastic

sheets of neo-hookean material", Zeitschrift fiir Ang. Math. und Phys., 20,

-199, 1969.

Downloads

Published

1997-01-25

How to Cite

Loppin, G. . (1997). Calcul do champ de contrainte en pointe de fissure en elasticite plane en grandes deformations. European Journal of Computational Mechanics, 6(1), 99–112. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/3473

Issue

Section

Original Article