Calcul do champ de contrainte en pointe de fissure en elasticite plane en grandes deformations
Keywords:
iterative procedure, finite element, elasticity, large strains, crack, interface, stress intensity factorAbstract
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
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.