zbMATH — the first resource for mathematics

A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing. (English) Zbl 1112.74537
Summary: This paper presents a general study of the stability of variable-mesh dynamic calculations using an energy approach. This study, whose scope is limited to the calculation of dynamic crack propagation with remeshing, enables us to establish the conditions which are necessary to ensure stability and allow control of energy transfers during the evolution of the mesh. The problem of the implicit calculation of the crack length is also presented. The results obtained on an sample problem are analyzed to illustrate the effectiveness of the proposed methods.

74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
Full Text: DOI
[1] R.A. Einsfeld, L.F. Martha, T.N. Bittencourt, Combination of smeared and discrete approaches with the use of interface elements, in: European Congress on Computational Methods in Applied Sciences and Engineering, 2000
[2] Nishioka, T.; Tokudome, H.; Kinoshita, M., Dynamic fracture-path prediction in impact fracture phenomena using moving finite element method based on Delaunay automatic mesh generation, Int. J. solids and structures, 38, 5273-5301, (2001) · Zbl 0997.74066
[3] Li, S.; Liu, W.K.; Rosakis, A.J.; Belytschko, T.; Hao, W., Mesh-free Galerkin simulations of dynamic shear band propagation and failure transition, Int. J. solids and structures, 39, 1213-1240, (2002) · Zbl 1090.74698
[4] Krysl, P.; Belytschko, T., Dynamic propagation of arbitrary 3-d cracks, Int. J. numer. methods engrg, 44, 6, 767-800, (1999) · Zbl 0953.74078
[5] Bui, H.D., Mécanique de la rupture fragile, (1978), Masson
[6] Irwin, G.R., Analysis of stress and strains near the end of a crack traversing a plate, J. appl. mech, 24, 3, 361-364, (1957)
[7] Freund, L.B., Dynamic fracture mechanics, Cambridge monographs mech. appl. math, (1990), Cambridge University Press
[8] Rice, J.R., A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. appl. mech, 35, 379-386, (1968)
[9] D. Anderson, Experimental investigation of quasistatic and dynamic fracture properties of titanium alloys, Ph.D. thesis, Californian Institute of Technology, 2002
[10] Broek, D., Elementary engineering fracture mechanics, (1982), Martinus Nijhoff Publishers
[11] Suo, X.S.; Combescure, A., On the application of the \(Gθ\) method and its comparison with de Lorenzi’s approach, Nucl. engrg. design, 135, 207-224, (1992)
[12] Attigui, M.; Petit, C., Mixed-mode separation in dynamic fracture mechanics: new path independent integrals, Int. J. fracture, 84, 1, 19-36, (1997)
[13] T.J.R. Hughes, T. Belytschko, Nonlinear finite element analysis, ICE Division, Zace Services Ltd., 2000
[14] A. Gravouil, Méthode multi-échelles en temps et en espace avec décomposition de domaines pour la dynamique non-linéaire des structures, Ph.D. thesis, LMT-Cachan, 2000
[15] Hughes, T.J.R.; Liu, W.K., Implict – explicit finite element transient analysis: stability theory, J. appl. mech, 45, 371-374, (1978) · Zbl 0392.73076
[16] J.F. Kalthoff, J. Beinert, S. Winkler, W. Klemm, Experimentational analysis of dynamic effects in different crack arrest test specimens, in: ASTM E-24, Symposium on Crack Arrest Methodology and Applications, Philadelphia, 1978
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.