# zbMATH — the first resource for mathematics

A new method for modelling cohesive cracks using finite elements. (English) Zbl 1013.74074
Summary: We present a model which allows the introduction of displacements jumps to conventional finite elements. The path of the discontinuity is completely independent of the mesh structure. Unlike so-called ‘embedded discontinuity’ models, which are based on incompatible strain modes, there is no restriction on the type of underlying solid finite element that can be used, and displacement jumps are continuous across element boundaries. Using finite element shape functions as partitions of unity, the displacement jump across a crack is represented by extra degrees of freedom at existing nodes. To model fracture in quasi-brittle heterogeneous materials, we use a cohesive crack model. Numerical simulations illustrate the ability of the method to objectively simulate fracture on unstructured meshes.

##### MSC:
 74S05 Finite element methods applied to problems in solid mechanics 74R10 Brittle fracture
Full Text:
##### References:
 [1] Schellekens, International Journal for Numerical Methods in Engineering 26 pp 43– (1993) · Zbl 0825.73840 · doi:10.1002/nme.1620360104 [2] Swenson, Computational Mechanics 3 pp 381– (1988) · Zbl 0663.73074 · doi:10.1007/BF00301139 [3] Simulation of arbitrary, cohesive crack propagation. In Fracture Mechanics of Concrete Structures, (ed.). Elsevier: London, 1992; 339-350. [4] De Borst, Engineering Computations 10 pp 99– (1993) · doi:10.1108/eb023897 [5] Dvorkin, International Journal for Numerical Methods in Engineering 30 pp 541– (1990) · Zbl 0729.73209 · doi:10.1002/nme.1620300311 [6] Klisinski, ASCE Journal of Engineering Mechanics 117 pp 575– (1991) · doi:10.1061/(ASCE)0733-9399(1991)117:3(575) [7] Simo, Computational Mechanics 12 pp 277– (1993) · Zbl 0783.73024 · doi:10.1007/BF00372173 [8] Oliver, International Journal for Numerical Methods in Engineering 39 pp 3601– (1996) · doi:10.1002/(SICI)1097-0207(19961115)39:21<3601::AID-NME64>3.0.CO;2-4 [9] Armero, International Journal of Solids and Structures 33 pp 2863– (1996) · Zbl 0924.73084 · doi:10.1016/0020-7683(95)00257-X [10] Wells, Engineering Fracture Mechanics 65 pp 263– (2000) · doi:10.1016/S0013-7944(99)00120-4 [11] Wells, International Journal of Solids and Structures 38 pp 897– (2001) · Zbl 1004.74065 · doi:10.1016/S0020-7683(00)00029-9 [12] Simo, International Journal for Numerical Methods in Engineering 29 pp 1595– (1990) · Zbl 0724.73222 · doi:10.1002/nme.1620290802 [13] Duarte, Numerical Methods for Partial Differential Equations 12 pp 673– (1996) · Zbl 0869.65069 · doi:10.1002/(SICI)1098-2426(199611)12:6<673::AID-NUM3>3.0.CO;2-P [14] Melenk, Computer Methods in Applied Mechanics and Engineering 139 pp 289– (1996) · Zbl 0881.65099 · doi:10.1016/S0045-7825(96)01087-0 [15] Fleming, International Journal for Numerical Methods in Engineering 40 pp 1483– (1997) · doi:10.1002/(SICI)1097-0207(19970430)40:8<1483::AID-NME123>3.0.CO;2-6 [16] Belytschko, International Journal for Numerical Methods in Engineering 45 pp 601– (1999) · Zbl 0943.74061 · doi:10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S [17] Möes, International Journal for Numerical Methods in Engineering 46 pp 131– (1999) · Zbl 0955.74066 · doi:10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J [18] Belytschko, International Journal for Numerical Methods in Engineering 37 pp 229– (1994) · Zbl 0796.73077 · doi:10.1002/nme.1620370205 [19] Oden, Computer Methods in Applied Mechanics and Engineering 153 pp 117– (1998) · Zbl 0956.74062 · doi:10.1016/S0045-7825(97)00039-X [20] Babu?ka, International Journal for Numerical Methods in Engineering 40 pp 727– (1997) · Zbl 0949.65117 · doi:10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N [21] Hillerborg, Cement and Concrete Research 6 pp 773– (1976) · doi:10.1016/0008-8846(76)90007-7 [22] Computational modeling of concrete fracture. Ph.D. Thesis, Delft University of Technology, 1988. [23] Embedded crack models for concrete fracture. In EURO-C 1998 Computer Modelling of Concrete Structures, (eds). Balkema: Rotterdam, 1998; 291-300. [24] Experimental and numerical analysis of fracture processes in concrete. Ph.D. Thesis, Delft University of Technology, 1993. [25] Peerlings, Mechanics of Cohesive-Frictional Materials 3 pp 323– (1998) · doi:10.1002/(SICI)1099-1484(1998100)3:4<323::AID-CFM51>3.0.CO;2-Z
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.