×

zbMATH — the first resource for mathematics

Analysis of concrete fracture using a novel cohesive crack method. (English) Zbl 1201.74288
Summary: Numerical analysis of fracture in concrete is studied with a simplified discrete crack method. The discrete crack method is a meshless method in which the crack is modeled by discrete cohesive crack segments passing through the nodes. The cohesive crack segments govern the non-linear response of concrete in tension softening and introduce anisotropy in the material model. The advantage of the presented discrete crack method over other discrete crack method is its simplicity and applicability to many cracks. In contrast to most other discrete crack methods, no representation of the crack surface is needed. On the other hand, the accuracy of discrete crack methods is maintained. This is demonstrated through several examples.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74R10 Brittle fracture
PDF BibTeX Cite
Full Text: DOI
References:
[1] Bazant, Z.P.; Oh, B.H., Crack band theory for fracture in concrete, Mater. struct., 16, 155-177, (1983)
[2] Hao, S.; Liu, W.K.; Klein, P.A.; Rosakis, A.J., Modeling and simulation of intersonic crack growth, Int. J. solids struct., 41, 7, 1773-1799, (2004) · Zbl 1045.74588
[3] Papa, E.; Nappi, A., Numerical modelling of masonry: a material model accounting for damage effects and plastic strains, Appl. math. model., 21, 6, 319-335, (1997) · Zbl 0969.74580
[4] Ray, A.; Tangirala, S.; Phoha, S., Stochastic modeling of fatigue crack propagation, Appl. math. model., 22, 3, 197-204, (1998) · Zbl 0906.73050
[5] Jirasek, M.; Zimmermann, T., Analysis of rotating crack model, J. eng. mech., 124, 842-851, (1998)
[6] Malvar, L.J.; Fourney, M.E., A three dimensional application of the smeared crack approach, Eng. fract. mech., 35, 1-3, 251-260, (1990)
[7] Dorgan, J., A mixed finite element implementation of a gradient-enhanced coupled damage-plasticity model, Int. J. damage mech., 15, 201-235, (2006)
[8] Rabczuk, T.; Eibl, J., Simulation of high velocity concrete fragmentation using SPH/MLSPH, Int. J. numer. methods eng., 56, 1421-1444, (2003) · Zbl 1106.74428
[9] Rabczuk, T.; Eibl, J.; Stempniewski, L., Numerical analysis of high speed concrete fragmentation using a meshfree Lagrangian method, Eng. fract. mech., 71, 4-6, 547-556, (2004)
[10] Rabczuk, T.; Eibl, J., Numerical analysis of prestressed concrete beams using a coupled element free Galerkin/finite element method, Int. J. solids struct., 41, 3-4, 1061-1080, (2004) · Zbl 1075.74670
[11] Rabczuk, T.; Belytschko, T., Adaptivity for structured meshfree particle methods in 2d and 3d, Int. J. numer. methods eng., 63, 11, 1559-1582, (2005) · Zbl 1145.74041
[12] Rabczuk, T.; Akkermann, J.; Eibl, J., A numerical model for reinforced concrete structures, Int. J. solids struct., 42, 5-6, 1327-1354, (2005) · Zbl 1120.74790
[13] Rabczuk, T.; Eibl, J., Modelling dynamic failure of concrete with mesh-free methods, Int. J. impact eng., 32, 11, 1878-1897, (2006)
[14] Abu Al-Rub, R.K.; Voyiadiis, G.Z., A finite strain plastic damage model for high velocity impact using combined viscosity and gradient localization limiters. part I: theoretical formulation, Int. J. damage mech., 15, 293-334, (2006)
[15] Khan, A.R.; Al-Gadhib, A.H.; Baluch, M.H., Elasto-damage model for high strength concrete subjected to multiaxial loading, Int. J. damage mech., 16, 361-398, (2007)
[16] Barenblatt, G., The mathematical theory of equilibrium of cracks in brittle fracture, Adv. appl. fract., 7, 55-129, (1962)
[17] Hillerborg, A.; Modeer, M.; Peterson, P.E., Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements, Cement concrete res., 6, 773-782, (1976)
[18] Ortiz, M.; Leroy, Y.; Needleman, A., Finite element method for localized failure analysis, Comput. methods appl. mech. eng., 61, 189-213, (1987) · Zbl 0597.73105
[19] Xu, X.-P.; Needleman, A., Numerical simulations of fast crack growth in brittle solids, J. mech. phys. solids, 42, 1397-1434, (1994) · Zbl 0825.73579
[20] Carol, I.; Lopez, C.M.; Roa, O., Micromechanical analysis of quasi-brittle materials using fracture-based interface elements, Int. J. numer. methods eng., 52, 193-215, (1996)
[21] Galves, J.C.; Cervenka, J.; Cendon, D.A.; Saouma, V., A discrete crack approach to normal/shear cracking of concrete, Cement concrete res., 32, 10, 1567-1585, (2002)
[22] Lee, K.M.; Park, J.H., A numerical model for elastic modulus of concrete considering interfacial transition zone, Cement concrete res., 38, 3, 396-402, (2008)
[23] Rabczuk, T.; Zi, G.; Gerstenberger, A.; Wall, W.A., A new crack tip element for the phantom node method with arbitrary cohesive cracks, Int. J. numer. methods eng., 75, 577-599, (2008) · Zbl 1195.74193
[24] T. Rabczuk, S. Bordas, G. Zi, On three-dimensional modelling of crack growth using partition of unity methods, Comput. Struct., in press, doi:10.1016/j.compstruc.2008.08.010. · Zbl 1161.74054
[25] Rabczuk, T.; Zi, G.; Bordas, S.; Nguyen-Xuan, H., A geometrically nonlinear three dimensional cohesive crack method for reinforced concrete structures, Eng. fract. mech., 75, 4740-4758, (2008)
[26] Bolotin, V.V., Fracture from the standpoint of nonlinear stability, Int. J. non-linear mech., 29, 4, 569-585, (1994) · Zbl 0812.73043
[27] Bazant, Z.P.; Belytschko, T., Wave propagation in a strain softening bar: exact solution, J. eng. mech. ASCE, 11, 381-389, (1985)
[28] Yang, X.H.; Chen, C.Y.; Hu, Y.T., Damage analysis and fracture criteria for piezoelectric ceramics, Int. J. non-linear mech., 40, 9, 1204-1213, (2005) · Zbl 1349.74065
[29] Haussler-Combe, U.; Hartig, J., Formulation and numerical implementation of a constitutive law for concrete with strain-based damage and plasticity, Int. J. non-linear mech., 43, 5, 399-415, (2008)
[30] De Borst, R., Modern domain-based discretization methods for damage and fractures, Int. J. fract., 138, 1-4, 241–262, (2006) · Zbl 1113.74420
[31] Organ, D.; Fleming, M.; Terry, T.; Belytschko, T., Continuous meshless approximations for nonconvex bodies by diffraction and transparency, Comput. mech., 18, 225-235, (1996) · Zbl 0864.73076
[32] Hao, S.; Liu, W.K.; Chang, C.T., Computer implementation of damage models by finite element and meshfree methods, Comput. methods appl. mech. eng., 187, 3-4, 401-440, (2000) · Zbl 0980.74063
[33] Hao, S.; Liu, W.K.; Qian, D., Localization-induced band and cohesive model, J. appl. mech. - trans. ASME, 67, 4, 803-812, (2000) · Zbl 1110.74469
[34] Rabczuk, T.; Areias, P.M.A.; Belytschko, T., A meshfree thin shell method for non-linear dynamic fracture, Int. J. numer. methods eng., 72, 524-548, (2007) · Zbl 1194.74537
[35] Li, S.; Simonson, Bo C., Meshfree simulation of ductile crack propagation, Int. J. comput. methods eng. sci. mech., 6, 1-19, (2003)
[36] Hao, S.; Liu, W.K., Moving particle finite element method with super-convergence: nodal integration formulation and applications, Comput. methods appl. mech. eng., 195, 44-47, 6059-6072, (2006) · Zbl 1120.74051
[37] Bordas, S.; Rabczuk, T.; Zi, G., Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by extrinsic discontinuous enrichment of meshfree methods without asymptotic enrichment, Eng. fract. mech., 75, 943-960, (2008)
[38] Rabczuk, T.; Bordas, S.; Zi, G., A three-dimensional meshfree method for continuous multiple crack initiation, nucleation and propagation in statics and dynamics, Comput. mech., 40, 3, 473-495, (2007) · Zbl 1161.74054
[39] Rabczuk, T.; Areias, P., A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis, Comput. model. eng. sci., 16, 2, 115-130, (2006)
[40] Rabczuk, T.; Gracie, R.; Song, J.-H.; Belytschko, T., Immersed particle method for fluid – structure interaction, Int. J. numer. methods eng., 81, 48-71, (2010) · Zbl 1183.74367
[41] Rabczuk, T.; Belytschko, T., Cracking particles: a simplified meshfree method for arbitrary evolving cracks, Int. J. numer. methods eng., 61, 13, 2316-2343, (2004) · Zbl 1075.74703
[42] Rabczuk, T.; Belytschko, T., Application of particle methods to static fracture of reinforced concrete structures, Int. J. fract., 137, 1-4, 19-49, (2006) · Zbl 1197.74175
[43] Rabczuk, T.; Areias, P.M.A., A new approach for modelling slip lines in geological materials with cohesive models, Int. J. numer. anal. methods geomech., 30, 11, 1159-1172, (2006) · Zbl 1196.74137
[44] Rabczuk, T.; Belytschko, T., A three dimensional large deformation meshfree method for arbitrary evolving cracks, Comput. methods appl. mech. eng., 196, 2777-2799, (2007) · Zbl 1128.74051
[45] Rabczuk, T.; Areias, P.M.A.; Belytschko, T., A simplified meshfree method for shear bands with cohesive surfaces, Int. J. numer. methods eng., 69, 5, 993-1021, (2007) · Zbl 1194.74536
[46] Rabczuk, T.; Samaniego, E., Discontinuous modelling of shear bands using adaptive meshfree methods, Comput. methods appl. mech. eng., 197, 641-658, (2008) · Zbl 1169.74655
[47] Rabczuk, T.; Song, J.-H.; Belytschko, T., Simulations of instability in dynamic fracture by the cracking particles method, Eng. fract. mech., 76, 730-741, (2009)
[48] Belytschko, T.; Lu, Y.Y.; Gu, L., Element-free Galerkin methods, Int. J. numer. eng., 37, 229-256, (1994) · Zbl 0796.73077
[49] Melenk, J.M.; Babuska, I., The partition of unity finite element method: basic theory and applications, Comput. methods appl. mech. eng., 139, 289-314, (1996) · Zbl 0881.65099
[50] Needleman, A., A continuum model for void nucleation by inclusion debonding, J. appl. mech. - trans. ASME, 54, 525-531, (1987) · Zbl 0626.73010
[51] Belytschko, T.; Lu, Y.Y., Element-free Galerkin methods for static and dynamic fracture, Int. J. solids struct., 32, 2547-2570, (1995) · Zbl 0918.73268
[52] Belytschko, T.; Lu, Y.Y.; Gu, L., Crack propagation by element-free Galerkin methods, Eng. fract. mech., 51, 2, 295–315, (1995)
[53] Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P., Mesh-less methods: an overview and recent developments, Comput. methods appl. mech. eng., 139, 3-47, (1996) · Zbl 0891.73075
[54] G.N. Wells, Discontinuous Modelling of Strain Localisation and Failure, Ph.D. Thesis, Technische Universiteit Delft, The Netherlands, 2001.
[55] Ventura, G.; Xu, J.; Belytschko, T., A vector level set method and new discontinuity approximation for crack growth by EFG, Int. J. numer. methods eng., 54, 6, 923-944, (2002) · Zbl 1034.74053
[56] Oliver, J.; Huespe, A.E.; Sanchez, P.J., A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM, Comput. methods appl. mech. eng., 195, 4732-4752, (2006) · Zbl 1144.74043
[57] Zi, G.; Rabczuk, T.; Wall, W., Extended meshfree methods without branch enrichment for cohesive cracks, Comput. mech., 40, 2, 367-382, (2007) · Zbl 1162.74053
[58] Rabczuk, T.; Zi, G., A meshfree method based on the local partition of unity for cohesive cracks, Comput. mech., 39, 6, 743-760, (2007) · Zbl 1161.74055
[59] Dolbow, J.; Belytschko, T., An introduction to programming the mesh-less element free Galerkin method, Arch. comput. methods eng., 5, 3, 207-241, (1998)
[60] Rabczuk, T.; Belytschko, T.; Xiao, S.P., Stable particle methods based on Lagrangian kernels, Comput. methods appl. mech. eng., 193, 1035-1063, (2004) · Zbl 1060.74672
[61] M. Arrea, A.R. Ingraffea, Mixed-mode crack propagation in mortar and concrete, Technical Report 81-13, Department of Structural Engineering, Cornell University, New York, 1982.
[62] M.B. Nooru-Mohamed, Mixed-Mode Fracture of Concrete: An Experimental Approach, Ph.D. Thesis, Delft University of Technology, 1992.
[63] Ballatore, E.; Carpinteri, A.; Ferrara, G.; Melchiorri, G., Mixed mode fracture energy of concrete, Eng. fract. mech., 35, 145-157, (1990)
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.