Abstract
We propose a methodology to model complex fracture processes in reinforced concrete beams subjected to static loading. The discrete cohesive approach, accompanied by an insertion algorithm, is adopted and a modified dynamic relaxation method is chosen as an alternative solver. The concrete matrix and steel re-bars are modeled explicitly; the connection in between is represented by means of interface elements. Such elements allow for slip of re-bars and transmit forces to the matrix that may generate secondary cracking around the reinforcement. The methodology is validated against three-point bending tests on lightly reinforced concrete (LRC) beams.
Similar content being viewed by others
References
Arbilla I (2000) Modelización de la fractura del hormigón en geometrías sin entallas. Ph. D. thesis, Departamento de Ciencia de Materiales, ETS de Ingenieros de Caminos, C. y P., Universidad Politécnica de Madrid, Spain. (Modeling of fracture of unnotched concrete specimens, in Spanish).
Baluch MH, Azad AK, Ashmawi W (1992) Fracture mechanics application to reinforced concrete members in flexure. In: Carpinteri A (ed) Applications of fracture mechanics to reinforced Concrete. Elsevier, London, pp 413–436
Bažant ZP, Planas J (1998) Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press, Boca Raton, Florida
Ben Romdhane M, Ulm D (2002) Computational mechanics of the steel–concrete interface. Intl J Numerical Analyt Met Geomech 26:99–120
Bosco C, Carpinteri A (1992a) Fracture behaviour of beam cracked across reinforcement. Theoret Appl Fract Mech 17:61–68
Bosco C, Carpinteri A (1992b) Fracture mechanics evaluation of minimum reinforcement in concrete structures. In: Carpinteri A (ed) Applications of fracture mechanics to reinforced concrete. Elsevier, London, pp 347–377
Brew J, Brotton DM (1971) Non-linear structural analysis by dynamic relaxation. Intl J Numerical Met Eng 3:436–483
Brincker R, Henriksen MS, Christensen FA, Heshe G (1999) Size effects on the bending behaviour of reinforced concrete beams. In: Carpinteri A (ed) Minimum reinforcement in concrete members. Elsevier, London, pp 127–180
Camacho GT, Ortiz M (1996) Computational modeling of impact damage in brittle materials. Intl J Solids and Struct 33(20–22):2899–2938
Cendón DA (2002) Estudio de la fractura en modo mixto de hormigones y morteros. Ph. D. thesis, Departamento de Ciencia de Materiales, ETS de Ingenieros de Caminos, C. y P., Universidad Politécnica de Madrid, Spain. (Study on mixed-mode fracture of concrete and mortar, in Spanish)
Cendón DA, Ruiz G (2002) Local fracture and steel–concrete decohesion phenomena studied by means of cohesive and interface elements. In: Proceedings of the V World Congress on Computational Mechanics. On-line publication
Cendón DA, Ruiz G (2003) Propagación de una fisura cohesiva a través de una capa de refuerzo: Modelo de las tensiones de adherencia distribuidas. Anales de Mecanica de la Fractura 20:131–136
Comite Euro-International du Beton (CEB) and the Federation Internationale de la Precont (FIP) (1993) CEB-FIP Model Code 1990. Thomas Telford Ltd, London, UK
Day A (1965) An introduction to dynamic relaxation. The Engineer 219:218–221
De Andrés A, Pérez JL, Ortiz M (1999) Elastoplastic finite-element analysis of three-dimensional fatigue crack growth in aluminum shafts subjected to axial loading. Intl J Solids Struct 36(15):2231–2258
Fantilli AP, Ferretti D, Iori I, Vallini P (1999) Behaviour of R/C elements in bending and tension: the problem of minimum reinforcement ratio. In: Carpinteri A (ed) Minimum Reinforcement in Concrete Members. Elsevier, London, pp 99–125
Gerstle WH, Parsha PD, Prasad NNV, Rahulkumar P, Ming X (1992) Crack growth in flexural members—A fracture mechanics approach. ACI Struct J 89:617–625
Hawkins NM, Hjorsetet K (1992) Minimum reinforcement requirement for concrete flexural members. In: Carpinteri A (ed) Applications of fracture mechanics to reinforced concrete. Elsevier, London, pp 379–412
Hededal O, Kroon IB (1991) Lightly reinforced high-strength concrete. University of Åalborg, Denmark, M. Sc. Thesis.
Lettow S, Ožbolt J, Eligehausen R, Mayer U (2004) Bond of RC members using nonlinear 3D FE analysis. In: Li VC, Leung CKY, Willam K, Billington S (Eds) Fracture mechanics of concrete structures. IA-FraMCoS, pp 861–868
Massabò R (1994) Meccanismi di Rottura nei Materiali Fibrorinforzati. Ph. D. thesis, Dip. Ingegneria Strutturale, Politecnico di Torino, Italy (Fracture Mechanisms in Fiber-Reinforced Materials, in Italian)
Metzger D (2003) Adaptive damping for dynamic relaxation problems with non-monotonic spectral response. Intl J Numer Methods Eng 56:57–80
Metzger DR, Sauvé RG (1997) The effect of discretization and boundary conditions on the convergence rate of the dynamic relaxation method. Curr Top Design Anal Pres Vessels Piping ASME PVP 354:105–110
Oakley DR, Knight NFJ (1995a) Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures. part i. formulation. Comput Methods Appl Mech Eng 126:67–89
Oakley DR, Knight NFJ (1995b) Adaptive dynamic relaxation algorithm for non-linear hyperelastic structures. part ii. single processor implementation. Comput Methods Appl Mech Eng 126:91–109
Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Intl J Numer Methods Eng 44:1267–1282
Otter J (1965) Computations for prestressed concrete reactor pressure vessels using dynamic relaxation. Nucl Struct Eng 1:61–75
Ozbolt J, Bruckner M (1999) Minimum reinforcement requirement for RC beams. In: Carpinteri A (ed) Minimum Reinforcement in Concrete Members. Elsevier, London, pp 181–201
Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18(2):148–159
Papadrakakis M (1981) A method for automated evaluation of the dynamic relaxation parameters. Comput Methods Appl Mech Eng 25:35–48
Rericha P (1986) Optimum load time history for non-linear analysis using dynamic relaxation. Intl J Numer Methods Eng 23:2313–2324
Ruiz G (2001) Propagation of a cohesive crack crossing a reinforcement layer. Intl J Fract 111:265–282
Ruiz G, Carmona JR (2006) Experimental study on the influence of the shape of the cross-section and of the rebar arrangement on the fracture of lightly reinforced beams. Mater Struct 39:311–320
Ruiz G, Elices M, Planas J (1998, December) Experimental study of fracture of lightly reinforced concrete beams. Mater Struct 31:683–691
Ruiz G, Elices M, Planas J (1999) Size effect and bond-slip dependence of lightly reinforced concrete beams. Elsevier, ESIS Publication 24, Kidlington, Oxford, UK, pp 67–98
Ruiz G, Ortiz M, Pandolfi A (2000) Three-dimensional finite-element simulation of the dynamic Brazilian tests on concrete cylinders. Intl J Numer Methods Eng 48:963–994
Ruiz G, Pandolfi A, Ortiz M (2001) Three-dimensional cohesive modeling of dynamic mixed-mode fracture. Intl J Numer Methods Eng 52:97–120
Ruiz G, Carmona JR, Cendón DA (2006) Local fracture and steel–concrete decohesion phenomena studied by means of cohesive interface elements. Comput Methods Appl Mech Eng
Sauvé RG, Metzger D (1995) Advances in dynamic relaxation techniques for nonlinear finite element analysis. Trans ASME 117:170–176
Sauvé RG, Metzger D (1996) A hybrid explicit solution technique for quasi-static transients. In: GM Hulbert (ed.) Computer technology: applications and methodology, ASME PVP, vol. 326, pp 151–157
Siddiquee M, Tanaka T, Tatsouka F (1995) Tracing the equilibrium path by dynamic relaxation in materially nonlinear finite element problems. Intl J Numer Anal Methods Geomech 19:749–767
Ulfkjr JP, Hededal O, Kroon I, Brincker R (1994) Simple application of fictitious crack model. In: Mihashi H, Okamura H, Bažant ZP (eds) Size effect in concrete structures. E & FN Spon, London, pp 281–292
Underwood P (1983) Dyanmic relaxation. Comput Methods Trans Anal 1:145–265
Yu RC, Ruiz G (2004) Static multi-crack modeling in concrete solved by a modified DR method. Comput Concrete 1(4):371–388
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Yu, R.C., Ruiz, G. Explicit finite element modeling of static crack propagation in reinforced concrete. Int J Fract 141, 357–372 (2006). https://doi.org/10.1007/s10704-006-9002-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-006-9002-0