Abstract
In the paper, the results of numerical failure analysis of plain concrete beams loaded by impact three-point bending load are presented and discussed. The theoretical framework for the numerical analysis is continuum mechanics and irreversible thermodynamics. The spatial discretization is performed by the finite element method using update Lagrange formulation. Green–Lagrange stain tensor is used as a strain measure. To account for cracking and damage of concrete, the beam is modeled by the rate sensitive microplane model with the use of the so-called co-rotational stress tensor. Damage and cracking phenomena are modeled within the concept of smeared cracks. To assure objectivity of the analysis with respect to the size of the finite elements, crack band method is used. The contact-impact analysis is based on the mechanical interaction between two bodies—concrete beam (master) and dropping hammer (slave) falling on the mid span of the beam. The contact constrains are satisfied by Lagrange multiplier method, which is adapted for the explicit time integration scheme. To investigate the influence of loading rate on the failure mode of the beam parametric study is carried out. The numerical results are evaluated, discussed and compared with test results known from the literature. It is shown that the beam resistance and failure mode strongly depend on loading rate. For lower loading rates beam fails in bending (mode-I fracture). However, with increasing loading rate there is a transition of the failure mechanism from bending to shear. The results are in good agreement with theoretical and experimental results known from the literature.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
Banthia NP, Mindess S, Bentur A (1987) Impact behaviour of concrete beams. Mater Struct (MatOriaux et Constructions) 20: 293–302
Bažant ZP, Oh BH (1983) Crack band theory for fracture of concrete. RILEM 93(16): 155–177
Bažant ZP, Prat PC (1988) Microplane model for brittle-plastic material—parts I and II. J Eng Mech ASCE 114: 1672–1702
Bažant ZP, Gettu R (1992) Rate effect and load relaxation in static fracture of concrete. ACI Mater J 89: 456–468
Bažant ZP, Adley MD, Carol I, Jirasek M, Akers SA, Rohani B, Cargile JD, Caner FC (2000a) Large-strain generalization of microplane model for concrete and application. J Eng Mech ASCE 126(9): 971–980
Bažant ZP, Caner FC, Adley MD, Akers SA (2000b) Fracturing rate effect and creep in microplane model for dynamics. J Eng Mech ASCE 126(9): 962–970
Belytschko T, Liu WK, Moran M (2001) Nonlinear finite elements for continua and structures. Wiley, New Jersey
Bentur A, Mindess S, Banthia N (1987) The behaviour of concrete under impact loading: experimental procedures and method of analysis. Materials and Structures MatOriaux et Constructions 19- N ~ 113
Carpenter NJ, Taylor JR, Katona MG (1991) Lagrange constraints for transient finite element surface contact. Int J Numer Methods Eng 32: 103–128
Comite Euro-International Du Beton (CEB) (1988) Concrete structures under impact and impulsive loading. Syntesis report, Bulletin D’Information N0 187
Crisfield MA (1991) Non-linear finite element analysis of solid and structures vol I. Wiley, NY
Curbach M. (1987) Festigkeitssteigerung von Beton bei hohen Belastungs-geschwindigkeiten. PhD. Thesis, Karlsruhe University, Germany
Dilger WH, Koch R, Kowalczyk R (1978) Ductility of plained and confined concrete under different strain rates. American Concrete Institute, Special publication, Detroit, Michigen
Freund LB (1972a) Crack propagation in an elastic solid subjected to general loading-I constant rate of extension. J Mech Phys Solids 20: 129–140
Freund LB (1972b) Crack propagation in an elastic solid subjected to general loading-II non-uniform rate of extension. J Mech Phys Solids 20: 141–152
Hutter M, Fuhrmann A (2007) Optimized continuous collision detection for deformable triangle meshes, research grant KF0157401SS5 in the PRO INNO II program, Germany
Krausz AS, Krausz K (1988) Fracture kinetics of crack growth. Kluwer, Dordrecht
Ožbolt J, Bažant ZP (1996) Numerical smeared fracture analysis: nonlocal microcrack interaction approach. Int J Numer Methods Eng 39: 635–661
Ožbolt J, Reinhardt HW (2001) Three-dimensional finite element model for creep-cracking interaction of concrete. In: Ulm, Bažant, Wittmann (eds) Proceedings of the sixth international conference CONCREEP-6, pp 221–228
Ožbolt J, Li Y, Kožar I (2001) Microplane model for concrete with relaxed kinematic constraint. Int J Solid Struct 38: 2683–2711
Ožbolt J, Reinhardt HW (2005a) Dehnungsgeschwindigkeitsabhängiger Bruch eines Kragträgers aus Beton. Bauingenieur Springer VDI Band 80: 283–290
Ožbolt J, Reinhardt HW (2005b) Rate dependent fracture of notched plain concrete beams. In: Pijaudier-Cabot, Gerard, Acker (eds) Proceedings of the 7th international conference CONCREEP-7, pp 57–62
Ožbolt J, Rah KK, Mestrović D (2006) Influence of loading rate on concrete cone failure. Int J Fract 139: 239–252
Reinhardt HW (1982) Concrete under impact loading tensile strength and bond. Heron 27: 3
Saatci S, Vecchio JV (2009) Effect of shear mechanisms on impact behavior of reinforced concrete beams. ACI Struct J 106(1): 78–86
Sukontasukkul P, Mindess S (2003) The shear fracture of concrete under impact loading using end confined beams. Mater Struct (Matdriaux et Constructions) 36: 372–378
Weerheijm J (1992) Concrete under impact tensile loading and lateral compression. Dissertation, TU Delft
Wriggers P (2002) Computational Contact Mechanics, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ
Zienkiewicz OC, Taylor RL, Zhu JZ (2005) The finite element method—its basis and fundamentals, 6th edn. Elsevier Butterworth-Heinemann, Massachusetts
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Travaš, V., Ožbolt, J. & Kožar, I. Failure of plain concrete beam at impact load: 3D finite element analysis. Int J Fract 160, 31–41 (2009). https://doi.org/10.1007/s10704-009-9400-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-009-9400-1