Finite Element Analysis of Concrete Beam under Flexural Stresses Using Meso-Scale Model

Alaa H. Al-Zuhairi, Ali Ihsan Taj


Two dimensional meso-scale concrete modeling was used in finite element analysis of plain concrete beam subjected to bending. The plane stress 4-noded quadrilateral elements were utilized to model coarse aggregate, cement mortar. The effect of aggregate fraction distribution, and pores percent of the total area – resulting from air voids entrapped in concrete during placement on the behavior of plain concrete beam in flexural was detected. Aggregate size fractions were randomly distributed across the profile area of the beam. Extended Finite Element Method (XFEM) was employed to treat the discontinuities problems result from double phases of concrete and cracking that faced during the finite element analysis of concrete beam. Cracking was initiated at a small notch located at the middle of the bottom face of the concrete beam. The response of plain concrete beam subjected to pure bending via two point load application was detected using (XFEM) analysis of meso-scale concrete model. Assuming full bond between aggregate particles, and mortar at interfacial zone, the flexural strength of plain concrete beam is increased when aggregate particles size is increased, so that bending and shear stress were affected by void percentage and aggregate particles distribution. The maximum deflection at midspan was increased when the aggregate particles size decreases.


Meso-Scale Modeling; Extended Finite Element; Fracture Mechanics; Concrete Flexural Strength.


Grassl, Peter, David Grégoire, Laura Rojas Solano, and Gilles Pijaudier-Cabot. “Meso-Scale Modelling of the Size Effect on the Fracture Process Zone of Concrete.” International Journal of Solids and Structures 49, no. 13 (June 2012): 1818–1827. doi:10.1016/j.ijsolstr.2012.03.023.

Ren, W. Y., Z. J. Yang, and Phil Withers. "Meso-scale fracture modelling of concrete based on X-ray computed tomography images." In The 5th Asia-Pacific congress on computational mechanics (APCOM). Singapore. 2013.

Lu, Yong, and Zhenguo Tu. “Mesoscale Modelling of Concrete for Static and Dynamic Response Analysis -Part 2: Numerical Investigations.” Structural Engineering and Mechanics 37, no. 2 (January 25, 2011): 215–231. doi:10.12989/sem.2011.37.2.215.

Wang, Xiaofeng, Zhenjun Yang, and Andrey P. Jivkov. "Monte Carlo simulations of mesoscale fracture of concrete with random aggregates and pores: a size effect study." Construction and Building Materials 80 (2015): 262-272.

Wang, Xiaofeng, Mingzhong Zhang, and Andrey P. Jivkov. “Computational Technology for Analysis of 3D Meso-Structure Effects on Damage and Failure of Concrete.” International Journal of Solids and Structures 80 (February 2016): 310–333. doi:10.1016/j.ijsolstr.2015.11.018.

Mostafavi, M., N. Baimpas, E. Tarleton, R. C. Atwood, S. A. McDonald, A. M. Korsunsky, and T. J. Marrow. "Three-dimensional crack observation, quantification and simulation in a quasi-brittle material." Acta Materialia 61, no. 16 (2013): 6276-6289.

Jivkov AP, Engelberg DL, Stein R, Petkovski M. Pore space and brittle damage evolution in concrete. Eng Fract Mech 2013;110:378–95.

Yang, Z.J., X.T. Su, J.F. Chen, and G.H. Liu. “Monte Carlo Simulation of Complex Cohesive Fracture in Random Heterogeneous Quasi-Brittle Materials.” International Journal of Solids and Structures 46, no. 17 (August 2009): 3222–3234. doi:10.1016/j.ijsolstr.2009.04.013.

Leite, J.P.B., V. Slowik, and H. Mihashi. “Computer Simulation of Fracture Processes of Concrete Using Mesolevel Models of Lattice Structures.” Cement and Concrete Research 34, no. 6 (June 2004): 1025–1033. doi:10.1016/j.cemconres.2003.11.011.

Schlangen, E., and E.J. Garboczi. “Fracture Simulations of Concrete Using Lattice Models: Computational Aspects.” Engineering Fracture Mechanics 57, no. 2–3 (May 1997): 319–332. doi:10.1016/s0013-7944(97)00010-6.

Oliver, J. “A Consistent Characteristic Length for Smeared Cracking Models.” International Journal for Numerical Methods in Engineering 28, no. 2 (February 1989): 461–474. doi:10.1002/nme.1620280214.

Rots, Jan Gerrit. "Computational modeling of concrete fracture." PhD diss., Technische Hogeschool Delft, 1988.

Bažant, Zdeněk P., and B. H. Oh. “Crack Band Theory for Fracture of Concrete.” Matériaux et Constructions 16, no. 3 (May 1983): 155–177. doi:10.1007/bf02486267.

Melenk, J.M., and I. Babuška. “The Partition of Unity Finite Element Method: Basic Theory and Applications.” Computer Methods in Applied Mechanics and Engineering 139, no. 1–4 (December 1996): 289–314. doi:10.1016/s0045-7825(96)01087-0.

Rabczuk, T., and T. Belytschko. “Cracking Particles: a Simplified Meshfree Method for Arbitrary Evolving Cracks.” International Journal for Numerical Methods in Engineering 61, no. 13 (2004): 2316–2343. doi:10.1002/nme.1151.

Unger, Jörg F., Stefan Eckardt, and Carsten Könke. "Modelling of cohesive crack growth in concrete structures with the extended finite element method." Computer Methods in Applied Mechanics and Engineering 196, no. 41-44 (2007): 4087-4100.

Monteiro, A.B., A.R.V. Wolenski, F.B. Barros, R.L.S. Pitangueira, and S.S. Penna. “A Computational Framework for G/XFEM Material Nonlinear Analysis.” Advances in Engineering Software 114 (December 2017): 380–393. doi:10.1016/j.advengsoft.2017.08.002.

Huang, Yucheng, Yanhua Guan, Linbing Wang, Jian Zhou, Zhi Ge, and Yue Hou. “Characterization of Mortar Fracture Based on Three Point Bending Test and XFEM.” International Journal of Pavement Research and Technology (September 2017). doi:10.1016/j.ijprt.2017.09.005.

Du, Xiuli, Liu Jin, and Guowei Ma. “Numerical Modeling Tensile Failure Behavior of Concrete at Mesoscale Using Extended Finite Element Method.” International Journal of Damage Mechanics 23, no. 7 (December 11, 2013): 872–898. doi:10.1177/1056789513516028.

López, Carlos M., Ignacio Carol, and Antonio Aguado. “Meso-Structural Study of Concrete Fracture Using Interface Elements. I: Numerical Model and Tensile Behavior.” Materials and Structures 41, no. 3 (November 6, 2007): 583–599. doi:10.1617/s11527-007-9314-1.

ACI 318-95 (1995), “Building Code Requirements for Structural Concrete”, American Concrete Institution, United State.

Callister Jr, William D. “Materials Science and Engineering - An Introduction (5th Ed.).” Anti-Corrosion Methods and Materials 47, no. 1 (February 2000). doi:10.1108/acmm.2000.12847aae.001.

Bazant, Z. P. (Ed.). (1992). Fracture Mechanics of Concrete Structures: Proceedings of the First International Conference on Fracture Mechanics of Concrete Structures (FraMCoS1), held at Beaver Run Resort, Breckenridge, Colorado, USA, 1-5 June 1992 (Vol. 1). CRC Press.

ASTM C33 / C33M-16, Standard Specification for Concrete Aggregates, ASTM International, West Conshohocken, PA, 2016,, doi: 10.1520/C0033_C0033M-16.

Shahbazi, Siamak, and Iraj Rasoolan. “Meso-Scale Finite Element Modeling of Non-Homogeneous Three-Phase Concrete.” Case Studies in Construction Materials 6 (June 2017): 29–42. doi:10.1016/j.cscm.2016.10.002.

Khoei A. R. “Extended Finite Element Method Theory and Application” (December 18, 2014), doi: 10.1002/9781118869673.

Asferg, J.L., Poulsen, P. N. and Nielsen, L. O., “A direct XFEM formulation for modeling of cohesive crack growth in concrete”, Computer and Concrete 4(2), (April 25 2007): 83-100. doi: 10.12989/cac.2007.4.2.083.

Osher, Stanley, and James A Sethian. “Fronts Propagating with Curvature-Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations.” Journal of Computational Physics 79, no. 1 (November 1988): 12–49. doi:10.1016/0021-9991(88)90002-2.

Sukumar, N., D.L. Chopp, N. Moës, and T. Belytschko. “Modeling Holes and Inclusions by Level Sets in the Extended Finite-Element Method.” Computer Methods in Applied Mechanics and Engineering 190, no. 46–47 (September 2001): 6183–6200. doi:10.1016/s0045-7825(01)00215-8.

Erdogan, F., and G. C. Sih. “On the Crack Extension in Plates under Plane Loading and Transverse Shear.” Journal of Basic Engineering 85, no. 4 (1963): 519. doi:10.1115/1.3656897.

Full Text: PDF

DOI: 10.28991/cej-0309173


Copyright (c) 2018 Alaa H. Al-Zuhairi, Ali Ihsan Taj

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.