Numerical simulation and shear strength research of reinforced concrete beam based on peridynamics

Abstract

To explore the applicability of three-dimensional (3D) peridynamics (PD) in complex stress, 36 reinforced concrete (RC) beams without web reinforcement were designed and tested, and investigated the effects of shear span ratio, longitudinal reinforcement, and flange width on the shear strength of beams. A 3D discretization model of all specimens in the test was established, and the specimens were simulated using the PD method. To consider the heterogeneity of concrete, a non-homogeneous PD model considering aggregate size was established, and the simulation results were compared with the original model. The results indicate that the shear span ratio, longitudinal reinforcement, and flange width have a significant impact on the shear strength of RC beams without web reinforcement. The 3D PD model has a good applicability for RC beams under complex stress. Without considering computational costs, heterogeneous models can obtain more accurate results than homogeneous models and better reflect the process of concrete beam failure.

Graphical abstract

Keywords

peridynamics / numerical simulation / heterogeneous model / shear strength / flange width

References

[1] Fayyad T M, Lees J M. Experimental investigation of crack propagation and crack branching in lightly reinforced concrete beams using digital image correlation. Engineering Fracture Mechanics, 2017, 182: 487–505

[2] Filiagi PastoreM. Influence of loading arrangement on shear enhancement in reinforced concrete beams. Dissertation for the Doctoral Degree. London: Imperial College London, 2021

[3] Joint ASCE-ACI Task Committee 426 on Shear, Diagonal Tension of the Committee on Masonry, Reinforced Concrete of the Structural Division. The shear strength of reinforced concrete members. Journal of the Structural Division, 1973, 99(6): 1091–1187

[4] ASCE-ACI Committee 445 on Shear. Recent approaches to shear design of structural concrete. Journal of Structural Engineering, 1998, 124(12): 1375–1417

[5] Hawileh R A, Mhanna H H, Abdalla J A. Effect of flange geometry on the shear capacity of RC T-beams. Procedia Structural Integrity, 2022, 42: 1198–1205

[6] GB50010-2010. Code for Design of Concrete Structures. Beijing: Ministry of Housing and Urban-Rural Development of the People’s Republic of China, 2010

[7] Firouzi N, Alzaidi A S. Non-linear elastic beam deformations with four-parameter Timoshenko beam element considering through-the-thickness stretch parameter and reduced integration. Symmetry, 2024, 16(8): 984

[8] Živaljić N, NikolićŽ, Smoljanović H, Munjiza A. Numerical simulation of reinforced concrete structures under impact loading. Materials Science and Engineering Technology, 2019, 50(5): 599–610

[9] Jiang P, Zheng H, Xiong J, Wen P. Nonlinear elastic–plastic analysis of reinforced concrete column-steel beam connection by RBF-FD method. Engineering Analysis with Boundary Elements, 2021, 128: 188–194

[10] Kozlowski M, Kadela M, Gwozdz-Lason M. Numerical fracture analysis of foamed concrete beam using XFEM method. Applied Mechanics and Materials, 2016, 837: 183–186

[11] Bouziadi F, Haddi A, Tahenni T, Boulekbache B, Hamrat M, Naser M Z, Amziane S. Development of a local bond shear stress-slip model of RC beams externally strengthened with FRP materials. Journal of Composite Materials, 2023, 57(14): 2261–2285

[12] Mokhatar S N, Sonoda Y, Kueh A B H, Jaini Z M. Quantitative impact response analysis of reinforced concrete beam using the Smoothed Particle Hydrodynamics (SPH) method. Structural Engineering and Mechanics, 2015, 56(6): 917–938

[13] Wang Y T, Zhou X P, Kou M M. Three-dimensional numerical study on the failure characteristics of intermittent fissures under compressive-shear loads. Acta Geotechnica, 2019, 14(4): 1161–1193

[14] Silling S A. Reformulation of elasticity theory for discontinuities and long-range forces. Journal of the Mechanics and Physics of Solids, 2000, 48(1): 175–209

[15] Silling S A, Askari E. A meshfree method based on the peridynamic model of solid mechanics. Computers & Structures, 2005, 83(17–18): 1526–1535

[16] Silling S A, Epton M, Weckner O, Xu J, Askari E. Peridynamic states and constitutive modeling. Journal of Elasticity, 2007, 88(2): 151–184

[17] Wu L, Huang D. Peridynamic modeling and simulations on concrete dynamic failure and penetration subjected to impact loadings. Engineering Fracture Mechanics, 2022, 259: 108135

[18] Shi C, Shi Q, Tong Q, Li S. Peridynamics modeling and simulation of meso-scale fracture in recycled coarse aggregate (RCA) concretes. Theoretical and Applied Fracture Mechanics, 2021, 114: 102949

[19] Torrence C E, Trageser J E, Jones R E, Rimsza J M. Sensitivity of the strength and toughness of concrete to the properties of the interfacial transition zone. Construction & Building Materials, 2022, 336: 126875

[20] Ren H, Zhuang X, Rabczuk T. Dual-horizon peridynamics: A stable solution to varying horizons. Computational Methods in Applied Mathematics, 2017, 318: 762–782

[21] Ren H, Zhuang X, Cai Y, Rabczuk T. Dual-horizon peridynamics. International Journal for Numerical Methods in Engineering, 2016, 108(12): 1451–1476

[22] Rabczuk T, Ren H, Zhuang X. A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. Computers, Materials & Continua, 2019, 59(1): 31–55

[23] Ren H, Zhuang X, Rabczuk T. A nonlocal operator method for solving partial differential equations. Computational Methods in Applied Mathematics, 2020, 358: 112621

[24] Friedrich L F, Iturrioz I, Colpo A B, Vantadori S. Fracture failure of quasi-brittle materials by a novel peridynamic model. Composite Structures, 2023, 323: 117402

[25] Liu Y, Li W, Guan J, Zhou X, Guo L. Fully coupled peridynamic model for analyzing the chemo-diffusion-mechanical behavior of sulfate attack in concrete. Construction & Building Materials, 2023, 409: 133874

[26] Lu D, Song Z, Wang G, Zhou X, Du X. A developed 3D peridynamic method incorporating non-conservative force for brittle materials. Engineering Fracture Mechanics, 2022, 274: 108772

[27] Liu Z, Cheng A, Wang H. An hp-Galerkin method with fast solution for linear peridynamic models in one dimension. Computers & Mathematics with Applications, 2017, 73(7): 1546–1565

[28] Hermann A, Shojaei A, Steglich D, Höche D, Zeller-Plumhoff B, Cyron C J. Combining peridynamic and finite element simulations to capture the corrosion of degradable bone implants and to predict their residual strength. International Journal of Mechanical Sciences, 2022, 220: 107143

[29] Mossaiby F, Sheikhbahaei P, Shojaei A. Multi-adaptive coupling of finite element meshes with peridynamic grids: robust implementation and potential applications. Engineering with Computers, 2023, 39(4): 2807–2828

[30] Wu P, Zhao J, Chen Z, Bobaru F. Validation of a stochastically homogenized peridynamic model for quasi-static fracture in concrete. Engineering Fracture Mechanics, 2020, 237: 107293

[31] Yaghoobi A, Chorzepa M G, Kim S S, A S. Mesoscale fracture analysis of multiphase cementitious composites using peridynamics. Materials, 2017, 10(2): 162

[32] Li W, Guo L. Meso-fracture simulation of cracking process in concrete incorporating three-phase characteristics by peridynamic method. Construction & Building Materials, 2018, 161: 665–675

[33] Wu P, Liu Y, Peng X, Chen Z. Peridynamic modeling of freeze-thaw damage in concrete structures. Mechanics of Advanced Materials and Structures, 2023, 30(14): 2826–2837

[34] MadenciEOterkus E. Peridynamic Theory and Its Applications. New York: Springer New York, 2013, 19–43

[35] Gerstle W, Sau N, Silling S. Peridynamic modeling of concrete structures. Nuclear Engineering and Design, 2007, 237(12–13): 1250–1258

[36] SillingS A. Introduction to Peridynamics. Handbook of Peridynamic Modeling. Florida: Chapman and Hall/CRC, 2016, 63–98

[37] Sheikhbahaei P, Mossaiby F, Shojaei A. An efficient peridynamic framework based on the arc-length method for fracture modeling of brittle and quasi-brittle problems with snapping instabilities. Computers & Mathematics with Applications, 2023, 136: 165–190

[38] Sfer D, Carol I, Gettu R, Etse G. Study of the behavior of concrete under triaxial compression. Journal of Engineering Mechanics, 2002, 128(2): 156–163

[39] Jin Y, Li L, Jia Y, Shao J, Rougelot T, Burlion N. Numerical study of shrinkage and heating induced cracking in concrete materials and influence of inclusion stiffness with peridynamics method. Computers and Geotechnics, 2021, 133: 103998

[40] Hobbs M, Hattori G, Orr J. Predicting shear failure in reinforced concrete members using a three-dimensional peridynamic framework. Computers & Structures, 2022, 258: 106682

[41] Li G, Zhao Y, Pang S S, Li Y. Effective Young’s modulus estimation of concrete. Cement and Concrete Research, 1999, 29(9): 1455–1462

[42] Zhang N L, Guo X M, Zhu B B, Guo L. A mesoscale model based on Monte-Carlo method for concrete fracture behavior study. Science China Technological Sciences, 2012, 55(12): 3278–3284

RIGHTS & PERMISSIONS

Higher Education Press