Abstract
The difficulties in dealing with steel skeleton frames and low computational efficiency are the major obstacles for applying peridynamics (PD) to model reinforced concrete (RC) structures. This paper proposes a new reinforced concrete model, named PDROD, in which the concrete is modeled by PD theory and the reinforcement is modeled by rod elements. A bonding formulation is derived to characterize the interaction between the concrete and reinforcements, guaranteeing the consistence of load transfer between the two mediums. Thanks to the new bonding model, the discretization of the concrete and reinforcements does not necessarily need to be coincident, facilitating the application of PDROD in modeling RC structures whose skeleton frames are with complex geometries. The PDROD model not only gives full play to the advantages of PD theory in damage problems without additional failure criteria and stiffness degradation model, but also significantly increases the numerical efficiency of computation, which extends the applicability of PD to modeling real-scale RC structures. The accuracy and efficiency of the PDROD model are demonstrated by simulating a series of examples of concrete plates with reinforcing bars. Good agreements have been observed between the results from PDROD and the classical FEM predictions. The challenging benchmarks on the Stuttgart Shear Tests were also simulated to demonstrate the capability of the PDROD model in quasi-brittle fracture problems of large-scale RC structures.
































Similar content being viewed by others
References
Wu J-Y (2018) A geometrically regularized gradient-damage model with energetic equivalence. Comput Methods Appl Mech Engrg 328:612–637
Kuhl E, Ramm E, de Borst R (2000) An anisotropic gradient damage model for quasi-brittle materials. Comput Methods Appl Mech Engrg 183(1–2):87–103
Bažant ZP, Oh BH (1983) Crack band theory for fracture of concrete. Mat Constr 16(3):155–177
Wu J-Y, Li F-B (2015) An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks. Comput Methods Appl Mech Eng 295:77–107
Song J-H, Areias P, Belytschko T (2006) A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Methods Eng 67:868–893
Chau-Dinh T, Zi G, Lee P-S, Rabczuk T, Song J-H (2012) Phantom-node method for shell models with arbitrary cracks. Comput Struct 9293:242–246
Wang Y, Waisman H, Harari I (2017) Direct evaluation of stress intensity factors for curved cracks using Irwin’s integral and XFEM with high-order enrichment functions. Int J Numer Methods Eng 112(7):629–654
Geers M, Borst RD, Peerlings R (2000) Damage and crack modeling in single-edge and double-edge notched concrete beams. Eng Fract Mech 65:247–261
Saloustros S, Pel L, Cervera M, Roca P (2017) Finite element modelling of internal and multiple localized cracks. Comput Mech 59:299–316
Zhou S, Rabczuk T, Zhuang X (2018) Phase field modeling of quasi-static and dynamic crack propagation: comsol implementation and case studies. Adv Eng Software 122:31–49
Zhang Y, Zhuang X (2019) Cracking elements method for dynamic brittle fracture. Theor Appl Fract Mec 102:1–9
Zhang Y, Mang HA (2020) Global cracking elements: a novel tool for Galerkin-based approaches simulating quasi-brittle fracture. Int J Numer Methods Eng 121:2462–2480
Zhang Y, Lackner R, Zeiml M, Mang HA (2015) Strong discontinuity embedded approach with standard SOS formulation: element formulation, energy-based crack-tracking strategy, and validations. Comput Methods Appl Mech Engrg 287:335–366
Zhang Y, Huang J, Yuan Y, Mang HA (2021) Cracking elements method with a dissipation-based arc-length approach. Finite Elem Anal Des 195:103573
Rabczuk T, Zi G, Bordas S, Nguyen-Xuan H (2010) A simple and robust three-dimensional cracking-particle method without enrichment. Comput Methods Appl Mech Engrg 199:2437–2455
Fédération Internationale du Béton (fib) (2008) Practitioners’ guide to fnite element modelling of reinforced concrete structures
Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209
Silling SA, Lehoucq RB (2010) Peridynamic theory of solid mechanics. Adv Appl Mech 44:73–168
Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 3:1526–1535
Hu W, Wang Y, Yu J et al (2013) Impact damage on a thin glass plate with a thin polycarbonate backing. Int J Impact Eng 62:152–165
Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fracture 162(1):229–244
Madenci E, Oterkus E (2014) Peridynamic Theory and Its Applications. Springer, New York
Bobaru F et al (2016) Handbook of peridynamic modeling. Crc Press
Yang D, Dong W, Liu X et al (2018) Investigation on mode-I crack propagation in concrete using bond-based peridynamics with a new damage model. Eng Fract Mech 199:567–581
Zhang N, Gu Q, Huang S et al (2021) A practical bond-based peridynamic modeling of reinforced concrete structures. Eng Struct 244:112748
Gu X, Zhang Q (2020) A modified conjugated bond-based peridynamic analysis for impact failure of concrete gravity dam. Meccanica 55:547–566
Chen W, Gu X, Zhang Q, Xia X (2021) A refined thermo-mechanical fully coupled peridynamics with application to concrete cracking. Eng Fract Mech 242:107463
Li W, Guo L (2019) Dual-horizon peridynamics analysis of debonding failure in FRP-to-concrete bonded joints. Int J Concr Struct Mater 13(1):26
Huang D, Zhang Q, Qiao P (2011) Damage and progressive failure of concrete structures using non-local peridynamic modeling. Sci China Techn Sci 54(003):591–596
Wu L, Huang D, Xu Y, Wang L (2019) A non-ordinary state-based peridynamic formulation for failure of concrete subjected to impacting loads. Comput Model Eng Sci 118(3):561–581
Lu J, Zhang Y, Muhammad H, Chen Z et al (2019) 3D analysis of anchor bolt pullout in concrete materials using the non-ordinary state-based peridynamics. Eng Fract Mech 207:68–85
Lu J, Zhang Y, Muhammad H et al (2018) Peridynamic model for the numerical simulation of anchor bolt pullout in concrete. Math Probl Eng 3:1–10
Huang X, Kong X, Chen Z, Fang Q (2021) Peridynamics modelling of dynamic tensile failure in concrete. Int J Impact Eng 155:103918
Shi C, Shi Q, Tong Q, Li S (2021) Peridynamics modeling and simulation of meso-scale fracture in recycled coarse aggregate (RCA) concretes. Theor Appl Fract Mec 114:102949
Jin Y, Li L, Jia Y et al (2021) Numerical study of shrinkage and heating induced cracking in concrete materials and influence of inclusion stiffness with Peridynamics method. Comput Geotech 133:103998
Zhao J, Chen Z, Mehrmashhadi J, Bobaru F (2020) A stochastic multiscale peridynamic model for corrosion-induced fracture in reinforced concrete. Eng Fract Mech 229:106969
Wu P, Zhao J, Chen Z, Bobaru F (2020) Validation of a stochastically homogenized peridynamic model for quasi-static fracture in concrete. Eng Fract Mech 237:107293
Zhao J, Jafarzadeh S, Rahmani M et al (2021) A peridynamic model for galvanic corrosion and fracture. Electrochim Acta 391:138968
Gerstle W, Sau N, Silling S (2007) Peridynamic modeling of concrete structures. Nucl Eng Des 237:1250–1258
Gerstle W, Sakhavand N, Chapman S (2010) Peridynamic and continuum models of reinforced concrete lap splice compared, in: Proceedings of the 7th International Conference on Fracture Mechanics of Concrete and Concrete Structures, FraMCoS-7, Jeju, South Korea, ISBN 978-89-5708-180-8.
Chen X, Yong Y, Zhang Y, Yuan X (2021) Peridynamic modeling of prefabricated beams post-cast with steelfiber reinforced high-strength concrete. Struct Concr 22:445–456.
Xia Y, Fan C, Shen F, Qian W (2021) Peridynamic simulation of failure process of reinforced concrete structures. Chin J Appl Mech 38(1):143–149
Sau N, Mendoza JM, Almada AB (2019) Peridynamic modelling of reinforced concrete structures. Eng Fail Anal 103:266–274
Yaghoobi A, Chorzepa MG (2017) Fracture analysis of fiber reinforced concrete structures in the micropolar peridynamic analysis framework. Eng Fract Mech 169:238–250
Shi H, Qian S, Xu T et al (2016) Study on reinforced concrete structure failure based on peridynamic theories. Guizhou Science 34(6):64–68
Hattori G, Hobbs M, Orr J (2021) A review on the developments of peridynamics for reinforced concrete structures. Arch Comput Method Eng 28:4655–4686
Macek RW, Silling SA (2007) Peridynamics via finite element analysis. Finite Elem Anal Des 43(15):1169–1178
Kilic B, Madenci E (2010) An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory. Theor Appl Fract Mec 53(3):194–204
Leonhardt F, Walther R (1964) The Stuttgart Shear Tests, 1961: Contributions to the treatment of the problems of shear in reinforced concrete construction. A translation of articles that appeared in Beton- und Stahlbetonbau. 56 (12) (1961) and 57 (2, 3, 6, 7, 8) (1962), Cement and Concrete Association, London
Hobbs M, Hattori G, Orr J (2022) Predicting shear failure in reinforced concrete members using a three-dimensional peridynamic framework. Comput Struct 258:106682
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Yang, X., Li, F., Gao, W. et al. A PDROD model of reinforced concrete based on peridynamics and rod elements. Engineering with Computers 39, 3629–3650 (2023). https://doi.org/10.1007/s00366-022-01774-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-022-01774-8