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This study presents an approach to finite element (FE) modelling in Abaqus FEA for analysis of the nonlinear bending behavior of ultra-high-performance fiber-reinforced concrete (UHPC) beams. The Concrete Damaged Plasticity (CDP) model was utilized to capture UHPC’s distinctive mechanical properties, including high tensile strength, nearly linear compressive behavior up to peak stress, and unique failure modes of UHPC beams compared to normal strength reinforced concrete beams. Experimentally validated constitutive laws available in literature for plain and fiber-reinforced UHPC under compression and tension were incorporated, with tensile behavior calibrated through inverse modeling based on average strains in the tensile zone of beams. Other CDP parameters, such as eccentricity, viscosity, and dilation angle, were established based on prior research on standard UHPC specimens and simulations of beams. Three-dimensional FE models of UHPC beams, featuring fiber volume fractions 1–2 % and longitudinal reinforcement ratios 0.31–5.13 %, were developed and validated against experimental data from the authors and other researchers. The model accurately predicts load-deflection curves, moment capacities, cross-sectional strains, cracking pattern, and localization of cracks at all loading stages. This FE modeling approach provides a reliable tool for design of UHPC beams, enhancing the structural performance of critical infrastructure, including bridges, viaducts, and marine structures, under complex loading conditions.
1 Tamov M.M., Salib M.I.F., Abuizeih Y.Q.Y, Sofianikov O.D. Mix design and investigation of strength characteristics of self-compacting ultra-high-performance steel fiber reinforced concrete. News of higher educational institutions. Construction. 2022. 4. P. 25 – 39. DOI: 10.32683/0536-1052-2022-760-4-25-39
2 Yerofeyev V.T., Tarakanov O.V., Makridin N.I. Powder-activated high-strength and ultra-high strength fiber and textile concretes of a new generation with improved strength indicators. Building materials and products. 2024. 2. P. 13 – 21. DOI: 10.54734/20722958_2024_2_13
3 Jabbar A.M., Hamood M.J., Mohammed D.H. Structural Behavior of Ultra-High-Performance Concrete Beams Under Flexural and Shear Action: A Review. Engineering and Technology Journal. 2022. 40. P. 743 – 758. DOI: 10.30684/etj.2021.131102.1003
4 Pyo S., El-Tawil S. Capturing the strain hardening and softening responses of cementitious composites subjected to impact loading. Construction and Building Materials. 2015. 81 (15). P. 276 – 283.
5 Hung C.C., El-Tawil S., Chao S.H. A Review of Developments and Challenges for UHPC in Structural Engineering: Behavior, Analysis, and Design. Journal of Structural Engineering. 2021. 147 (9). P. 1 – 19. DOI: 10.1061/(ASCE)ST.1943-541X.0003073
6 Helou R., Graybeal B. Flexural Behavior and Design of Ultrahigh-Performance Concrete Beams. Journal of Structural Engineering. 2022. 148. DOI: 10.1061/(ASCE)ST.1943-541X.0003246
7 Kodsy A., Morcous G. Flexural strength prediction models of non-prestressed Ultra-High Performance Concrete (UHPC) components. Structures. 2021. 34 (19). P. 4532 – 4547. DOI: 10.1016/j.istruc.2021.10.047
8 Shafieifar M., Farzad M., Azizinamini A. A comparison of existing analytical methods to predict the flexural capacity of Ultra High Performance Concrete (UHPC) beams. Construction and Building Materials. 2018. 2 (1). P. 10 – 18. DOI:10.1016/j.conbuildmat.2018.03.229
9 Chen S., Zhang R., Jia L.J., Wang J. Y. Flexural behaviour of rebar-reinforced ultra-high-performance concrete beams. Magazine of Concrete Research. 2017. 70 (19). P. 997 – 1015. DOI: 10.1680/jmacr.17.00283
10 Yang I. H., Joh C., Kim B.S. Structural behavior of ultra high performance concrete beams subjected to bending. Engineering Structures. 2010. 32 (11). P. 3478 – 3487. DOI: 10.1016/j.engstruct.2010.07.017
11 Hasgul U., Turker K., Birol T., Yavas A. Flexural behavior of ultra-high-performance fiber reinforced concrete beams with low and high reinforcement ratios. Structural Concrete. 2018. 19 (7). P. 1577 – 1590. DOI: 10.1002/suco.201700089
12 Zhang Y., Zhu Y., Qiu J., Hou C., Huang J. Impact of reinforcing ratio and fiber volume on flexural hardening behavior of steel reinforced UHPC beams. Engineering Structures. 2023. 285 (2). P. 116067. DOI: 10.1016/j.engstruct.2023.116067
13 Rimshin V.I., Suleymanova L.A., Amelin P.A., Anoprienko D.S. Finite element modeling of the work of bent reinforced concrete products operating in a chloride-aggressive environment. Structural Mechanics and Structures. 2025. 1 (44). P. 40 – 51. DOI: 10.36622/2219-1038.2025.44.1.004
14 Rimshin V.I., Amelin P.A. Numerical calculation of bent reinforced concrete elements of rectangular cross section in the Abaqus software environment. Structural mechanics of engineering constructions and buildings. 2022. 18 (6). P. 552 – 563.
15 Shalobyta N.N., Polonskiy M.Ch. Features of constructing an analytical model and numerical study of the redistribution of forces in reinforced concrete beams with hybrid reinforcement. International scientific and technical conference « Theory and practice of research and design in construction using computer-aided design (CAD) systems». 2017. Brest.
16 Chen L., Graybeal B.A. Modeling Structural Performance of Ultra high Performance Concrete I-Girders. Journal of Bridge Engineering. 2012. 17 (5). P. 754 – 764. DOI: 10.1061/(ASCE)BE.1943-5592.0000305
17 Singh M., Sheikh A.H., Ali M., Visintin P., Griffith M.C. Experimental and numerical study of the flexural behaviour of ultra-high performance fibre reinforced concrete beams. Construction and Building Materials. 2017. 138. P. 12 – 25. DOI: 10.1016/j.conbuildmat.2017.02.002
18 Solhmirzaei R., Kodur V.R. A numerical model for tracing structural response of ultra-high performance concrete beams. Modelling. 2021. 2 (4). P. 448 – 466. DOI: 10.3390/modelling2040024
19 Zhu Y., Zhang Y., Hussein H. H., Chen G. Numerical modeling for damaged reinforced concrete slab strengthened by ultra-high performance concrete (UHPC) layer. Engineering Structures. 2019. 209. DOI: 10.1016/j.engstruct.2019.110031
20 Concrete damaged plasticity. ABAQUS Analysis User's Manual URL:https:// classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/default.htm?startat=pt05ch18s05abm36.html (date access: 11.07.24)
21 Fehling E., Schmidt M., Walraven J., Leutbecher T., Fröhlich S. Ultra-High Performance Concrete UHPC: Fundamentals, Design, Examples. 2014. Berlin: Wilhelm Ernst & Sohn. DOI: 10.1002/9783433604076
22 Fakeh M., Jawdhari A., Fam A. Calibration of ABAQUS Concrete Damage Plasticity (CDP) Model for UHPC Material. Third International Interactive Symposium on Ultra-High Performance Concrete. 2023. DOI: 10.21838/uhpc.16675
23 Ji-zhi Z., Gong-feng X., Mu-xuan N., Wen-tao C. Mechanical Properties and Constitutive Model of Ultra-High Performance Concrete Material Under Uniaxial Tension and Compression Cycles. Engineering Mechanics. 2024. 41 (4). P. 81 – 93.
24 Wang Z., Wang J., Liu N., Zhang F. Modeling Seismic Performance of High-Strength Steel–Ultra-High-Performance Concrete Piers with Modified Kent-Park Model Using Fiber Elements. Advances in Mechanical Engineering. 2016. 8. DOI: 10.1177/1687814016633411
25 Yan G. Experimental Study on Strength and Deformation of Reactive Powder Concrete Under Triaxial Compression. Yantai, People’s Republic of China, CI-Premier Pte Ltd. 2010. P. 383 – 386.
26 Graybeal B. Compressive Behavior of Ultra-High-Performance Fiber-Reinforced Concrete. ACI Materials Journal. 2007. 104 (2). P. 146 – 152.
27 Prem P.R., Bharatkumar B.H., Murthy A.R. Influence of Curing Regime and Steel Fibres on the Mechanical Properties of UHPC. Magazine of Concrete Research. 2015. 67 (18). P. 1 –15. DOI: 10.1680/macr.14.00333
28 Zhang Y., Xin H., Correia J.A.F.O. Fracture evaluation of ultra-high-performance fiber reinforced concrete (UHPFRC). Engineering Failure Analysis. 2021. 120. P. 1 – 21. DOI: 10.1016/j.engfailanal.2020.105076
29 Rahdar H., Ghalehnovi M. Post-cracking behavior of UHPC on the concrete members reinforced by steel rebar. Computers and Concrete. 2016. 18 (1). P. 139 – 154. DOI: 10.12989/cac.2016.18.1.139
30 Haber Z.B. Varga I.D.I., Graybeal B.A. Properties and Behavior of UHPC-Class Materials. FHWA-HRT-18-036. 2018.
31 Kanakubo T. Tensile characteristics evaluation method for ductile fiber-reinforced cementitious composites. Journal of Advanced Concrete Technology. 2006. 4 (1). P. 3 – 17. DOI: 10.3151/jact.4.3
32 Shao Y., Billington S.L. Predicting the two predominant flexural failure paths of longitudinally reinforced high-performance fiber-reinforced cementitious composite structural members. Engineering Structures. 2019. 199. DOI: 10.1016/j.engstruct.2019.109581
33 Hoffman, N.S. Constitutive relationships of prestressed steel fiber concrete membrane elements. University of Houston. Texas. 2010. P. 232.
34 Jabbar A.M., Hamood M.J., Mohammed D.H. Impact of Dilation Angle and Viscosity on the Ultra-High Performance Concrete Behavior in Abaqus. 2010. DOI: 10.1109/ICASEA53739. 2021.9733087
35 Hashim D.T., Hejazi F., Voo Y.L. Simplified Constitutive and Damage Plasticity Models for UHPFRC with Different Types of Fiber. International Journal of Concrete Structures and Materials. 2020. 14 (1). P. 1 – 21.
36 Dao C.B., Viet C.M., Quanh V.N., Pham H. Investigation of the shear behavior of ultra-high performance concrete girder by simulation approach. IOP Conference Series Materials Science and Engineering. 2023. 1289 (1). DOI: 10.1088/1757-899X/1289/1/012029
37 Tamov M.M., Abuizeih Y. Q. Y. The Effect of the Longitudinal Reinforcement Ratio on the Behavior of Ultra-High Performance Fibre-Reinforced Concrete Beams. Scientific Works of the Kuban State Technological University. 2025. 2. P. 56 – 71. DOI: 10.26297/2312-9409.2025.2.6
38 Yang I.H., Park J., Bui T.Q., Kim K.C., Joh C., Lee H. An Experimental Study on the Ductility and Flexural Toughness of Ultrahigh-Performance Concrete Beams Subjected to Bending. Materials. 2020. 13 (10). P. 2225. DOI: 10.3390/ma13102225
39 Turker K., Hasgul U., Birol T., Yavas A., Yazici H. Hybrid fiber use on flexural behavior of ultra high performance fiber reinforced concrete beams. Composite Structures. 2019. 229 (6). P. 111400. DOI: 10.1016/j.compstruct.2019.111400
40 Yoo D.Y., Banthia N., Yoon Y.S. Experimental and numerical study on flexural behavior of ultra-high-performance fiber-reinforced concrete beams with low reinforcement ratios. Canadian Journal of Civil Engineering. 2017. 44 (1). P. 18 – 28. DOI: 10.1139/cjce-2015-0384
41 Graybeal B., Davis M. Cylinder or Cube: Strength Testing of 80 to 200 MPa (11.6 to 29 ksi) Ultra-High-Performance Fiber-Reinforced Concrete. Aci Materials Journal. 2008. 105. (6). P. 603-609. DOI: 10.14359/20202
42 Esfahani M.H., Hejazi F., Jaafar M.S.B., Karimzadeh K. Simplified Damage Plasticity Model for Concrete. Structural Engineering International. 2017. 27 (1). P. 68 – 78. DOI: 10.2749/101686616X1081
2 Yerofeyev V.T., Tarakanov O.V., Makridin N.I. Powder-activated high-strength and ultra-high strength fiber and textile concretes of a new generation with improved strength indicators. Building materials and products. 2024. 2. P. 13 – 21. DOI: 10.54734/20722958_2024_2_13
3 Jabbar A.M., Hamood M.J., Mohammed D.H. Structural Behavior of Ultra-High-Performance Concrete Beams Under Flexural and Shear Action: A Review. Engineering and Technology Journal. 2022. 40. P. 743 – 758. DOI: 10.30684/etj.2021.131102.1003
4 Pyo S., El-Tawil S. Capturing the strain hardening and softening responses of cementitious composites subjected to impact loading. Construction and Building Materials. 2015. 81 (15). P. 276 – 283.
5 Hung C.C., El-Tawil S., Chao S.H. A Review of Developments and Challenges for UHPC in Structural Engineering: Behavior, Analysis, and Design. Journal of Structural Engineering. 2021. 147 (9). P. 1 – 19. DOI: 10.1061/(ASCE)ST.1943-541X.0003073
6 Helou R., Graybeal B. Flexural Behavior and Design of Ultrahigh-Performance Concrete Beams. Journal of Structural Engineering. 2022. 148. DOI: 10.1061/(ASCE)ST.1943-541X.0003246
7 Kodsy A., Morcous G. Flexural strength prediction models of non-prestressed Ultra-High Performance Concrete (UHPC) components. Structures. 2021. 34 (19). P. 4532 – 4547. DOI: 10.1016/j.istruc.2021.10.047
8 Shafieifar M., Farzad M., Azizinamini A. A comparison of existing analytical methods to predict the flexural capacity of Ultra High Performance Concrete (UHPC) beams. Construction and Building Materials. 2018. 2 (1). P. 10 – 18. DOI:10.1016/j.conbuildmat.2018.03.229
9 Chen S., Zhang R., Jia L.J., Wang J. Y. Flexural behaviour of rebar-reinforced ultra-high-performance concrete beams. Magazine of Concrete Research. 2017. 70 (19). P. 997 – 1015. DOI: 10.1680/jmacr.17.00283
10 Yang I. H., Joh C., Kim B.S. Structural behavior of ultra high performance concrete beams subjected to bending. Engineering Structures. 2010. 32 (11). P. 3478 – 3487. DOI: 10.1016/j.engstruct.2010.07.017
11 Hasgul U., Turker K., Birol T., Yavas A. Flexural behavior of ultra-high-performance fiber reinforced concrete beams with low and high reinforcement ratios. Structural Concrete. 2018. 19 (7). P. 1577 – 1590. DOI: 10.1002/suco.201700089
12 Zhang Y., Zhu Y., Qiu J., Hou C., Huang J. Impact of reinforcing ratio and fiber volume on flexural hardening behavior of steel reinforced UHPC beams. Engineering Structures. 2023. 285 (2). P. 116067. DOI: 10.1016/j.engstruct.2023.116067
13 Rimshin V.I., Suleymanova L.A., Amelin P.A., Anoprienko D.S. Finite element modeling of the work of bent reinforced concrete products operating in a chloride-aggressive environment. Structural Mechanics and Structures. 2025. 1 (44). P. 40 – 51. DOI: 10.36622/2219-1038.2025.44.1.004
14 Rimshin V.I., Amelin P.A. Numerical calculation of bent reinforced concrete elements of rectangular cross section in the Abaqus software environment. Structural mechanics of engineering constructions and buildings. 2022. 18 (6). P. 552 – 563.
15 Shalobyta N.N., Polonskiy M.Ch. Features of constructing an analytical model and numerical study of the redistribution of forces in reinforced concrete beams with hybrid reinforcement. International scientific and technical conference « Theory and practice of research and design in construction using computer-aided design (CAD) systems». 2017. Brest.
16 Chen L., Graybeal B.A. Modeling Structural Performance of Ultra high Performance Concrete I-Girders. Journal of Bridge Engineering. 2012. 17 (5). P. 754 – 764. DOI: 10.1061/(ASCE)BE.1943-5592.0000305
17 Singh M., Sheikh A.H., Ali M., Visintin P., Griffith M.C. Experimental and numerical study of the flexural behaviour of ultra-high performance fibre reinforced concrete beams. Construction and Building Materials. 2017. 138. P. 12 – 25. DOI: 10.1016/j.conbuildmat.2017.02.002
18 Solhmirzaei R., Kodur V.R. A numerical model for tracing structural response of ultra-high performance concrete beams. Modelling. 2021. 2 (4). P. 448 – 466. DOI: 10.3390/modelling2040024
19 Zhu Y., Zhang Y., Hussein H. H., Chen G. Numerical modeling for damaged reinforced concrete slab strengthened by ultra-high performance concrete (UHPC) layer. Engineering Structures. 2019. 209. DOI: 10.1016/j.engstruct.2019.110031
20 Concrete damaged plasticity. ABAQUS Analysis User's Manual URL:https:// classes.engineering.wustl.edu/2009/spring/mase5513/abaqus/docs/v6.6/books/usb/default.htm?startat=pt05ch18s05abm36.html (date access: 11.07.24)
21 Fehling E., Schmidt M., Walraven J., Leutbecher T., Fröhlich S. Ultra-High Performance Concrete UHPC: Fundamentals, Design, Examples. 2014. Berlin: Wilhelm Ernst & Sohn. DOI: 10.1002/9783433604076
22 Fakeh M., Jawdhari A., Fam A. Calibration of ABAQUS Concrete Damage Plasticity (CDP) Model for UHPC Material. Third International Interactive Symposium on Ultra-High Performance Concrete. 2023. DOI: 10.21838/uhpc.16675
23 Ji-zhi Z., Gong-feng X., Mu-xuan N., Wen-tao C. Mechanical Properties and Constitutive Model of Ultra-High Performance Concrete Material Under Uniaxial Tension and Compression Cycles. Engineering Mechanics. 2024. 41 (4). P. 81 – 93.
24 Wang Z., Wang J., Liu N., Zhang F. Modeling Seismic Performance of High-Strength Steel–Ultra-High-Performance Concrete Piers with Modified Kent-Park Model Using Fiber Elements. Advances in Mechanical Engineering. 2016. 8. DOI: 10.1177/1687814016633411
25 Yan G. Experimental Study on Strength and Deformation of Reactive Powder Concrete Under Triaxial Compression. Yantai, People’s Republic of China, CI-Premier Pte Ltd. 2010. P. 383 – 386.
26 Graybeal B. Compressive Behavior of Ultra-High-Performance Fiber-Reinforced Concrete. ACI Materials Journal. 2007. 104 (2). P. 146 – 152.
27 Prem P.R., Bharatkumar B.H., Murthy A.R. Influence of Curing Regime and Steel Fibres on the Mechanical Properties of UHPC. Magazine of Concrete Research. 2015. 67 (18). P. 1 –15. DOI: 10.1680/macr.14.00333
28 Zhang Y., Xin H., Correia J.A.F.O. Fracture evaluation of ultra-high-performance fiber reinforced concrete (UHPFRC). Engineering Failure Analysis. 2021. 120. P. 1 – 21. DOI: 10.1016/j.engfailanal.2020.105076
29 Rahdar H., Ghalehnovi M. Post-cracking behavior of UHPC on the concrete members reinforced by steel rebar. Computers and Concrete. 2016. 18 (1). P. 139 – 154. DOI: 10.12989/cac.2016.18.1.139
30 Haber Z.B. Varga I.D.I., Graybeal B.A. Properties and Behavior of UHPC-Class Materials. FHWA-HRT-18-036. 2018.
31 Kanakubo T. Tensile characteristics evaluation method for ductile fiber-reinforced cementitious composites. Journal of Advanced Concrete Technology. 2006. 4 (1). P. 3 – 17. DOI: 10.3151/jact.4.3
32 Shao Y., Billington S.L. Predicting the two predominant flexural failure paths of longitudinally reinforced high-performance fiber-reinforced cementitious composite structural members. Engineering Structures. 2019. 199. DOI: 10.1016/j.engstruct.2019.109581
33 Hoffman, N.S. Constitutive relationships of prestressed steel fiber concrete membrane elements. University of Houston. Texas. 2010. P. 232.
34 Jabbar A.M., Hamood M.J., Mohammed D.H. Impact of Dilation Angle and Viscosity on the Ultra-High Performance Concrete Behavior in Abaqus. 2010. DOI: 10.1109/ICASEA53739. 2021.9733087
35 Hashim D.T., Hejazi F., Voo Y.L. Simplified Constitutive and Damage Plasticity Models for UHPFRC with Different Types of Fiber. International Journal of Concrete Structures and Materials. 2020. 14 (1). P. 1 – 21.
36 Dao C.B., Viet C.M., Quanh V.N., Pham H. Investigation of the shear behavior of ultra-high performance concrete girder by simulation approach. IOP Conference Series Materials Science and Engineering. 2023. 1289 (1). DOI: 10.1088/1757-899X/1289/1/012029
37 Tamov M.M., Abuizeih Y. Q. Y. The Effect of the Longitudinal Reinforcement Ratio on the Behavior of Ultra-High Performance Fibre-Reinforced Concrete Beams. Scientific Works of the Kuban State Technological University. 2025. 2. P. 56 – 71. DOI: 10.26297/2312-9409.2025.2.6
38 Yang I.H., Park J., Bui T.Q., Kim K.C., Joh C., Lee H. An Experimental Study on the Ductility and Flexural Toughness of Ultrahigh-Performance Concrete Beams Subjected to Bending. Materials. 2020. 13 (10). P. 2225. DOI: 10.3390/ma13102225
39 Turker K., Hasgul U., Birol T., Yavas A., Yazici H. Hybrid fiber use on flexural behavior of ultra high performance fiber reinforced concrete beams. Composite Structures. 2019. 229 (6). P. 111400. DOI: 10.1016/j.compstruct.2019.111400
40 Yoo D.Y., Banthia N., Yoon Y.S. Experimental and numerical study on flexural behavior of ultra-high-performance fiber-reinforced concrete beams with low reinforcement ratios. Canadian Journal of Civil Engineering. 2017. 44 (1). P. 18 – 28. DOI: 10.1139/cjce-2015-0384
41 Graybeal B., Davis M. Cylinder or Cube: Strength Testing of 80 to 200 MPa (11.6 to 29 ksi) Ultra-High-Performance Fiber-Reinforced Concrete. Aci Materials Journal. 2008. 105. (6). P. 603-609. DOI: 10.14359/20202
42 Esfahani M.H., Hejazi F., Jaafar M.S.B., Karimzadeh K. Simplified Damage Plasticity Model for Concrete. Structural Engineering International. 2017. 27 (1). P. 68 – 78. DOI: 10.2749/101686616X1081
Abuizeih Y.Q.Y., Tamov M.M., Leonova A.N., Mailyan D.R., Nikora N.I. Numerical simulation of nonlinear bending behaviour of uhpc beams. Construction Materials and Products. 2025. 8 (4). 6. 10.58224/2618-7183-2025-8-4-6