A Dynamic Elastoplastic Model of Concrete Based on a Modeling Method with Environmental Factors as Constitutive Variables
Publication: Journal of Engineering Mechanics
Volume 149, Issue 12
Abstract
This paper develops a modeling method with an incremental stress–strain–environment constitutive model to predict the change in the plastic mechanical behavior of concrete caused by environmental action. The model regards the environmental factor as a constitutive variable, similar to stress and strain. The yield condition of the model is a function of stress, the plastic internal variable, and the environmental variable. The loading–unloading criterion is established in the space constructed by the strain and the environmental variable to determine the contribution of mechanical loads and environmental factors to plastic deformation. By considering the strain rate as an environmental factor and applying the proposed method, a stress–strain–strain rate constitutive model of concrete is developed to describe the plastic flow caused by the combined action of stress and strain rate. In addition, constant- and variable-strain rate loading tests are performed to evaluate the performance of the established model. In particular, the model’s capabilities are further highlighted by comparing the simulation results of the dynamic stress–strain model and the proposed model under loading conditions with rapidly decreasing strain rates.
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Data Availability Statement
All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
This work was sponsored by the National Natural Science Foundation of China (Grant No. 52025084) and Postdoctoral Research Foundation of China (Grant No. 2022M721884).
References
Aráoz, G., and B. Luccioni. 2015. “Modeling concrete like materials under sever dynamic pressures.” Int. J. Impact Eng. 76 (Feb): 139–154. https://doi.org/10.1016/j.ijimpeng.2014.09.009.
Bai, Z., Y. Liu, J. Yang, and S. He. 2020. “A constitutive model for concrete subjected to extreme dynamic loadings.” Int. J. Impact Eng. 138 (Apr): 103483. https://doi.org/10.1016/j.ijimpeng.2019.103483.
Borrvall, T., and W. Riedel. 2011. “The RHT concrete model in LS-DYNA.” In Proc., 8th European LS-DYNA Users Conf. Strasbourg, France: The Alyotech Group.
Candappa, D. C., J. G. Sanjayan, and S. Setunge. 2001. “Complete triaxial stress-strain curves of high-strength concrete.” J. Mater. Civ. Eng. 13 (3): 209–215. https://doi.org/10.1061/(ASCE)0899-1561(2001)13:3(209).
Chang, Y. F., Y. H. Chen, M. S. Sheu, and G. C. Yao. 2006. “Residual stress–strain relationship for concrete after exposure to high temperatures.” Cem. Concr. Res. 36 (10): 1999–2005. https://doi.org/10.1016/j.cemconres.2006.05.029.
Chen, L., Q. Fang, X. Jiang, Z. Ruan, and J. Hong. 2015. “Combined effects of high temperature and high strain rate on normal weight concrete.” Int. J. Impact Eng. 86 (Dec): 40–56. https://doi.org/10.1016/j.ijimpeng.2015.07.002.
Drucker, D. C. 1950. “Some implications of work hardening and ideal plasticity.” Q. Appl. Math. 7 (4): 411–418. https://doi.org/10.1090/qam/34210.
Etse, G., and K. Willam. 1994. “Fracture energy formulation for inelastic behavior of plain concrete.” J. Eng. Mech. 120 (9): 1983–2011. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:9(1983).
Fan, Y., L. Chen, R. Yu, H. Xiang, and Q. Fang. 2022. “Experimental study of damage to ultra-high performance concrete slabs subjected to partially embedded cylindrical explosive charges.” Int. J. Impact Eng. 168 (Oct): 104298. https://doi.org/10.1016/j.ijimpeng.2022.104298.
Gao, Z. W., and J. D. Zhao. 2017. “A non-coaxial critical-state model for sand accounting for fabric anisotropy and fabric evolution.” Int. J. Solids Struct. 106 (Feb): 200–212. https://doi.org/10.1016/j.ijsolstr.2016.11.019.
Gasch, T., R. Malm, and A. Ansell. 2016. “A coupled hygro-thermo-mechanical model for concrete subjected to variable environmental conditions.” Int. J. Solids Struct. 91 (Aug): 143–156. https://doi.org/10.1016/j.ijsolstr.2016.03.004.
Gebbeken, N., and T. Krauthammer. 2013. “Understanding the dynamic response of concrete to loading: Practical examples.” In Understanding the tensile properties of concrete, 338–369. Cambridge, UK: Woodhead.
Grassl, P., and M. Jirásek. 2006. “Damage-plastic model for concrete failure.” Int. J. Solids Struct. 43 (22–23): 7166–7196. https://doi.org/10.1016/j.ijsolstr.2006.06.032.
Grote, D. L., S. W. Park, and M. Zhou. 2001. “Dynamic behavior of concrete at high strain rates and pressures: I. Experimental characterization.” Int. J. Impact Eng. 25 (9): 869–886. https://doi.org/10.1016/S0734-743X(01)00020-3.
Heeres, O. M., A. S. J. Suiker, and R. de Borst. 2002. “A comparison between the Perzyna viscoplastic model and the consistency viscoplastic model.” Eur. J. Mech. A-Solids 21 (1): 1–12. https://doi.org/10.1016/S0997-7538(01)01188-3.
Holmquist, T. J., and G. R. Johnson. 2011. “A computational constitutive model for glass subjected to large strains, high strain rates and high pressures.” J. Appl. Mech. 78 (5): 051003. https://doi.org/10.1115/1.4004326.
Hossain, A. B., and J. Weiss. 2004. “Assessing residual stress development and stress relaxation in restrained concrete ring specimens.” Cem. Concr. Compos. 26 (5): 531–540. https://doi.org/10.1016/S0958-9465(03)00069-6.
Il’Iushin, A. A. 1961. “On the postulate of plasticity.” J. Appl. Math. Mech. 25 (3): 746–752. https://doi.org/10.1016/0021-8928(61)90044-2.
Imran, I., and S. J. Pantazopoulou. 1996. “Experimental study of plain concrete under triaxial stress.” ACI Mater. J. 93 (6): 589–601. https://doi.org/10.14359/9865.
Jia, P. C., H. Wu, and Q. Fang. 2023. “An improved 2DOF model for dynamic behaviors of RC members under lateral low-velocity impact.” Int. J. Impact Eng. 173 (Mar): 104460. https://doi.org/10.1016/j.ijimpeng.2022.104460.
Kang, H. D., and K. J. Willam. 2000. “Performance evaluation of elastoviscoplastic concrete model.” J. Eng. Mech. 126 (9): 995–1000. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:9(995).
Khan, A. S., and H. Liu. 2012. “Variable strain rate sensitivity in an aluminum alloy: Response and constitutive modeling.” Int. J. Plast. 36 (Sep): 1–14. https://doi.org/10.1016/j.ijplas.2012.02.001.
Kong, X., Q. Fang, L. Chen, and H. Wu. 2018. “A new material model for concrete subjected to intense dynamic loadings.” Int. J. Impact Eng. 120 (Oct): 60–78. https://doi.org/10.1016/j.ijimpeng.2018.05.006.
Kong, X., Q. Fang, Q. M. Li, H. Wu, and J. E. Crawford. 2017. “Modified K&C model for cratering and scabbing of concrete slabs under projectile impact.” Int. J. Impact Eng. 108 (Oct): 217–228. https://doi.org/10.1016/j.ijimpeng.2017.02.016.
Kupfer, H., H. K. Hilsdorf, and H. Rusch. 1969. “Behavior of concrete under biaxial stresses.” J. Proc. 66 (8): 656–666. https://doi.org/10.14359/7388.
Li, Q. M., Y. B. Lu, and H. Meng. 2009. “Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part II: Numerical simulations.” Int. J. Impact Eng. 36 (12): 1335–1345. https://doi.org/10.1016/j.ijimpeng.2009.04.010.
Lu, D., F. Meng, X. Zhou, G. Wang, and X. Du. 2022a. “Double scalar variables plastic-damage model for concrete.” J. Eng. Mech. 148 (2): 4021143. https://doi.org/10.1061/(ASCE)EM.1943-7889.0002050.
Lu, D., C. Su, X. Zhou, G. Wang, and X. Du. 2022b. “A cohesion-friction combined hardening plastic model of concrete with the nonorthogonal flow rule: Theory and numerical implementation.” Constr. Build. Mater. 325 (Mar): 126586. https://doi.org/10.1016/j.conbuildmat.2022.126586.
Lu, D., G. Wang, X. Du, and Y. Wang. 2017. “A nonlinear dynamic uniaxial strength criterion that considers the ultimate dynamic strength of concrete.” Int. J. Impact Eng. 103 (May): 124–137. https://doi.org/10.1016/j.ijimpeng.2017.01.011.
Lu, D., X. Zhou, X. Du, and G. Wang. 2019. “A 3D fractional elastoplastic constitutive model for concrete material.” Int. J. Solids Struct. 165 (Jun): 160–175. https://doi.org/10.1016/j.ijsolstr.2019.02.004.
Lu, D., X. Zhou, X. Du, and G. Wang. 2020. “3D dynamic elastoplastic constitutive model of concrete within the framework of rate-dependent consistency condition.” J. Eng. Mech. 146 (11): 4020124. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001854.
Lu, X. B., and C. T. Hsu. 2007. “Stress-strain relations of high-strength concrete under triaxial compression.” J. Mater. Civ. Eng. 19 (3): 261–268. https://doi.org/10.1061/(ASCE)0899-1561(2007)19:3(261).
Lucchesi, M., and P. Podio-Guidugli. 1995. “Elastic unloading, neutral loading, and plastic loading in the theory of materials with elastic range.” Int. J. Plast. 11 (1): 1–14. https://doi.org/10.1016/0749-6419(94)00036-0.
Ma, J., J. Chen, W. Chen, and L. Huang. 2022. “A coupled thermal-elastic-plastic-damage model for concrete subjected to dynamic loading.” Int. J. Plast. 153 (Jun): 103279. https://doi.org/10.1016/j.ijplas.2022.103279.
Malvar, L. J., J. E. Crawford, J. W. Wesevich, and D. Simons. 1997. “A plasticity concrete material model for DYNA3D.” Int. J. Impact Eng. 19 (9): 847–873. https://doi.org/10.1016/S0734-743X(97)00023-7.
Naghdi, P. M., and S. A. Murch. 1963. “On the mechanical behavior of viscoelastic/plastic solids.” J. Appl. Mech. 30 (3): 321–328. https://doi.org/10.1115/1.3636556.
Paliwal, B., Y. Hammi, M. Chandler, R. D. Moser, and M. F. Horstemeyer. 2020. “A three-invariant cap-viscoplastic rate-dependent-damage model for cementitious materials with return mapping integration in Haigh-Westergaard coordinate space.” Int. J. Solids Struct. 182 (Jan): 77–99. https://doi.org/10.1016/j.ijsolstr.2019.07.029.
Peng, Q., H. Wu, P. C. Jia, and L. L. Ma. 2023. “Dynamic behavior of UHPC member under lateral low-velocity impact: Mesoscale analysis.” Int. J. Impact Eng. 172 (Feb): 104418. https://doi.org/10.1016/j.ijimpeng.2022.104418.
Polanco-Loria, M., O. S. Hopperstad, T. Børvik, and T. Berstad. 2008. “Numerical predictions of ballistic limits for concrete slabs using a modified version of the HJC concrete model.” Int. J. Impact Eng. 35 (5): 290–303. https://doi.org/10.1016/j.ijimpeng.2007.03.001.
Qi, C. Z., M. Y. Wang, and Q. H. Qian. 2009. “Strain-rate effects on the strength and fragmentation size of rocks.” Int. J. Impact Eng. 36 (12): 1355–1364. https://doi.org/10.1016/j.ijimpeng.2009.04.008.
Qiao, Y. F., A. Ferrari, L. Laloui, and W. Ding. 2016. “Nonstationary flow surface theory for modeling the viscoplastic behaviors of soils.” Comput. Geotech. 76 (Jun): 105–119. https://doi.org/10.1016/j.compgeo.2016.02.015.
Rahnavard, R., H. D. Craveiro, R. A. Simões, L. Laím, and A. Santiago. 2022. “Fire resistance of concrete-filled cold-formed steel (CF-CFS) built-up short columns.” J. Build. Eng. 48 (May): 103854. https://doi.org/10.1016/j.jobe.2021.103854.
Reis, J. M. L., L. J. Pacheco, and H. S. Da Costa Mattos. 2014. “Temperature and variable strain rate sensitivity in recycled HDPE.” Polym. Test 39 (Oct): 30–35. https://doi.org/10.1016/j.polymertesting.2014.07.011.
Seneviratne, S. I., et al. 2023. Weather and climate extreme events in a changing climate, 1513–1766. Cambridge, UK: Cambridge University Press. https://doi.org/10.1017/9781009157896.013.
Shkolnik, I. E. 2008. “Influence of high strain rates on stress–strain relationship, strength and elastic modulus of concrete.” Cem. Concr. Compos. 30 (10): 1000–1012. https://doi.org/10.1016/j.cemconcomp.2007.10.001.
Torelli, G., P. Mandal, M. Gillie, and V. X. Tran. 2018. “A confinement-dependent load-induced thermal strain constitutive model for concrete subjected to temperatures up to 500°C.” Int. J. Mech. Sci. 144 (Aug): 887–896. https://doi.org/10.1016/j.ijmecsci.2017.12.054.
Wang, G. S., D. Lu, X. Du, and X. Zhou. 2018a. “Dynamic multiaxial strength criterion for concrete based on strain rate–dependent strength parameters.” J. Eng. Mech. 144 (5): 4018018. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001428.
Wang, G. S., D. Lu, X. Du, X. Zhou, and S. Cao. 2018b. “A true 3D frictional hardening elastoplastic constitutive model of concrete based on a unified hardening/softening function.” J. Mech. Phys. Solids 119 (Oct): 250–273. https://doi.org/10.1016/j.jmps.2018.06.019.
Wu, H., Q. Fang, Y. Peng, Z. M. Gong, and X. Z. Kong. 2015. “Hard projectile perforation on the monolithic and segmented RC panels with a rear steel liner.” Int. J. Impact Eng. 76 (Feb): 232–250. https://doi.org/10.1016/j.ijimpeng.2014.10.010.
Yan, D., and G. Lin. 2006. “Dynamic properties of concrete in direct tension.” Cem. Concr. Res. 36 (7): 1371–1378. https://doi.org/10.1016/j.cemconres.2006.03.003.
Yan, D., and G. Lin. 2007. “Dynamic behaviour of concrete in biaxial compression.” Mag. Concr. Res. 59 (1): 45–52. https://doi.org/10.1680/macr.2007.59.1.45.
Yu, S. S., Y. B. Lu, and Y. Cai. 2013. “The strain-rate effect of engineering materials and its unified model.” Lat. Am. J. Solids Struct. 10 (4): 833–844. https://doi.org/10.1590/S1679-78252013000400010.
Zeng, Y. Q., L. H. Xu, Y. Chi, M. Yu, and L. Huang. 2023. “Compressive behavior of circular GFRP tube-confined UHPC-filled steel-encased stub columns.” Compos. Struct. 309 (Apr): 116730. https://doi.org/10.1016/j.compstruct.2023.116730.
Zhang, Q. B., and J. Zhao. 2014. “A review of dynamic experimental techniques and mechanical behaviour of rock materials.” Rock Mech. Rock Eng. 47 (4): 1411–1478. https://doi.org/10.1007/s00603-013-0463-y.
Zheng, B. T., and J. G. Teng. 2022. “A plasticity constitutive model for concrete under multiaxial compression.” Eng. Struct. 251 (Jan): 113435. https://doi.org/10.1016/j.engstruct.2021.113435.
Zhen-jun, H., M. Yan-ni, W. Zhen-wei, Z. Xiao-jie, Z. Xue-sheng, D. Meng-jia, and F. Chuan. 2021. “Triaxial strength and deformation characteristics and its constitutive model of high-strength concrete before and after high temperatures.” Structures 30 (Apr): 1127–1138. https://doi.org/10.1016/j.istruc.2020.11.078.
Zhou, X., D. Lu, X. Du, G. Wang, and F. Meng. 2020. “A 3D non-orthogonal plastic damage model for concrete.” Comput. Methods Appl. Mech. Eng. 360 (Mar): 112716. https://doi.org/10.1016/j.cma.2019.112716.
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© 2023 American Society of Civil Engineers.
History
Received: Feb 7, 2023
Accepted: Jul 24, 2023
Published online: Oct 9, 2023
Published in print: Dec 1, 2023
Discussion open until: Mar 9, 2024
ASCE Technical Topics:
- Concrete
- Constitutive relations
- Design (by type)
- Dynamic models
- Engineering fundamentals
- Engineering materials (by type)
- Load factors
- Material mechanics
- Materials engineering
- Mathematics
- Models (by type)
- Plastics
- Strain
- Stress (by type)
- Stress strain relations
- Structural analysis
- Structural design
- Structural engineering
- Synthetic materials
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