3D Dynamic Elastoplastic Constitutive Model of Concrete within the Framework of Rate-Dependent Consistency Condition
Publication: Journal of Engineering Mechanics
Volume 146, Issue 11
Abstract
In this paper, the proposed yield function is the function of stress, hardening parameter, and strain rate. To fully describe the stress state and strain rate condition of material during dynamic loading, a new coordinate system, which is composed of a stress axis and strain rate axis, is employed to present the proposed rate-dependent yield surface. The strain rate is regarded as a variable in applying the consistency condition. The rate-dependent consistency is satisfied strictly during the whole dynamic loading. The nonassociated flow rule is employed to describe the dilatancy behavior of concrete. The loading–unloading criterion based on Ilyushin’s postulate is developed into the rate-dependent loading–unloading criterion that can consider reasonably the change of elastic domain caused by strain rate. Furthermore, a three-dimensional (3D) dynamic elastoplastic model of concrete is established within the framework of the rate-dependent consistency condition. Under the dynamic uniaxial compression loading condition, the model characteristics related to rate-dependent consistency condition are discussed and analyzed. Five sets of dynamic experiment results of concrete are employed to evaluate the performance of the model.
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Data Availability Statement
All data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
Support for this study is provided by the National Basic Research Program of China (Grant No. 2018YFC1504301) and the National Natural Science Foundation of China (Grant Nos. 51421005 and 51778026 U1839201).
References
Al-Salloum, Y., T. Almusallam, S. M. Ibrahim, H. Abbas, and S. Alsayed. 2015. “Rate dependent behavior and modeling of concrete based on SHPB experiments.” Cem. Concr. Compos. 55 (Jan): 34–44. https://doi.org/10.1016/j.cemconcomp.2014.07.011.
Barpi, F. 2004. “Impact behavior of concrete: A computational approach.” Eng. Fract. Mech. 71 (15): 2197–2213. https://doi.org/10.1016/j.engfracmech.2003.11.007.
Bischoff, P. H., and S. H. Perry. 1991. “Compressive behavior of concrete at high strain rates.” Mater. Struct. 24 (6): 425–450. https://doi.org/10.1007/BF02472016.
Buyukozturk, O., and S. S. Shareef. 1985. “Constitutive modeling of concrete in finite element analysis.” Comput. Struct. 21 (3): 581–610. https://doi.org/10.1016/0045-7949(85)90135-X.
CEB-FIP (Comité Euro-International du Béton–Fédération International de la Précontrainte). 1990. Design code. London: Thomas Telford.
Cela, J. J. L. 1998. “Analysis of reinforced concrete structures subjected to dynamic loads with a viscoplastic Drucker-Prager model.” Appl. Math. Model. 22 (7): 495–515. https://doi.org/10.1016/S0307-904X(98)10050-1.
Cervera, M., J. Oliver, and O. Manzoli. 1996. “A rate-dependent isotropic damage model for the seismic analysis of concrete dams.” Earthquake Eng. Struct. Dyn. 25 (9): 987–1010. https://doi.org/10.1002/(SICI)1096-9845(199609)25:9%3C987::AID-EQE599%3E3.0.CO;2-X.
Chen, X., S. Wu, J. Zhou, Y. Chen, and A. Qin. 2012. “Effect of testing method and strain rate on stress-strain behavior of concrete.” J. Mater. Civ. Eng. 25 (11): 1752–1761. https://doi.org/10.1061/(ASCE)MT.1943-5533.0000732.
Cui, J., H. Hao, and Y. C. Shi. 2017. “Discussion on the suitability of concrete constitutive models for high-rate response predictions of RC structures.” Int. J. Impact Eng. 106 (Aug): 202–216. https://doi.org/10.1016/j.ijimpeng.2017.04.003.
Du, X.-L., D.-C. Lu, Q.-M. Gong, and M. Zhao. 2010. “Nonlinear unified strength criterion for concrete under three-dimensional stress states.” J. Eng. Mech. 136 (1): 51–59. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000055.
Dubé, J.-F., G. Pijaudier-Cabot, and C. L. Borderie. 1996. “Rate dependent damage model for concrete in dynamics.” J. Eng. Mech. 122 (10): 939–947. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:10(939).
Duvaut, G., and J. L. Lions. 1972. Inequalities in mechanics and physics. Paris: Dunod.
Eibl, J., and B. Schmidt-Hurtienne. 1999. “Strain-rate-sensitive constitutive law for concrete.” J. Eng. Mech. 125 (12): 1411–1420. https://doi.org/10.1061/(ASCE)0733-9399(1999)125:12(1411).
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, L. F., and L. Wong. 2013. “Stress wave transmission across a filled joint with different loading/unloading behavior.” Int. J. Rock Mech. Min. Sci. 60 (Jun): 227–234. https://doi.org/10.1016/j.ijrmms.2012.12.046.
Fu, Q., Y. Xie, G. Long, D. Niu, and H. Song. 2018. “Effect of strain rate on compressive behavior and modeling of cement and asphalt mortar.” J. Mater. Civ. Eng. 30 (3): 4018018. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002151.
Grady, D. E. 1998. “Shock-wave compression of brittle solids.” Mech. Mater. 29 (3): 181–203. https://doi.org/10.1016/S0167-6636(98)00015-5.
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.
Hao, Y. F., and H. Hao. 2011. “Numerical evaluation of the Influence of aggregates on concrete compressive strength at high strain rate.” Int. J. Protective Struct. 2 (2): 177–206. https://doi.org/10.1260/2041-4196.2.2.177.
Hao, Y. F., and H. Hao. 2013. “Dynamic compressive behavior of spiral steel fiber reinforced concrete in split Hopkinson pressure bar tests.” Constr. Build. Mater. 48 (Nov): 521–532. https://doi.org/10.1016/j.conbuildmat.2013.07.022.
Hao, Y. F., and H. Hao. 2014. “Influence of the concrete DIF model on the numerical predictions of RC wall responses to blast loadings.” Eng. Struct. 73 (Aug): 24–38. https://doi.org/10.1016/j.engstruct.2014.04.042.
Harsh, S., Z. Shen, and D. Darwin. 1990. “Strain-rate sensitive behavior of cement paste and mortar in compression.” ACI Mater. J. 87 (5): 508–516. https://doi.org/doi.org/10.14359/1931.
Hervé, G., F. Gatuingt, and A. Ibrahimbegovi. 2005. “On numerical implementation of a coupled rate dependent damage-plasticity constitutive model for concrete in application to high-rate dynamics.” Eng. Comput. 22 (5): 583–604. https://doi.org/10.1108/02644400510603023.
Holqmuist, T. J., G. R. Johnson, and W. Cook. 1993. “A computational constitutive model for concrete subjected to large strains, high strain rate, and high pressures.” In Proc., 14th Int. Symp. on Ballistics, 591–600. Sundbyberg, Sweden: National Defence Research Establishment.
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).
Kong, X. Z., 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. Z., Q. Fang, Q. M. Li, H. Wu, and J. E. Crawford. 2017a. “Modified K&C model for catering 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.
Kong, X. Z., Q. Fang, H. Wu, and J. Hong. 2017b. “A comparison of strain-rate enhancement approaches for concrete material subjected to high strain-rate.” Int. J. Protective Struct. 8 (2): 155–176. https://doi.org/10.1177/2041419617698320.
Leng, F., and G. Lin. 2010. “Dissipation-based consistent rate-dependent model for concrete.” Acta Mech. Solida Sin. 23 (2): 147–155. https://doi.org/10.1016/S0894-9166(10)60016-X.
Li, Q. M., and H. Meng. 2003. “About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test.” Int. J. Solids Struct. 40 (2): 343–360. https://doi.org/10.1016/S0020-7683(02)00526-7.
Liu, S., D. Zhu, Y. Yao, and C. Shi. 2018. “Effects of strain rate and temperature on the flexural behavior of basalt and glass textile–reinforced concrete.” J. Mater. Civ. Eng. 30 (8): 4018172. https://doi.org/10.1061/(ASCE)MT.1943-5533.0002387.
Lu, D. C., X. L. Du, G. S. Wang, A. N. Zhou, and A. K. Li. 2016. “A three-dimensional elastoplastic constitutive model for concrete.” Comput. Struct. 163 (Jan): 41–55. https://doi.org/10.1016/j.compstruc.2015.10.003.
Lu, D. C., and G. S. Wang. 2017. “Reply to the comments on ‘A nonlinear dynamic uniaxial strength criterion that considers the ultimate dynamic strength of concrete by Dechun Lu, Guosheng Wang, Xiuli Du, Yang Wang. Int J Impact Eng 103 (2017), 124–137’ by Xu and Wen.” Int. J. Impact Eng. 109 (Nov): 429–432. https://doi.org/10.1016/j.ijimpeng.2017.07.006.
Lu, D. C., G. S. Wang, X. L. 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. C., X. Zhou, X. L. Du, and G. S. 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.
Luccioni, B., F. Isla, D. Forni, and E. Cadoni. 2018. “Modelling UHPFRC tension behavior under high strain rates.” Cem. Concr. Comp. 91 (Aug): 209–220. https://doi.org/10.1016/j.cemconcomp.2018.05.001.
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.
Murray, Y., A. Y. Abu-Odeh, and R. P. Bligh. 2007. Users manual for LS-DYNA concrete material model 159. Washington, DC: Federal Highway Administration.
Needleman, A. 1988. “Material rate dependence and mesh sensitivity in localization problems.” Comput. Method Appl. Eng. 67 (1): 69–85. https://doi.org/10.1016/0045-7825(88)90069-2.
Perzyna, P. 1966. “Fundamental problems in viscoplasticity.” Adv. Appl. Mech. 9 (2): 243–377. https://doi.org/10.1016/S0065-2156(08)70009-7.
Plotzitza, A., T. Rabczuk, and J. Eibl. 2007. “Techniques for numerical simulations of concrete slabs for demolishing by blasting.” J. Eng. Mech. 133 (5): 523–533. https://doi.org/10.1061/(ASCE)0733-9399(2007)133:5(523).
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.
Qu, S. N., and Y. Q. Yin. 1981. “Drucker’s and Ilyushin’s postulate of plasticity.” Acta Mech. Sin. 13 (5): 467–473.
Ragueneau, F., and F. Gatuingt. 2003. “Inelastic behavior modeling of concrete in low and high strain rate dynamics.” Comput. Struct. 81 (12): 1287–1299. https://doi.org/10.1016/S0045-7949(03)00043-9.
Riedel, W., K. Thoma, S. Hiermaier, and E. Schmolinske. 1999. “Penetration of reinforced concrete by BETA-B-500 numerical analysis using a new macroscopic concrete model for hydrocodes.” In Proc., 9th Int. Symp. on the Effects of Munitions with Structures, 315–322. Hannover, Germany: TIB Technik/Naturwissenschaften (Science/Technology).
Su, Y., J. Li, C. Q. Wu, P. T. Wu, and Z. X. Li. 2016. “Influences of nano-particles on dynamic strength of ultra-high performance concrete.” Composites, Part B 91 (Apr): 595–609. https://doi.org/10.1016/j.compositesb.2016.01.044.
Tu, Z. G., and Y. Lu. 2010. “Modifications of RHT material model for improved numerical simulation of dynamic response of concrete.” Int. J. Impact Eng. 37 (10): 1072–1082. https://doi.org/10.1016/j.ijimpeng.2010.04.004.
Wang, G., 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., D. Lu, X. Du, X. Zhou, and S. Cao. 2018b. “A true 3D frictional hardening elastoplastic constitutive model of concrete based on a united hardening/softening function.” J. Mech. Phys. Solids 119 (Oct): 250–273. https://doi.org/10.1016/j.jmps.2018.06.019.
Wang, W. M. 1997. “Stationary and propagative instabilities in metals—A computational point of view.” Ph.D. thesis, Faculty of Civil Engineering, Delft Univ. of Technology.
Winnicki, A., C. J. Pearce, and N. Bićanić. 2001. “Viscoplastic Hoffman consistency model for concrete.” Comput. Struct. 79 (1): 7–19. https://doi.org/10.1016/S0045-7949(00)00110-3.
Wu, J. Y., and J. Li. 2007. “Unified plastic-damage model for concrete and its applications to dynamic nonlinear analysis of structures.” Struct. Eng. Mech. 25 (5): 519–540. https://doi.org/10.12989/sem.2007.25.5.519.
Wu, W., W. D. Zhang, and G. W. Ma. 2010. “Mechanical properties of copper slag reinforced concrete under dynamic compression.” Constr. Build. Mater. 24 (6): 910–917. https://doi.org/10.1016/j.conbuildmat.2009.12.001.
Xiao, J. Z., L. Li, L. M. Shen, and J. Q. Yuan. 2015. “Effects of strain rate on mechanical behavior of modeled recycled aggregate concrete under uniaxial compression.” Constr. Build. Mater. 93 (Sep): 214–222. https://doi.org/10.1016/j.conbuildmat.2015.04.053.
Xiao, S. Y., H. N. Li, and G. Lin. 2010. “3-D consistency dynamic constitutive model of concrete.” Earthquake Eng. Vib. 9 (2): 233–246. https://doi.org/10.1007/s11803-010-0009-1.
Yan, D. M., 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. M., and G. Lin. 2007. “Dynamic behavior of concrete in biaxial compression.” Mag. Concr. Res. 59 (1): 45–52. https://doi.org/10.1680/macr.2007.59.1.45.
Yan, D. M., G. Lin, and G. D. Chen. 2009. “Dynamic properties of plain concrete in triaxial stress state.” ACI Mater. J. 106 (1): 89–94. https://doi.org/10.14359/56321.
Yao, Y. P., D. C. Lu, A. N. Zhou, and B. Zou. 2004. “Generalized non-linear strength theory and transformed stress space.” Sci. China, Ser. E. 47 (6): 691–709. https://doi.org/10.1360/04ye0199.
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.
Zhao, J. 2000. “Applicability of Mohr-Coulomb and Hoek-Brown strength criteria to the dynamic strength of brittle rock.” Int. J. Rock Mech. Min. Sci. 37 (7): 1115–1121. https://doi.org/10.1016/S1365-1609(00)00049-6.
Zheng, D., Q. B. Li, and L. B. Wang. 2005. “A microscopic approach to rate effect on compressive strength of concrete.” Eng. Fract. Mech. 72 (15): 2316–2327. https://doi.org/10.1016/j.engfracmech.2005.01.012.
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Published In
Journal of Engineering Mechanics
Volume 146 • Issue 11 • November 2020
Copyright
© 2020 American Society of Civil Engineers.
History
Received: May 15, 2019
Accepted: Jun 5, 2020
Published online: Aug 26, 2020
Published in print: Nov 1, 2020
Discussion open until: Jan 26, 2021
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