混凝土动态力学行为数值模拟研究

李晓琴; 廖俊智; 陈建飞; 陆勇; 陈前均

doi:10.6052/j.issn.1000-4750.2022.10.0865

混凝土动态力学行为数值模拟研究

李晓琴^1, ,,
廖俊智^1,,
陈建飞^2,,
陆勇^3,,
陈前均^4,

1.
昆明理工大学建筑工程学院，云南，昆明 650500
2.
南方科技大学海洋科学与工程系，广东，深圳 518055
3.
爱丁堡大学工程学院基础设施与环境研究所，英国 EH93JL
4.
克劳斯塔尔工业大学地下能源系统研究所，德国 38678

基金项目: 国家自然科学基金项目(52168029，51968035)；云南省万人计划青年拔尖人才项目(云人社通[2020]150号 YNWR-QNBJ-2020-049)

详细信息

作者简介:
廖俊智(1998−)，男，江西九江人，硕士生，主要从事混凝土结构动力分析研究(E-mail: junzhiliao@foxmail.com)

陈建飞(1963−)，男，浙江温州人，教授，博士，主要从事FRP在土木工程中的应用研究(E-mail: Chenjf3@sustech.edu.cn)

陆　勇(1962−)，男，江苏南京人，教授，博士，主要从事冲击振动与结构抗爆应用研究(E-mail: yong.lu@ed.ac.uk)

陈前均(1993−)，男，四川阆中人，博士生，主要从事结构工程、盐岩力学与工程应用研究(E-mail: chen_qianjun@qq.com)

通讯作者:
李晓琴(1983−)，女，云南丽江人，教授，博士，主要从事FRP加固混凝土结构抗爆炸和冲击研究(E-mail: Xiaoqin.Li@foxmail.com)

中图分类号: TU528.1
计量
- 文章访问数: 561
- HTML全文浏览量: 98
- PDF下载量: 146
出版历程
- 收稿日期: 2022-10-08
- 修回日期: 2023-01-27
- 网络出版日期: 2023-02-19
- 刊出日期: 2024-12-24

NUMERICAL ANALYSIS ON DYNAMIC MECHANICAL BEHAVIOR OF CONCRETE

1.
Faculty of Civil Engineering, Kunming University of Science and Technology, Kunming, Yunnan 650500, China
2.
Department of Ocean Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China
3.
Institute for Infrastructure and Environment, School of Engineering, University of Edinburgh, Edinburgh EH93JL, UK
4.
Institute of Subsurface Energy System, TU Clausthal, Clausthal-Zellerfeld 38678, Germany

摘要

摘要:
混凝土动态强度的增强效应DIF(dynamic increase factor)一般由混凝土霍普金森杆SHPB(split Hopkinson pressure bar)试验进行测量，而基于不同应变率 $\dot \varepsilon$ 条件下的试块尺度的SHPB试验结果得到的宏观DIF- $\dot{\varepsilon }$ 关系不能直接应用于数值模型定义。运用ANSYS /LS-DYNA有限元软件和K&C混凝土模型，对混凝土SHPB直接拉伸、劈裂和层裂试验进行了模拟研究。提出了局部和非局部损伤模型中引入网格和应变率 $\dot \varepsilon$ 双修正的DIF- $\dot \varepsilon$ 模拟方案，并对混凝土非局部损伤模型中非局部特征长度L在数值模拟中的应用方案进行了讨论。SHPB和混凝土梁冲击试验模拟研究和试验数据的比较结果均表明，提出的分别基于局部和非局部损伤混凝土模型的双修正DIF- $\dot \varepsilon$ 模拟方案能够较为准确描述混凝土动态力学行为。
- 混凝土 /
- DIF /
- 应变率 /
- SHPB /
- 有限元分析 /
- 局部损伤模型 /
- 非局部损伤模型
Abstract:
The dynamic increasing factor (DIF) of concrete is normally measured via split Hopkinson pressure bar (SHPB) tests. However, the tested macro-scale DIF- $\dot \varepsilon$ relationship from the specific SHPB test specimens under different strain rates $\dot \varepsilon$ cannot be directly introduced to finite element (FE) modelling. Based on the ANSYS/LS-DYNA and K&C concrete damage model, the SHPB direct tension, split and spalling tests were modelled, and a modified DIF- $\dot \varepsilon$ relationship with both mesh and $\dot \varepsilon$ corrections for dynamic mechanic behaviour of concrete material was proposed for local and non-local damage modelling of concrete respectively, also the numerical application of the nonlocal characteristic length L was detailed discussed. The comparison between the SHPB/impact test modelling and the relevant test results indicated that the proposed doubly corrected DIF- $\dot \varepsilon$ numerical application schemes could properly capture the concrete dynamic mechanical property.
- concrete /
- DIF /
- strain rate /
- SHPB /
- FE analysis /
- local damage model /
- non-local damage model

HTML全文

非局部损伤模型中的特征长度 $L$ ^[26]

Characteristic length $L$ in nonlocal damage model ^[26]

下载: 全尺寸图片幻灯片

现有动态抗拉试验数据与宏观抗拉DIF- $\dot \varepsilon$ 经验公式^[3]

Existing dynamic tensile test results and the empirical tensile DIF- $\dot \varepsilon$ curve^[3]

下载: 全尺寸图片幻灯片

图 3 SHPB试验设置

Figure 3. SHPB test arrangements

下载: 全尺寸图片幻灯片

基于不同DIF- $\dot \varepsilon$ 关系的透射应力波模拟结果与试验数据的对比(网格尺寸1.5875 mm，入射应力峰值67 MPa)

Comparison of computed transmitted stress waves using different DIF- $\dot \varepsilon$ formula options with the test data (Mesh size 1.5875 mm, Incident impulse peak value 67 MPa)

下载: 全尺寸图片幻灯片

不同网格下基于双修正DIF- $\dot \varepsilon$ 曲线的模拟透射应力波与试验结果对比(入射应力峰值67 MPa)

Comparison of transmitted stress waves with different mesh sizes and doubly-corrected DIF- $\dot \varepsilon$ formula with the test data (Incident impulse peak value 67 MPa)

下载: 全尺寸图片幻灯片

图 6 SHPB 劈裂试验结果^{[12, 38]} 、模拟结果和式(12)曲线比较

Figure 6. The comparison of SHPB FE modelling results, splitting test results^{[12, 38]} and calculated curve based on Equation (12)

下载: 全尺寸图片幻灯片

图 7 SHPB层裂试验结果^{[10, 39]}、模拟结果和式(12)曲线比较

Figure 7. The comparison of SHPB spalling test results^{[10, 39]}, FE modelling results and calculated curves based on Equation (12)

下载: 全尺寸图片幻灯片

不同 $f_{\rm{c}}'$ 和 $\dot \varepsilon$ 下SHPB模拟结果与式(12)对比

SHPB FE modelling results compared with the calculated results from Equation (12) under different $f_{\rm{c}}'$ and $\dot \varepsilon$

下载: 全尺寸图片幻灯片

不同网格尺寸 ${h_{\rm{c}}}$ 下不同 $L$ 的非局部损伤模型透射波模拟结果和试验结果比较

Transmitted stress waves with different characteristic length $L$ under different mesh sizes h_c based on nonlocal damage model compared with the test data

下载: 全尺寸图片幻灯片

不同网格尺寸 ${h_{\rm{c}}}$ 下同一 $L$ 的非局部损伤模型透射波模拟结果与试验结果比较( $L$ = 6.735 mm)

Transmitted stress waves with different mesh sizes ${h_{\rm{c}}}$ based on nonlocal damage model compared with the test data ( $L$ =6.735 mm)

下载: 全尺寸图片幻灯片

引入不同局部与非局部DIF- $\dot \varepsilon$ 关系的透射波模拟结果与试验结果比较( $L$ = 6.735 mm, ${h_{\rm{c}}}$ =1.5875 mm)

Transmitted stress waves with different DIF- $\dot \varepsilon$ relationships based on local or nonlocal damage model compared with the test data ( $L$ = 6.735 mm, ${h_{\rm{c}}}$ =1.5875 mm)

下载: 全尺寸图片幻灯片

图 12 冲击试验装置　/mm

Figure 12. Impact test arrangement

下载: 全尺寸图片幻灯片

图 13 冲击试验模拟结果与试验结果

Figure 13. The modelling and test result comparison of the impact test

下载: 全尺寸图片幻灯片

表 1 加载条件

Table 1 Loading conditions

加载条件	入射杆应力/MPa	入射波耗时/μs			透射杆应力/MPa	动态抗压强度/MPa	应变率/ s⁻¹	动力增强因子 DIF
加载条件	入射杆应力/MPa	上升	峰值持续	总耗时	透射杆应力/MPa	动态抗压强度/MPa	应变率/ s⁻¹	动力增强因子 DIF
1	26.5	45	100	190	4.5	9.31	4.9	2.06
2	67.0	45	100	190	4.0	7.59	5.3	1.68
3	75.0	35	100	170	4.1	7.93	5.8	1.75

下载: 导出CSV

表 2 有限元模型尺寸及参数

Table 2 Dimensions and parameters of finite element (FE) model

名称	长度/m	直径/m	弹性模量/GPa	密度/(kg/m³)	泊松比
入射杆	1.3208	0.0508	200.00	7800	0.3
透射杆	1.3208	0.0508	200.00	7800	0.3
试样	0.0508	0.0508	37.93	2405	0.2

下载: 导出CSV

K&C混凝土模型参数( $f_{\rm{c}}'$ =57.7 MPa, ${h_{\rm{c}}}$ =3.175 mm)

K&C concrete model parameters ( $f_{\rm{c}}'$ =57.7 MPa, ${h_{\rm{c}}}$ =3.175 mm)

参数	取值	参数	取值	参数	取值	参数	取值	参数	取值
${a_{0{\rm{y}}}}$	$1.288 \times {10^7}$	${\lambda _1}$	0.000	${\lambda _9}$	$5.200 \times {10^{ - 4}}$	${\eta _4}$	0.99	${\eta _{12}}$	0.00
${a_{1{\rm{y}}}}$	0.625	${\lambda _2}$	$8.000 \times {10^{ - 6}}$	${\lambda _{10}}$	$5.700 \times {10^{ - 4}}$	${\eta _5}$	1.00	${\eta _{13}}$	0.00
${a_{2{\rm{y}}}}$	$4.463 \times {10^{ - 9}}$	${\lambda _3}$	$2.400 \times {10^{ - 5}}$	${\lambda _{11}}$	1.000	${\eta _6}$	0.99	${b_1}$	1.6
${a_0}$	$1.706 \times {10^7}$	${\lambda _4}$	$4.000 \times {10^{ - 5}}$	${\lambda _{12}}$	1.000	${\eta _7}$	0.97	${b_2}$	−0.5
${a_1}$	$4.463 \times {10^{ - 1}}$	${\lambda _5}$	$5.600 \times {10^{ - 5}}$	${\lambda _{13}}$	1.000	${\eta _8}$	0.50	$f_{\rm{c}}'$	57.7 MPa
${a_2}$	$1.400 \times {10^{ - 9}}$	${\lambda _6}$	$7.200 \times {10^{ - 5}}$	${\eta _1}$	0.00	${\eta _9}$	0.10	${f_{\rm{t}}}$	4.53 MPa
${a_{1{\rm{f}}}}$	$4.417 \times {10^{ - 1}}$	${\lambda _7}$	$8.800 \times {10^{ - 5}}$	${\eta _2}$	0.85	${\eta _{10}}$	0.00	${\rm{Locwidth}}$	3.175 mm
${a_{2{\rm{f}}}}$	$2.050 \times {10^{ - 9}}$	${\lambda _8}$	$3.200 \times {10^{ - 4}}$	${\eta _3}$	0.97	${\eta _{11}}$	0.00	$\omega$	0.5
注： ${a_{0{\rm{y}}}}$ 为初始屈服面内聚力， ${a_{1{\rm{y}}}}$ 和 ${a_{2{\rm{y}}}}$ 为初始屈服面参数； ${a_0}$ 、 ${a_1}$ 和 ${a_2}$ 为最大剪切破坏面参数； ${a_{1{\rm{f}}}}$ 和 ${a_{2{\rm{f}}}}$ 为残余破坏面参数； ${\lambda _1}$ ~ ${\lambda _{13}}$ 为第1至第13个损伤函数参数； ${\eta _1}$ ~ ${\eta _{13}}$ 为第1至第13个比例因子； ${\rm{Locwidth}}$ 为混凝土断裂带局部宽度； $f_{\rm{c}}'$ 和 ${f_{\rm{t}}}$ 分别为混凝土圆柱体准静态单轴抗压和抗拉强度； $\omega$ 为混凝土剪切膨胀系数； ${b_1}$ 为抗压损伤比例参数； ${b_2}$ 为拉伸损伤比例指数。

下载: 导出CSV

参考文献(41)

[1]	GUO Y B, GAO G F, JING L, et al. Quasi-static and dynamic splitting of high-strength concretes–tensile stress–strain response and effects of strain rate [J]. International Journal of Impact Engineering, 2019, 125: 188 − 211. doi: 10.1016/j.ijimpeng.2018.11.012
[2]	LI Q M, MENG H. About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test [J]. International Journal of Solids and Structures, 2003, 40(2): 343 − 360. doi: 10.1016/S0020-7683(02)00526-7
[3]	MALVAR L J, CRAWFORD J E. Dynamic increase factors for concrete [R]. Orlando: Naval Facilities Engineering Service Center, 1998.
[4]	LU Y, SONG Z H, TU Z G. Analysis of dynamic response of concrete using a mesoscale model incorporating 3D effects [J]. International Journal of Protective Structures, 2010, 1(2): 197 − 217. doi: 10.1260/2041-4196.1.2.197
[5]	ZHANG M, WU H J, LI Q M, et al. Further investigation on the dynamic compressive strength enhancement of concrete-like materials based on split Hopkinson pressure bar tests. Part I: Experiments [J]. International Journal of Impact Engineering, 2009, 36(12): 1327 − 1334. doi: 10.1016/j.ijimpeng.2009.04.009
[6]	LI X Q, CHEN Q J, CHEN J F, et al. Dynamic increase factor (DIF) for concrete in compression and tension in FE modelling with a local concrete model [J]. International Journal of Impact Engineering, 2022, 163: 104079. doi: 10.1016/j.ijimpeng.2021.104079
[7]	FIB model code for concrete structures 2010 [S]. Lausanne, Switzerland: International Federation for Structural Concrete, 2013: 100 − 101.
[8]	LU Y B, LI Q M. About the dynamic uniaxial tensile strength of concrete-like materials [J]. International Journal of Impact Engineering, 2011, 38(4): 171 − 180. doi: 10.1016/j.ijimpeng.2010.10.028
[9]	BRARA A, KLEPACZKO J R. Experimental characterization of concrete in dynamic tension [J]. Mechanics of Materials, 2006, 38(3): 253 − 267. doi: 10.1016/j.mechmat.2005.06.004
[10]	WU H J, ZHANG Q M, HUANG F L, et al. Experimental and numerical investigation on the dynamic tensile strength of concrete [J]. International Journal of Impact Engineering, 2005, 32(1/2/3/4): 605 − 617.
[11]	TEDESCO J W, ROSS C A, MCGILL P B, et al. Numerical analysis of high strain rate concrete direct tension tests [J]. Computers & Structures, 1991, 40(2): 313 − 327.
[12]	TEDESCO J W, ROSS C A. Strain-rate-dependent constitutive equations for concrete [J]. Journal of Pressure Vessel Technology, 1998, 120(4): 398 − 405. doi: 10.1115/1.2842350
[13]	SCHULER H, MAYRHOFER C, THOMA K. Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates [J]. International Journal of Impact Engineering, 2006, 32(10): 1635 − 1650. doi: 10.1016/j.ijimpeng.2005.01.010
[14]	AL-SALLOUM Y, ALMUSALLAM T, IBRAHIM S M, et al. Rate dependent behavior and modeling of concrete based on SHPB experiments [J]. Cement and Concrete Composites, 2015, 55: 34 − 44. doi: 10.1016/j.cemconcomp.2014.07.011
[15]	ERZAR B, FORQUIN P. An experimental method to determine the tensile strength of concrete at high rates of strain [J]. Experimental Mechanics, 2010, 50(7): 941 − 955. doi: 10.1007/s11340-009-9284-z
[16]	TEDESCO J W, ROSS C A, BRUNAIR R M. Numerical analysis of dynamic split cylinder tests [J]. Computers & Structures, 1989, 32(3/4): 609 − 624.
[17]	孟龙, 黄瑞源, 蒋东, 等. 不同强度混凝土高温下动态劈拉性能研究[J]. 工程力学, 2021, 38(3): 202 − 213. doi: 10.6052/j.issn.1000-4750.2020.05.0310 MENG Long, HUANG Ruiyuan, JIANG Dong, et al. Research on dynamic splitting-tensile properties of concretes with different strength at high temperature [J]. Engineering Mechanics, 2021, 38(3): 202 − 213. (in Chinese) doi: 10.6052/j.issn.1000-4750.2020.05.0310
[18]	俞鑫炉, 付应乾, 董新龙, 等. 轴向钢筋增强混凝土一维应力层裂实验研究[J]. 工程力学, 2020, 37(1): 80 − 87. doi: 10.6052/j.issn.1000-4750.2019.01.0026 YU Xinlu, FU Yingqian, DONG Xinlong, et al. Experimental study on one-dimensional stress spall of unidirectional reinforced concrete [J]. Engineering Mechanics, 2020, 37(1): 80 − 87. (in Chinese) doi: 10.6052/j.issn.1000-4750.2019.01.0026
[19]	BAŽANT Z P, OH B H. Crack band theory for fracture of concrete [J]. Matériaux et Construction, 1983, 16(3): 155 − 177.
[20]	ROTS J G, NAUTA P, KUSTER G M A, et al. Smeared crack approach and fracture localization in concrete [J]. HERON, 1985, 30(1): 1 − 48.
[21]	KONG X Z, FANG Q, HONG J. A new damage-based nonlocal model for dynamic tensile failure of concrete material [J]. International Journal of Impact Engineering, 2019, 132: 103336. doi: 10.1016/j.ijimpeng.2019.103336
[22]	PIJAUDIER-CABOT G, BAŽANT Z P. Nonlocal damage theory [J]. Journal of Engineering Mechanics, 1987, 113(10): 1512 − 1533. doi: 10.1061/(ASCE)0733-9399(1987)113:10(1512)
[23]	Malvar L J, Crawford J E, Morrill K B. K&C concrete material model release III-automated generation of material model input[R]. Glendale: Karagozian and Case Structural Engineers, 2000: 1 − 17.
[24]	李晓琴, 陈建飞, 陆勇. K&C局部损伤混凝土材料模型在精细有限元模拟中的应用[J]. 云南大学学报(自然科学版), 2015, 37(4): 541 − 547. LI Xiaoqin, CHEN Jianfei, LU Yong. Numerical applications of K&C concrete damage model in meso-scale finite element modelling [J]. Journal of Yunnan University (Natural Sciences Edition), 2015, 37(4): 541 − 547. (in Chinese)
[25]	LI X Q, CHEN J F, LU Y. Meso-scale modelling of FRP-to-concrete bond behaviour using LSDYNA [M]// YE L P, FENG P, YUE Q R. Advances in FRP Composites in Civil Engineering. Berlin: Springer, 2011: 494 − 498.
[26]	LS-DYNA keyword User's manual version 971:Volume II Material Models [M]. California, U.S: Livermore Software Technology Corporation (LSTC), 2013: 38 − 41.
[27]	KONG X Z, QIN F, LI C, et al. Nonlocal formulation of the modified K&C model to resolve mesh-size dependency of concrete structures subjected to intense dynamic loadings [J]. International Journal of Impact Engineering, 2018, 122: 318 − 332. doi: 10.1016/j.ijimpeng.2018.09.007
[28]	滕骁, 卢玉斌, 陈兴, 等. 再生混凝土动态直接拉伸的试验研究[J]. 振动与冲击, 2016, 35(9): 43 − 51. doi: 10.13465/j.cnki.jvs.2016.09.008 TENG Xiao, LU Yubin, CHEN Xing, et al. Tests for dynamic direct tensile of recycled aggregate concrete [J]. Journal of Vibration and Shock, 2016, 35(9): 43 − 51. (in Chinese) doi: 10.13465/j.cnki.jvs.2016.09.008
[29]	吴胜兴, 王瑶, 周继凯, 等. 水泥砂浆动态轴向拉伸本构关系试验研究[J]. 土木工程学报, 2012, 45(1): 13 − 22. WU Shengxing, WANG Yao, ZHOU Jikai, et al. Experimental study of dynamic axial tensile constitutive relationship for mortar [J]. China Civil Engineering Journal, 2012, 45(1): 13 − 22. (in Chinese)
[30]	肖诗云, 田子坤. 混凝土单轴动态受拉损伤试验研究[J]. 土木工程学报, 2008, 41(7): 14 − 20. doi: 10.3321/j.issn:1000-131X.2008.07.003 XIAO Shiyun, TIAN Zikun. Experimental study on the uniaxial dynamic tensile damage of concrete [J]. China Civil Engineering Journal, 2008, 41(7): 14 − 20. (in Chinese) doi: 10.3321/j.issn:1000-131X.2008.07.003
[31]	ANTOUN T H. Constitutive/failure model for the static and dynamic behaviors of concrete incorporating effects of damage and anisotropy [D]. Dayton: The University of Dayton, 1991.
[32]	BIRKIMER D L, LINDEMANN R. Dynamic tensile strength of concrete materials [J]. Journal Proceedings, 1971, 68(1): 47 − 49.
[33]	COWELL W L. Dynamic properties of plain portland cement concrete [R]. Port Hueneme: Naval Civil Engineering Lab, 1966.
[34]	JOHN R, ANTOUN T, RAJENDRAN A M. Effect of strain rate and size on tensile strength of concrete [M]// SCHMIDT S C, DICK R D, FORBES J W, et al. Shock Compression of Condensed Matter–1991. Amsterdam: Elsevier, 1992: 501 − 504.
[35]	MCVAY M K. Spall damage of concrete structures [R]. Vicksburg: U.S. Army Corps of Engineers, Waterways Experiment Station, 1988: 95 − 100.
[36]	MELLINGER F M, BIRKIMER D L. Measurements of stress and strain on cylindrical test specimens of rock and concrete under impact loading [R]. Cincinnati: U.S. Army Corps of Engineers, Ohio River Division Laboratories, 1966: 6 − 8.
[37]	TEDESCO J W, HUGHES M L, ROSS C A. Numerical simulation of high strain rate concrete compression tests [J]. Computers & Structures, 1994, 51(1): 65 − 77.
[38]	ROSS C A. Split-Hopkinson pressure bar tests [R]. Florida: Air Force Engineering and Services Center Tyndall AFB FL Engineering and Services Lab, 1989: 38 − 53.
[39]	KLEPACZKO J R, BRARA A. An experimental method for dynamic tensile testing of concrete by spalling [J]. International Journal of Impact Engineering, 2001, 25(4): 387 − 409. doi: 10.1016/S0734-743X(00)00050-6
[40]	Richard J. Wasley. Stress wave propagation in solids [M]. New York: M. Dekker, 1973.
[41]	DU J, YON J H, HAWKINS N, et al. Fracture process zone for concrete for dynamic loading [J]. Materials Journal, 1992, 89(3): 252 − 258.

施引文献

资源附件(0)

图(13) / 表(3)

计量

文章访问数: 561
HTML全文浏览量: 98
PDF下载量: 146
被引次数: 0

混凝土动态力学行为数值模拟研究

通讯作者: 李晓琴(1983−)，女，云南丽江人，教授，博士，主要从事FRP加固混凝土结构抗爆炸和冲击研究(E-mail: Xiaoqin.Li@foxmail.com)

计量

出版历程

NUMERICAL ANALYSIS ON DYNAMIC MECHANICAL BEHAVIOR OF CONCRETE

计量

出版历程

目录

通讯作者:
李晓琴(1983−)，女，云南丽江人，教授，博士，主要从事FRP加固混凝土结构抗爆炸和冲击研究(E-mail: Xiaoqin.Li@foxmail.com)