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一种新的混凝土各向异性弹塑性损伤本构模型及其数值实施

焦延涛 程立平

焦延涛, 程立平. 一种新的混凝土各向异性弹塑性损伤本构模型及其数值实施[J]. 工程力学, 2022, 39(8): 122-137. doi: 10.6052/j.issn.1000-4750.2021.04.0297
引用本文: 焦延涛, 程立平. 一种新的混凝土各向异性弹塑性损伤本构模型及其数值实施[J]. 工程力学, 2022, 39(8): 122-137. doi: 10.6052/j.issn.1000-4750.2021.04.0297
JIAO Yan-tao, CHENG Li-ping. A NEW ANISOTROPIC PLASTIC-DAMAGE MODEL AND ITS NUMERICAL IMPLEMENTATION FOR PLAIN CONCRETE[J]. Engineering Mechanics, 2022, 39(8): 122-137. doi: 10.6052/j.issn.1000-4750.2021.04.0297
Citation: JIAO Yan-tao, CHENG Li-ping. A NEW ANISOTROPIC PLASTIC-DAMAGE MODEL AND ITS NUMERICAL IMPLEMENTATION FOR PLAIN CONCRETE[J]. Engineering Mechanics, 2022, 39(8): 122-137. doi: 10.6052/j.issn.1000-4750.2021.04.0297

一种新的混凝土各向异性弹塑性损伤本构模型及其数值实施

doi: 10.6052/j.issn.1000-4750.2021.04.0297
基金项目: 华北水利水电大学高层次人才科研启动项目(40589)
详细信息
    作者简介:

    焦延涛(1983−),男,河南平顶山人,讲师,博士,从事混凝土损伤力学等相关研究(E-mail: tyjiao2000@sina.com)

    通讯作者:

    程立平(1981−),男,陕西渭南人,副教授,博士,副处长,从事非线性动力学及岩石力学等相关研究 (E-mail: 2839@pdsu.edu.cn)

  • 中图分类号: TU528.1;TU313

A NEW ANISOTROPIC PLASTIC-DAMAGE MODEL AND ITS NUMERICAL IMPLEMENTATION FOR PLAIN CONCRETE

  • 摘要: 该文的目的是建立一种新的、相对简单的混凝土各向异性塑性损伤本构模型,以方便的模拟混凝土结构的破坏行为。为了更好地描述混凝土在拉、压荷载作用下的不同损伤机制,建立了拉、压不同的两种损伤演化方程,用于确定各向异性的拉、压损伤变量。另外,根据应变等效假设,假定有效构型和损伤构型的应变相等,该方法不仅大大简化了模型的推导过程,而且可方便的通过解耦算法进行有效应力和损伤及名义应力的计算,也即塑性部分计算可通过现有的隐式算法实现,损伤部分及名义应力的计算则可通过较为简便的显式算法实现,从而可大大提高计算效率。模型结果与试验结果的对比分析表明:该模型能较好地描述混凝土在三维应力状态下的非线性行为;对双边开口四点弯曲梁试件的模拟也表明:该模型能反应混凝土损伤各向异性的特点,计算结果相比ABAQUS软件自带的混凝土损伤塑性本构模型(CDP模型)更符合实际情况,计算效率也更高。
  • 图  1  单轴拉伸荷载作用下混凝土柱有效构型与名义构型对比

    Figure  1.  The comparison of the nominal and effective configurations of cylindrical bar under uniaxial tension

    图  2  单轴荷载作用下混凝土力学特性

    Figure  2.  Concrete behavior under uniaxial

    图  3  文献[39]试验所得有效构型及名义构型中应力-应变曲线

    Figure  3.  Experimental stress-strain curves in the effective and nominal configurations from the experimental results of literature[39]

    图  4  本文模型计算的单轴压缩加载-卸载结果与文献[39]试验结果对比图

    Figure  4.  The model responses in uniaxial loading-unloading compression compared to experimental results presented in literature[39]

    图  5  本文模型计算的单轴拉伸加载-卸载结果与文献[40]试验结果对比图

    Figure  5.  The model responses in uniaxial loading-unloading tension compared to experimental results presented in literature[40]

    图  6  本文模型计算的单轴单调压缩加载结果与文献[39]试验结果对比图

    Figure  6.  The model responses in monotonic uniaxial compression compared to experimental results presented in literature[39]

    图  7  本文模型计算的单轴单调拉伸加载结果与文献[41]试验结果对比图

    Figure  7.  The model responses in monotonic uniaxial tension compared to experimental results presented in literature[41]

    图  8  本文模型计算的单轴及双轴单调压缩加载结果与文献[42]试验结果对比图

    Figure  8.  The model responses in monotonic uniaxial and biaxial compressive loading compared to experimental results reported by literature[42]

    图  9  文献[43]中双边开口混凝土梁试件采用的固定支座加载系统

    Figure  9.  The fixed loading supports of the DEN specimen in literature[43]

    图  10  双边开口混凝土梁试件三维有限元网格

    Figure  10.  3D mesh of the DEN specimen

    图  11  第1主应变方向对应的损伤区分布

    Figure  11.  Distribution of damage zone corresponding to the first principal strain direction

    图  12  第2主应变方向对应的损伤区分布

    Figure  12.  Distribution of damage zone corresponding to the second principal strain direction

    图  13  第3主应变方向对应的损伤区分布

    Figure  13.  Distribution of damage zone corresponding to the third principal strain direction

    图  14  文献[43]双边开口梁试验裂纹扩展路径

    Figure  14.  Crack modes reported in literature[43]

    图  15  由CDP模型计算的拉损伤云图

    Figure  15.  Distribution of damage in tension calculated by CDP model

    图  16  由CDP模型计算的压损伤云图

    Figure  16.  Distribution of damage in compression calculated by CDP model

    表  1  根据文献[39]试验结果得到的材料参数

    Table  1.   Material constants identified from the experimental results[39]

    材料参数数值材料参数数值
    初始弹性
    模量${E_0}/{\rm{GPa}} $
    31.00峰值应力$f_{\rm u}^ -$对应应变$\varepsilon _{\rm u}^ - /( \times {10^{ - 3} })$−1.19
    初始未损伤弹性模量${ {\bar E}_0}/{\rm{GPa}} $33.08极限应变$\varepsilon _{\rm f}^ - /( \times {10^{ - 3} })$−8.53
    泊松比ν0.20压缩硬化参数Q/MPa57.50
    初始损伤d00.063压缩硬化参数b1,082
    单轴抗压屈服
    强度$f_0^ - /{\rm{MPa}} $
    −17.08控制压缩应力-应变
    曲线形状参数c1
    3.21
    单轴受压峰值
    应力$f_{\rm u}^ - /{\rm{MPa} }$
    −28.13控制压缩应力-应变
    曲线形状参数c2
    −0.12
    注:Qb分别代表单轴压缩饱和应力及饱和率,用来控制单轴压缩时硬化曲线的形状。
    下载: 导出CSV

    表  2  根据文献[40]试验结果得到的材料参数表

    Table  2.   Material constants identified from the experimental results of literature[40]

    材料参数数值材料参数数值
    初始弹性
    模量${E_0}/{\rm{GPa} } $
    31.00 抗拉强度$f_0^ + $对应
    应变$\varepsilon _0^ + /( \times {10^{ - 4}}) $
    1.12
    初始未损伤弹性
    模量${ {\bar E}_0}/{\rm{GPa}} $
    33.08 拉伸硬化参数${h^ + }/{\rm{MPa} } $ 2,733
    泊松比ν 0.20 控制拉伸应力-应变曲线形状参数${\alpha _u} $ 4.14
    初始损伤d0 0.063 控制拉伸应力-应变曲线形状参数a 0.05
    单轴抗拉
    强度$f_0^ + /{\rm{MPa}} $
    3.47
    注:h+表示单轴拉伸饱和应力,用来控制单轴拉伸时硬化曲线的形状。
    下载: 导出CSV

    表  3  单轴单调压缩试验所用材料参数表

    Table  3.   Material properties used for the monotonic uniaxial compressive test

    材料参数数值材料参数数值
    初始弹性模量${E_0}/{\rm{GPa}}$31.70峰值应力$f_{\rm u}^ -$对应应变$\varepsilon _{\rm u}^ - /( \times {10^{ - 3} })$−1.61
    初始未损伤弹性模量${ {\bar E}_0}/{\rm{GPa}}$33.83极限应变$\varepsilon _{\rm f}^ - /( \times {10^{ - 3} })$−7.23
    泊松比ν0.20压缩硬化参数Q/MPa27.58
    初始损伤d00.063压缩硬化参数b1,655
    单轴抗压屈服强度$f_0^ - /{\rm{MPa}}$−11.74控制压缩应力-应变曲线形状参数c13.00
    单轴受压峰值应力$f_{\rm u}^ - /{\rm{MPa} }$−29.13控制压缩应力-应变曲线形状参数c2−1.96
    注:Qb分别代表单轴压缩饱和应力及饱和率,用来控制单轴压缩时硬化曲线的形状。
    下载: 导出CSV

    表  4  单轴单调拉伸加载试验所用材料参数表

    Table  4.   Material parameters used for the monotonic uniaxial tensile test

    材料参数数值材料参数数值
    初始弹性模量E0/GPa31.00抗拉强度$f_0^ + $对应应变$\varepsilon _0^ + /( \times {10^{ - 4}}) $1.24
    初始未损伤弹性模量${\bar E_0}/{\rm{GPa}}$33.08拉伸硬化参数${h^ + }/{\rm{MPa}}$14,600
    泊松比ν0.20控制拉伸应力-应变
    曲线形状参数${\alpha _{\rm u}}$
    4.20
    初始损伤d00.063控制拉伸应力-应变
    曲线形状参数a
    0.05
    单轴抗拉强度$f_0^ + /{\rm{MPa}}$3.84
    注:表示h+单轴拉伸饱和应力,用来控制单轴拉伸时硬化曲线的形状。
    下载: 导出CSV

    表  5  双轴压缩加载试验所用材料参数表

    Table  5.   Material constants used for the biaxial compressive test

    材料参数数值材料参数数值
    初始弹性模量${E_0}/{\rm{GPa}}$32.00单轴抗压屈服强度$f_0^ - /{\rm{MPa }}$−15.82
    初始未损伤弹性模量${ {\bar E}_0}/{\rm{GPa}}$34.15单轴受压峰值应力$f_{\rm u}^ - /{\rm{MPa} }$−33.50
    泊松比ν0.20峰值应力$f_{\rm u}^ -$对应应变$\varepsilon _{\rm u}^ - /( \times {10^{ - 3} })$−1.77
    初始损伤d00.063极限应变$\varepsilon _{\rm f}^ - /( \times {10^{ - 3} })$−6.81
    单轴抗拉强度$f_0^ + /{\rm{MPa}}$2.88压缩硬化参数${Q^ - }/{\rm{MPa}}$39.14
    抗拉强度$f_0^ + $对应应变$\varepsilon _0^ + /( \times {10^{ - 4}}) $0.91压缩硬化参数b875.97
    拉伸硬化参数h+/MPa13,175控制压缩应力-应变曲线形状参数c13.59
    控制拉伸应力-应变曲线形状参数${\alpha _{\rm u}}$1.07控制压缩应力-应变曲线形状参数c2−5.05
    控制拉伸应力-应变曲线形状参数a0.05
    注:h+表示单轴拉伸饱和应力,用来控制单轴拉伸时硬化曲线的形状;Qb分别代表单轴压缩饱和应力及饱和率,用来控制单轴压缩时硬化曲线的形状。
    下载: 导出CSV

    表  6  双边开口混凝土梁试件断裂数值模拟材料参数

    Table  6.   Material parameters used for the DEN specimen fracture simulation

    材料参数数值材料参数数值
    初始弹性模量${E_0}/{\rm{GPa}} $30.00单轴抗压屈服强度$f_0^ - /{\rm{MPa }} $−20.00
    初始未损伤弹性模量${ {\bar E}_0}/{\rm{GPa}} $32.02单轴受压峰值应力$f_{\rm u}^ - /{\rm{MPa} }$−46.60
    泊松比ν0.20峰值应力$f_{\rm u}^ -$对应应变$\varepsilon _{\rm u}^ - /( \times {10^{ - 3} })$−2.31
    初始损伤d00.063极限应变$\varepsilon _{\rm f}^ - /( \times {10^{ - 3} })$−17.73
    单轴抗拉强度$f_0^ + /{\rm{MPa}} $3.44压缩硬化参数${Q^ - }/{\rm{MPa}} $60.98
    抗拉强度$f_0^ + $对应应变$\varepsilon _0^ + /( \times {10^{ - 4}}) $1.19压缩硬化参数b837.00
    拉伸硬化参数h+/MPa13,552控制压缩应力-应变曲线形状参数c123.35
    控制拉伸应力-应变曲线形状参数${\alpha _{\rm u}}$3.43控制压缩应力-应变曲线形状参数c2−29.78
    控制拉伸应力-应变曲线形状参数a0.05
    注:h+表示单轴拉伸饱和应力,用来控制单轴拉伸时硬化曲线的形状;Qb分别代表单轴压缩饱和应力及饱和率,用来控制单轴压缩时硬化曲线的形状。
    下载: 导出CSV

    表  7  CDP模型计算时所用混凝土弹塑性参数

    Table  7.   Elasto-plastic mechanic parameters of concrete used by CDP model

    材料参数数值材料参数数值
    弹性模量E/GPa32.0流动势偏心率e0.1
    泊松比ν0.2粘性耗散系数$\mu $0.0005
    双轴极限抗压强度与单轴抗压强度之比fb0/fc01.16拉伸子午面上与压缩
    子午面上的第二应力
    不变量之比K
    0.6667
    膨胀角$\psi $/(°)30.0
    下载: 导出CSV

    表  8  CDP模型计算时所用混凝土损伤参数

    Table  8.   Damage parameters of concrete used by CDP model

    压缩屈服
    强度/MPa
    非弹性
    应变/(×10−3)
    压损伤
    因子
    拉伸屈服
    强度/MPa
    非弹性
    应变/(×10−3)
    拉损伤
    因子
    20.00 0.00 0.00 2.49 0.00 0.00
    31.67 0.10 0.06 1.43 0.12 0.11
    38.70 0.21 0.09 0.94 0.23 0.26
    43.83 0.37 0.14 0.67 0.34 0.41
    45.92 0.74 0.24 0.46 0.54 0.59
    43.35 1.16 0.33 0.38 0.67 0.67
    32.17 2.30 0.51 0.30 0.90 0.78
    19.08 3.88 0.69 0.26 1.10 0.86
    14.54 4.80 0.77 0.18 1.78 0.94
    7.10 8.12 0.91 0.16 2.12 0.95
    4.41 11.66 0.97 0.14 2.50 0.96
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-04-20
  • 录用日期:  2021-11-05
  • 修回日期:  2021-10-28
  • 网络出版日期:  2021-11-05
  • 刊出日期:  2022-08-25

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