A NEW STOCHASTIC DAMAGE CONSTITUTIVE MODEL OF CONCRETE CONSIDERING STRAIN RATE EFFECT
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摘要: 混凝土材料组分复杂且具有随机分布的特点, 其受力力学行为不可避免地存在非线性和随机性. 同时, 在动力荷载作用下, 混凝土材料具有不可忽视的率敏感性. 为了综合反映混凝土受力力学行为中的非线性、随机性与率敏感性, 本文从对材料的纳-微观裂纹扩展分析入手, 引入速率过程理论描述纳观裂纹的扩展速率, 并研究了对应的能量耗散过程. 在此基础上通过裂纹层级模型将纳观分析推演到微观尺度, 建立了微观能量耗散的基本表达式. 进而与微-细观随机断裂模型相结合, 形成了混凝土纳-微-细观随机损伤本构模型. 同时, 基于速率相关势垒的分析, 揭示了动力强度的提高源自加载速率和原子键断裂速率的竞争机制. 据此, 假定微裂纹间相互作用与应变率比值的相关关系以建立微弹簧能量耗散速率与应变率的联系, 实现了从静力本构模型向动力本构模型的扩展. 数值算例表明, 建议模型能够同时反映混凝土材料力学行为中的非线性、随机性和率敏感性. 最后通过与相关试验结果的对比, 验证了建议模型的正确性.Abstract: Due to the complex and randomly distributed components of concrete materials, the mechanical behavior of concrete materials inevitably exhibits nonlinearity and randomness. In addition, the mechanical properties of concrete materials are sensitive to strain rates. This work established the nano-micro-meso stochastic damage model to comprehensively reflect the three basic properties of nonlinearity, randomness, and strain rate sensitivity in the mechanical behavior of concrete. By introducing the rate process theory to describe the growth rate of nano-cracks, the related energy dissipation process can be obtained. The nanoscale analysis is upscaled to the micro scale by a crack hierarchy model, and the expression for micro energy dissipation is derived. The nano-micro-meso stochastic damage constitutive model for concrete was established by combining the micro energy dissipation expression with the micro-meso stochastic fracture model. In the meantime, a time-dependent energy barrier is used for analyzing the bond surviving probability under different loading rates. Assuming the evolution of reaction coordinate is governed by the Langevin equation, the surviving probability can be obtained by solving the corresponding Fokker-Planck-Kolmogorov equation. The results reveal that the increase of dynamic strength resulted from the competitive mechanism of loading rate and bond breaking rate. Since the first eigenvalue of the Fokker-Planck-Kolmogorov equation corresponds to the rate process theory, it is not applicable when the loading rate is too high. According to the analysis aforementioned, it is assumed that the interaction between micro-cracks is linearly related to the corresponding logarithmic strain rate, so the energy dissipation rate of the micro-spring is related to the strain rate, extending from the static constitutive model to the dynamic constitutive model. Numerical examples show that the proposed model can simultaneously reflect the nonlinearity, randomness, and strain rate sensitivity in the mechanical behavior of concrete materials. The correctness of the proposed model is verified by comparison with the relevant experimental results.
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Key words:
- concrete /
- constitutive model /
- stochastic damage /
- strain rate effect
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图 6 不同加载速率下F随
$\delta /{\delta _c}$ 的变化曲线Figure 6. Evolution of F with
$\delta /{\delta _c} $ under different loading rates
图 7 不同应变率下单轴受拉应力应变曲线均值和标准差对比
Figure 7. Comparison of mean and standard deviation of uniaxial tension stress-strain curves under different strain rates
图 8 不同应变率下一典型样本
${E_f} $ 随应变的演化Figure 8. Evolution of
${E_f}$ with strain of a tipical sample under different loading rates
图 10 不同应变率下单轴受压应力应变曲线均值和标准差对比
Figure 10. Comparison of mean and standard deviation of uniaxial compression stress-strain curves under different strain rates
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