Strain localization due to structural softening during pressure sensitive rate independent yielding
Strain localization due to structural softening during pressure sensitive rate independent yielding
复制标题
压力敏感率无关屈服过程中由于结构软化而导致的应变局部化
DOI：
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发表时间：
2013
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通讯作者：
L. L. Pourhiet
中科院分区：
文献类型：
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作者：
L. L. Pourhiet
在给出与莫尔-库仑非关联弹塑性流动法则（MC 模型）相关的应变软化模型的完整解析解后，本文证明了这种流变学具有有限极限载荷，可以将强度下降作为边值问题求解。 MC 模型产生无量纲强度下降，这取决于三个参数：剪切带相对于带 a0 外最小主应力轴的方向、峰值摩擦角 f 和膨胀角 β。使用该应变软化模型获得的最大强度降低约为围压 p0。对于这种最弱的状态，剪切带的有效摩擦力从峰值时的 µini = 0.85 下降到软化阶段结束时的 µss = 0.64。在该模型中，考虑了厚剪切带，对于与精确库仑方向相对应的方向，没有获得最弱的状态。相反，最弱剪切带的方向系统地偏离库仑方向一个角度，该角度随着其内摩擦角的增加而增加。实现稳态所需的特征剪切应变是半解析量化的，在对地球有效的参数范围内，发现该应变约为 7�8%。这些数字是在实验室中观察到的典型数字，这让我们相信 MC 模型是一个很好的模型，而且可能是最简单的模型，用于在数字代码中定位应变，旨在对地球的脆性部分进行建模。
After giving a complete analytical solution for the strain softening model associated to Mohr-Coulomb non associated elasto-plastic flow rule (MC-model), the paper demonstrates that this rheology possesses a finite limit load which allows solving for strength drop as a boundary value problem. The MC-model produces a non-dimensional strength drop, which depends on three parameters: the orientation of the shear band versus the least principal stress axis outside the band a0, the peak friction angle f and the dilatation angle ?. The maximum reduction of strength obtained with that strain-softening model is on the order of the confining stress p0. For this weakest regime, the effective friction of the shear band drops from µini = 0.85 at peak to µss = 0.64 at the end of the softening phase. In this model, which considers thick shear bands, the weakest regime is not obtained for an orientation corresponding to the exact Coulomb orientation. Instead, the orientation of the weakest shear zone systematically deviates from the coulomb orientation by an angle, which rises with its internal friction angle. The characteristic shear strain needed to achieve steady state is quantified semi analytically and in the range of parameters valid for Earth, this strain is found to be of the order of 7�8%. These numbers are typical of what is observed in the laboratory, which give us confidence on that MC-model is a good and probably the simplest model to localize strain in numerical codes aimed at modeling the brittle part of the Earth.