大理岩有限变形分岔分析 English Version
Bifurcation analyses of finite/large deformation for a marble
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摘要: 应用有限变形理论的塑性可膨胀本构关系 ,对大理岩进行反对称变形分岔分析 ,得到分岔的应力公式、特征方程和剪切带存在条件。结合大理岩实验进行分析 ,结果表明 :此方法得到的剪切带角度和最小分岔应力在围压较高时与实测结果基本一致 ,但低围压时存在差异 ,说明其可应用于韧性变形的分析 ;此方法可以较好地分析岩石的峰前行为 ,但峰后存在差异 ,表明大理岩峰后可能存在二次或更高次的后继分岔。Abstract: The plastic dilatable constitutive relationship of finite/large deformation theory is used in present paper to analyze anti symmetric deformation of a marble. The stress formula, the eigenvalue equation and the condition that shear bands generate are obtained. In analyses of bifurcation behavior of a marble, it could be concluded that:(1)Under high confining pressures, angles of shear bands and the minimum critical stress of bifurcation are consistent well with those in experiments, while there are evident differences under low confining pressures, which shows the method is suitable for ductile material;(2) The method describes well the behaviors of marble before peak, but not after peak, which shows there probably are recursive bifurcations, such as secondary bifurcation, etc.
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