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Contraction and expansion of a cylindrical cavity in an elastoplastic medium: A dislocation‐based approach
International Journal for Numerical and Analytical Methods in Geomechanics ( IF 3.4 ) Pub Date : 2024-08-28 , DOI: 10.1002/nag.3825
Yue Gao 1, 2 , Emmanuel Detournay 2
Affiliation  

The contraction or expansion of a cylindrical cavity in an elastoplastic medium is usually analyzed from a continuum based approach with a plasticity constitutive model. However, localized deformations, which are rooted in the post‐failure softening response of geomaterials, are observed in the form of spiral‐shaped fractures in laboratory tests. An alternative approach based on dislocation theory is introduced in this paper for modeling cavity contraction or expansion. In this model, several equally spaced spiral‐shaped shear fractures initiate and propagate away from the cavity within the linearly elastic medium. The Mohr‐Coulomb criterion and a dilatancy rule are imposed on the shear fractures to constrain the stresses and the displacement jumps. The direction of fracture propagation is determined by minimizing plastic dissipation. The displacement discontinuity method is used to discretize the shear and normal displacement jumps along the fracture and solve the problem numerically. The calculated crack path follows a logarithmic‐like spiral, similar to the slip lines predicted by plasticity theory. The relationship between the pressure and radial displacement at the cavity boundary converge towards the classical elastoplastic solution as the number of fracture branches increases.

中文翻译:


弹塑性介质中圆柱腔的收缩和膨胀:基于位错的方法



弹塑性介质中圆柱形空腔的收缩或膨胀通常通过基于连续介质的方法和塑性本构模型进行分析。然而,在实验室测试中以螺旋状裂缝的形式观察到源于岩土材料失效后软化响应的局部变形。本文介绍了一种基于位错理论的替代方法来模拟空腔收缩或膨胀。在该模型中,几个等距的螺旋形剪切裂缝在线弹性介质内产生并远离空腔传播。莫尔-库仑准则和剪胀规则应用于剪切断裂,以约束应力和位移跳跃。断裂扩展的方向是通过最小化塑性耗散来确定的。位移不连续法用于离散沿裂缝的剪切和法向位移跳跃并数值求解该问题。计算出的裂纹路径遵循对数螺旋线,类似于塑性理论预测的滑移线。随着裂缝分支数量的增加,空腔边界处的压力和径向位移之间的关系向经典弹塑性解收敛。
更新日期:2024-08-28
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