弹塑性介质中圆柱形空腔的收缩和膨胀:基于位错的方法

IF 3.4 2区 工程技术 Q2 ENGINEERING, GEOLOGICAL International Journal for Numerical and Analytical Methods in Geomechanics Pub Date : 2024-08-28 DOI:10.1002/nag.3825
Yue Gao, Emmanuel Detournay
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引用次数: 0

摘要

弹塑性介质中圆柱形空腔的收缩或膨胀通常采用基于连续体的塑性构造模型进行分析。然而,在实验室测试中,可以观察到螺旋状断裂形式的局部变形,这种变形源于土工材料的破坏后软化响应。本文介绍了另一种基于位错理论的空腔收缩或膨胀建模方法。在该模型中,在线性弹性介质中,几条等间距的螺旋形剪切裂缝从空腔开始并向外扩展。对剪切裂缝施加莫尔-库仑准则和扩张规则,以限制应力和位移跳跃。断裂扩展的方向通过最小化塑性耗散来确定。采用位移不连续法对沿断裂的剪切和法向位移跳跃进行离散化,并对问题进行数值求解。计算得出的裂纹路径呈对数螺旋状,与塑性理论预测的滑移线相似。随着断裂分支数量的增加,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法靠拢。
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Contraction and expansion of a cylindrical cavity in an elastoplastic medium: A dislocation-based approach

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.

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来源期刊
CiteScore
6.40
自引率
12.50%
发文量
160
审稿时长
9 months
期刊介绍: The journal welcomes manuscripts that substantially contribute to the understanding of the complex mechanical behaviour of geomaterials (soils, rocks, concrete, ice, snow, and powders), through innovative experimental techniques, and/or through the development of novel numerical or hybrid experimental/numerical modelling concepts in geomechanics. Topics of interest include instabilities and localization, interface and surface phenomena, fracture and failure, multi-physics and other time-dependent phenomena, micromechanics and multi-scale methods, and inverse analysis and stochastic methods. Papers related to energy and environmental issues are particularly welcome. The illustration of the proposed methods and techniques to engineering problems is encouraged. However, manuscripts dealing with applications of existing methods, or proposing incremental improvements to existing methods – in particular marginal extensions of existing analytical solutions or numerical methods – will not be considered for review.
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