Equivalent inclusion method for arbitrary cavities or cracks in an elastic infinite/semi-infinite space
Equivalent inclusion method for arbitrary cavities or cracks in an elastic infinite/semi-infinite space
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弹性无限/半无限空间中任意空腔或裂纹的等效包含法
DOI：
10.1016/j.ijmecsci.2020.106259
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发表时间：
2021-04
影响因子：
7.3
通讯作者：
Nhan Phan-Thien
中科院分区：
文献类型：
--
作者：
Yang Wanyou;Zhou Qinghua;Wang Jiaxu;Khoo Boo Cheong;Nhan Phan-Thien
在弹性岩体中开挖的无地表效应和有地表效应的浅埋隧道，力学上通常分别简化为带孔洞的弹性无限或半无限平面问题。本文将Eshelby提出的用于计算非均匀材料中夹杂引起的弹性场的经典方法--等效夹杂法（EIM）推广到计算任意形状孔洞引起的弹性场。与非均匀性问题类似，空洞问题的EIM方法的实现是将弹性模量为零的空洞作为与基体材料性质相同但含有本征应变的夹杂物处理。基于由本征应力产生的本征应变的基本解，可以借助于数值离散化和每个离散单元的贡献的叠加来计算代表任意形状的空腔。当圆孔或矩形孔的上下表面之间的距离接近无穷小但不为零时，可将圆孔或矩形孔简化为裂纹，从而用本文提出的求解方法也可求解裂纹引起的弹性场。对孔洞和裂纹的计算结果与有限元法的计算结果吻合较好。参数分析的深度，长度的裂纹和多个空腔和裂纹之间的相互作用的弹性场的影响表明，EIM作为一个很好的潜在的应用在一些重要的应用断裂行为的开挖材料。
Shallow tunnels free of or subjected to the surface effects excavated in an elastic rock mass are usually simplified as an elastic infinite or semi-infinite plane problem with cavities in mechanics, respectively. In this paper, the equivalent inclusion method (EIM), a classic solution due to Eshelby usually used for predicting the elastic field caused by inhomogeneities embedded in a heterogeneous material, is extended to predict the elastic field induced by an arbitrarily shaped cavity. Similar to that of the inhomogeneity problems, the implementation of the EIM for the cavity problem is conducted by treating a cavity whose elastic modulus is zero as an inclusion having identical material properties to the matrix but containing eigenstrains. Based on an elementary solution for the eigenstress arising from the eigenstrains representing the cavity of an arbitrary shape can be calculated with the help of numerical discretization and superposition of contributions from each discretized element. A circular or rectangular cavity can be reduced to a crack when the distance between their upper and lower surfaces approaches an infinitesimal but not a zero value, hence the elastic field caused by cracks can be also resolved with the proposed solution method. The results obtained with the proposed method and the finite element method (FEM) for both the cavity and the crack are in good agreements. Parametric analyses on the effects of depth, length of the crack and the interactions among multiple cavities and cracks on the elastic field demonstrates the EIM as a good potential application in some significant applications in fracture behaviors for the excavated material.
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