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A circular Eshelby inclusion with linear eigenstrains interacting with a coated non-parabolic inhomogeneity with internal uniform anti-plane stresses
European Journal of Mechanics - A/Solids ( IF 4.1 ) Pub Date : 2021-01-18 , DOI: 10.1016/j.euromechsol.2021.104219
Xu Wang , Ping Yang , Peter Schiavone

We establish criteria which guarantee the uniformity of stresses inside a coated non-parabolic open inhomogeneity located in the vicinity of a circular Eshelby inclusion undergoing linear anti-plane eigenstrains when the surrounding matrix is subjected to uniform remote anti-plane stresses. The associated inverse problem in anti-plane elasticity which identifies the required geometry of the constituents of the composite is successfully solved using conformal mapping techniques and analytic continuation. Three conditions on the remote loading in the matrix, uniform eigenstrains imposed on the non-parabolic inhomogeneity and linear eigenstrains imposed on the circular Eshelby inclusion for given geometric and material parameters of the composite are found in order to ensure the uniformity of internal stresses. The internal uniform stress field is found to be independent of the specific open shapes of the inhomogeneity-coating and coating-matrix interfaces, the shear modulus of the coating and also of the existence of the nearby circular Eshelby inclusion. However, the open shapes of the two interfaces are significantly influenced by the presence of the circular Eshelby inclusion. We also discuss the general case in which arbitrary polynomial eigenstrains are imposed on the circular Eshelby inclusion.



中文翻译:

具有线性特征应变的圆形Eshelby夹杂物与具有均匀内部反平面应力的涂层非抛物线不均匀性相互作用

我们建立了标准,当周围的基体受到均匀的远程反平面应力时,可以保证位于圆形埃舍尔比夹杂物附近的涂层非抛物线形开放非均质内部的应力均匀,该埃舍比圆形夹杂物经受线性反平面特征应变。使用共形映射技术和解析连续性成功解决了反平面弹性中确定复合材料成分所需几何形状的相关逆问题。对于复合材料的给定几何和材料参数,找到了三种条件,分别是矩阵的远程载荷,施加于非抛物线型不均匀性的均匀特征应变和施加于圆形埃舍尔比夹杂物的线性特征应变,以确保内部应力的均匀性。发现内部均匀应力场与不均匀涂层和涂层-基质界面的特定开口形状,涂层的剪切模量以及附近圆形埃舍尔比夹杂物的存在无关。但是,两个圆形界面的开放形状会受到圆形Eshelby夹杂物的影响。我们还讨论了将任意多项式特征应变强加到圆形Eshelby包含项的一般情况。

更新日期:2021-02-12
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