Contact analysis in the presence of an ellipsoidal inhomogeneity within a half space
Contact analysis in the presence of an ellipsoidal inhomogeneity within a half space
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DOI：
10.1016/j.ijsolstr.2013.12.035
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发表时间：
2014-03
影响因子：
3.6
通讯作者：
Koffi Espoir Koumi;Lv Zhao;J. Leroux;T. Chaise;D. Nélias
中科院分区：
文献类型：
--
作者：
Koffi Espoir Koumi;Lv Zhao;J. Leroux;T. Chaise;D. Nélias
许多材料含有不均匀或夹杂物，这可能极大地影响其机械性能。例如，在复合材料或含有沉淀物的材料的情况下会遇到这种不均匀性。本文分析了椭球形状各向异性弹性不均匀接触问题的接触压力和次表面应力场。解释任何取向和材料性质的不均匀性是这项工作的主要新奇之处。提出的求解接触问题的半解析方法是基于EShelby的形式，并使用2D和3D快速傅立叶变换来加速计算。与经典有限元方法相比，大大减少了所需的时间和内存。该模型可以看作是一种将非均质溶液中的富集场叠加到均质问题中的富集场技术。可以很容易地定义由夹杂物组合而成的复杂几何形状。对弹性性质和几何特征对非均质性(尺寸、深度和取向)的影响进行了参数分析。该模型允许获得接触压力分布--受非均质存在的干扰--以及次表面和基质/非均质界面应力。结果表明，当接触深度小于接触半径的0.7倍时，接触表面以下夹杂物的存在对接触压力和次表面应力分布有显著影响。各向异性方向和材料参数也是影响弹性接触解的关键因素。在球形压头与含有中心位于接触中心正下方的单一非均匀的弹性半空间之间的法向接触的情况下，非均匀/基质界面上的法向应力主要是压应力。当椭球夹杂的轴线与接触问题的轴线不重合时，压力分布是不对称的。
Many materials contain inhomogeneities or inclusions that may greatly affect their mechanical properties. Such inhomogeneities are for example encountered in the case of composite materials or materials containing precipitates. This paper presents an analysis of contact pressure and subsurface stress field for contact problems in the presence of anisotropic elastic inhomogeneities of ellipsoidal shape. Accounting for any orientation and material properties of the inhomogeneities are the major novelties of this work. The semi-analytical method proposed to solve the contact problem is based on Eshelby’s formalism and uses 2D and 3D Fast Fourier Transforms to speed up the computation. The time and memory necessary are greatly reduced in comparison with the classical finite element method. The model can be seen as an enrichment technique where the enrichment fields from the heterogeneous solution are superimposed to the homogeneous problem. The definition of complex geometries made by combination of inclusions can easily be achieved. A parametric analysis on the effect of elastic properties and geometrical features of the inhomogeneity (size, depth and orientation) is proposed. The model allows to obtain the contact pressure distribution – disturbed by the presence of inhomogeneities – as well as subsurface and matrix/inhomogeneity interface stresses. It is shown that the presence of an inclusion below the contact surface affects significantly the contact pressure and subsurfaces stress distributions when located at a depth lower than 0.7 times the contact radius. The anisotropy directions and material data are also key elements that strongly affect the elastic contact solution. In the case of normal contact between a spherical indenter and an elastic half space containing a single inhomogeneity whose center is located straight below the contact center, the normal stress at the inhomogeneity/matrix interface is mostly compressive. Finally when the axes of the ellipsoidal inclusion do not coincide with the contact problem axes, the pressure distribution is not symmetrical.