Materials used in various engineering applications are often anisotropic. Cracks may develop in them, and they, generally, reduce stiffness. Degradation of stiffness is obvious importance in continuum mechanics. The key problem is contribution of one crack to the overall stiffness reduction. Analysis of effective properties can be conveniently done in terms of the crack compliance tensor (or COD tensor of a crack) B, which depends on crack size and shape, on the elastic properties of the matrix and, in case of anisotropic matrix, on the orientation of the crack with respect to the matrix anisotropy axes. In case of a body of finite size, it also depends on the body's geometry. B tensor for a two-dimensional (2-D) orthotropic solid, expressed in coordinate system x 1, x2 of the matrix, is constant , independent of crack orientation. The center point of this study is to verify the hypothesis that B tensor is approximately constant in three-dimensional (3-D) transversely isotropic solid.; A finite element models are established to simulate the two and three dimensional "penny-shaped" crack analyses. Method development is first performed on the 2-D model, and data are compared to the analytically known solutions. Three dimensional analysis of the B tensor components is performed in several, with respect to the extent of anisotropy, transversely isotropic solids for 0°-90° crack orientations.
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机译：在各种工程应用中使用的材料通常是各向异性的。裂纹可能会出现，并且通常会降低刚度。刚度的降低在连续力学中很重要。关键问题是一个裂纹对整体刚度降低的贡献。可以根据裂纹顺应张量（或裂纹的COD张量）B方便地进行有效特性的分析，这取决于裂纹的大小和形状，基体的弹性，如果是各向异性基体，则取决于基体的弹性。裂纹相对于矩阵各向异性轴的方向。对于尺寸有限的物体，它还取决于物体的几何形状。二维（2-D）正交各向异性固体的B张量以矩阵的坐标系x 1 x 2表示，是常数，与裂纹取向无关。该研究的中心点是验证以下假设：在三维（3-D）横向各向同性固体中，B张量近似恒定。建立了有限元模型来模拟二维和三维“一分钱”形裂纹分析。首先在二维模型上进行方法开发，然后将数据与分析已知的解决方案进行比较。关于张量分量的三维分析，针对0°-90°裂纹取向的各向异性横向横观各向同性固体，进行了几种分析。
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