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Finite element analysis of a compliance of a three dimensional crack in an anisotropic material.

機(jī)譯：各向異性材料中三維裂紋柔度的有限元分析。

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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.
機(jī)譯：在各種工程應(yīng)用中使用的材料通常是各向異性的。裂紋可能會(huì)出現(xiàn)，并且通常會(huì)降低剛度。剛度的降低在連續(xù)力學(xué)中很重要。關(guān)鍵問題是一個(gè)裂紋對整體剛度降低的貢獻(xiàn)?？梢愿鶕?jù)裂紋順應(yīng)張量（或裂紋的COD張量）B方便地進(jìn)行有效特性的分析，這取決于裂紋的大小和形狀，基體的彈性，如果是各向異性基體，則取決于基體的彈性。裂紋相對于矩陣各向異性軸的方向。對于尺寸有限的物體，它還取決于物體的幾何形狀。二維（2-D）正交各向異性固體的B張量以矩陣的坐標(biāo)系x 1 x 2表示，是常數(shù)，與裂紋取向無關(guān)。該研究的中心點(diǎn)是驗(yàn)證以下假設(shè)：在三維（3-D）橫向各向同性固體中，B張量近似恒定。建立了有限元模型來模擬二維和三維“一分錢”形裂紋分析。首先在二維模型上進(jìn)行方法開發(fā)，然后將數(shù)據(jù)與分析已知的解決方案進(jìn)行比較。關(guān)于張量分量的三維分析，針對0°-90°裂紋取向的各向異性橫向橫觀各向同性固體，進(jìn)行了幾種分析。

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