Analysis of a method to compute mixed-mode stress intensity factors for non-planar cracks in three-dimensions
Analysis of a method to compute mixed-mode stress intensity factors for non-planar cracks in three-dimensions
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DOI：
10.1051/m2an/2023001
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Benjamin E. Grossman‐Ponemon;M. Negri;A. Lew
中科院分区：
文献类型：
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作者：
Benjamin E. Grossman‐Ponemon;M. Negri;A. Lew
在这项工作中，我们提出并证明了一种方法的结果，该方法使用从相互作用积分导出的函数来近似沿三维裂纹前沿的应力强度因子。我们首先证明泛函具有一对重要的性质。对于平方可积张量场，例如有限元解的梯度，泛函是定义明确且连续的。此外，应力强度因子代表了裂纹前沿函数空间中的此类函数。我们的第二个结果是通过我们的方法计算的数值应力强度因子的误差估计。泛函的后一个属性提供了数值应力强度因子的配方；我们将泛函应用于一组特定裂纹前沿变化的有限元近似梯度，并通过反转这些变化的质量矩阵来计算应力强度因子。
In this work, we present and prove results underlying a method which uses functionals derived from the interaction integral to approximate the stress intensity factors along a three-dimensional crack front. We first prove that the functionals possess a pair of important properties. The functionals are well-defined and continuous for square-integrable tensor fields, such as the gradient of a finite element solution. Furthermore, the stress intensity factors are representatives of such functionals in a space of functions over the crack front. Our second result is an error estimate for the numerical stress intensity factors computed via our method. The latter property of the functionals provides a recipe for numerical stress intensity factors; we apply the functionals to the gradient of a finite element approximation for a specific set of crack front variations, and we calculate the stress intensity factors by inverting the mass matrix for those variations.