具有长球体和扁球体的复合材料的平均场均匀化方案：方向张量的使用和应变二阶矩的计算
Mean field homogenization schemes for composites with prolate and oblate spheroids: use of the orientation tensors and computation of the strain second-moments
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中文总结 AI 辅助
研究含长球体和扁球体夹杂复合材料的均匀化刚度，利用二阶和四阶方向张量计算特定取向分布的均匀化刚度，并给出相关量对材料参数导数的计算公式，用于应变二阶矩计算。
中文摘要 AI 辅助
在本文中，我们给出了应用于含球体夹杂复合材料的Mori-Tanaka方案、Ponte-Castañeda和Willis方案的均匀化刚度。夹杂可以是长球体（“纤维”）或扁球体（“硬币形状”）。我们展示了如何使用二阶和四阶方向张量来计算特定球体取向分布的均匀化刚度。我们还提供了关于材料参数计算这些量的导数的公式，这对于计算应变的二阶矩特别有意义。
英文摘要
In this document we provide the homogenized stiffnesses from Mori-Tanaka scheme and Ponte-Casta{ñ}eda and Willis scheme applied to composites with spheroidal inclusions. The inclusions can be prolate spheroids ('fibers') or oblate spheroids ('penny-shapes'). We show how to compute the homogenized stiffnesses for particular distribution of spheroid orientations, using the second-order and fourth-order orientation tensors. We also provide formulas to compute the derivatives of these quantities w.r.t. the material parameters, which is of particular interest for computing the second-moments of the strains.
