The present work provides a profound analytical and numerical analysis of the material properties of SFRC on the mesoscale as well as the resulting correlation structure taking into account the probabilistic characteristics of the fiber geometry. This is done by calculating the engineering constants using the analytical framework given by Tandon and Weng as well as Halpin and Tsai. The input parameters like fiber length, diameter and orientation are chosen with respect to their probability density function. It is shown, that they are significantly influenced by the fiber length, the fiber orientation and the fiber volume fraction. The verification of the analytically obtained values is done on a numerical basis. Therefore, a two-dimensional microstructure is generated and transferred to a numerical model. The advantage of this procedure is, that there are several fibers with different geometrical properties placed in a preset area. The results of the numerical analysis meet the analytically obtained conclusions. Furthermore, the results of the numerical simulations are independent of the assumption of a plane strain and plane stress state, respectively. Finally, the correlation structure of the elasticity tensor is investigated. Not only the symmetry properties of the elasticity tensor characterize the correlation structure, but also the overall transversely-isotropic material behavior is confirmed. In contrast to the influencing parameters, the correlation functions vary for a plane strain and a plane stress state.

中文翻译：

---

短纤维增强复合材料弹性张量的相关结构

目前的工作对 SFRC 的中尺度材料特性以及由此产生的相关结构进行了深入的分析和数值分析，同时考虑了纤维几何的概率特性。这是通过使用 Tandon 和 Weng 以及 Halpin 和 Tsai 给出的分析框架计算工程常数来完成的。输入参数如纤维长度、直径和方向是根据其概率密度函数选择的。结果表明，它们受纤维长度、纤维取向和纤维体积分数的显着影响。分析获得的值的验证是在数字基础上进行的。因此，生成二维微观结构并将其转换为数值模型。这个程序的优点是，有几种不同几何特性的纤维放置在预设区域。数值分析的结果符合分析得出的结论。此外，数值模拟的结果分别独立于平面应变和平面应力状态的假设。最后，研究了弹性张量的相关结构。不仅弹性张量的对称特性表征了相关结构，而且确认了整体横向各向同性材料行为。与影响参数相反，相关函数因平面应变和平面应力状态而异。此外，数值模拟的结果分别独立于平面应变和平面应力状态的假设。最后，研究了弹性张量的相关结构。不仅弹性张量的对称特性表征了相关结构，而且确认了整体横向各向同性材料行为。与影响参数相反，相关函数因平面应变和平面应力状态而异。此外，数值模拟的结果分别独立于平面应变和平面应力状态的假设。最后，研究了弹性张量的相关结构。不仅弹性张量的对称特性表征了相关结构，而且确认了整体横向各向同性材料行为。与影响参数相反，相关函数因平面应变和平面应力状态而异。而且还确认了整体横向各向同性材料行为。与影响参数相反，相关函数因平面应变和平面应力状态而异。而且还确认了整体横向各向同性材料行为。与影响参数相反，相关函数因平面应变和平面应力状态而异。