In this paper we alleviate limitations of the conventional embedded reinforcement formulation for applications with dense fiber contents. We demonstrate that by condensing the fiber degrees of freedom during the assembly stage, the condition number of the resultant stiffness matrix is effectively reduced and the use of iterative solvers is facilitated even without preconditioning. Numerical benchmarks consisting of very large numbers of high aspect ratio discrete fibers are performed, and major advantages are reported in terms of the computational efficiency of the solution method. We apply the solution method to a set of examples in the modeling of the fiber reinforced composites, specifically the estimation of the homogenized mechanical properties of the discontinuous fiber composites and modeling of the compression molding process. In the latter case, a specimen containing more than 2 million discrete fibers is analyzed.

中文翻译：

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使用简化的嵌入公式对致密纤维增强材料进行有效分析

在本文中，我们减轻了传统嵌入增强配方在纤维含量高的应用中的局限性。我们证明，通过在组装阶段压缩纤维自由度，可以有效减少合成刚度矩阵的条件数，并且即使没有预处理也便于使用迭代求解器。执行由大量高纵横比离散纤维组成的数值基准，并报告了解决方法的计算效率方面的主要优势。我们将求解方法应用于纤维增强复合材料建模中的一组示例，特别是不连续纤维复合材料的均质力学性能的估计和压缩成型过程的建模。