A linear, periodic, three-dimensional shear-lag model of unidirectionally-reinforced composites that allows for fibre breakage, and matrix failure is proposed. Matrix failure can take the form of matrix splitting or interfacial debonding. A computationally efficient scheme for its solution is developed. This scheme exploits the translation invariance of the elastostatic fields due to failed elements in the periodic cell, and is asymptotically faster than the classical eigensolution-based approach. The new computational scheme is used to illustrate the influence of matrix failure on the elastostatic fields induced by small clusters of fibre breaks in several test problems. Monte Carlo simulations of fracture in model three-dimensional composite specimen with Weibull-distributed fibre segment strengths are also performed. Matrix failure is found to considerably alter fracture development, to weaken the median specimen, and to reduce the variability in composite strength.

中文翻译：

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一种代表三维纤维复合材料中纤维断裂和基体失效的断裂模拟快速算法

提出了一种允许纤维断裂和基体失效的单向增强复合材料的线性、周期性、三维剪切滞后模型。基质失效可以采取基质分裂或界面脱粘的形式。开发了其解决方案的计算有效方案。该方案利用了由于周期单元中的失效元素引起的弹性静力场的平移不变性，并且比经典的基于特征解的方法渐近地更快。新的计算方案用于说明在几个测试问题中基体失效对由小簇纤维断裂引起的弹性静力场的影响。还对具有威布尔分布的纤维段强度的模型三维复合材料试样中的断裂进行了蒙特卡罗模拟。