A fast algorithm for the elastic fields due to a single fiber break in a periodic fiber-reinforced composite

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• 作者：Ankit Gupta ; Sivasambu Mahesh ; Shyam M. Keralavarma
• 关键词：Composites ; Fracture ; Discrete Fourier transform ; Lattice models ; Circulant matrix ; Periodic boundary condition
• 刊名：International Journal of Fracture
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：204
• 期：1
• 页码：121-127
• 全文大小：
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Characterization and Evaluation of Materials; Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-2673
• 卷排序：204

文摘

The stress state in a shear-lag model of a unidirectional fiber composite with an arbitrary configuration of fiber breaks is obtained by the weighted superposition of the stress state due to a single broken fiber. In a periodic patch comprised of N fibers located at the points of a regular lattice, a method to determine the stress state due to a single break was proposed by Landis et al. (J Mech Phys Solids 48(3):621–648, 2000). This method entails the determination of the eigenspace of an \(N\times N\) matrix, at a computational cost of \(O(N^3)\). In the present work, an alternative algorithm is proposed. This algorithm exploits the circulant structure of the matrix describing the inter-fiber interactions. The asymptotic computational complexity of the present algorithm equals that of the discrete Fourier transform: \({O}(N \log N)\). Run times of the present method with the eigensolution based method are compared, and shown to be very favorable for the present method, even for small N. Power-law scaling of the overloads due to a single break to much larger distances than previously possible has been verified using the present method.