Load-Absorption and Interaction of Two Filaments in a Fiber-Reinforced Material
This investigation is concerned with the interaction - as far as load-absorption is concerned - of a pair of identical and parallel elastic filaments in a fiber-reinforced composite material. The filaments are assumed to have uniform circular cross-sections, are taken to be semi-infinite, and...
| Summary: | This investigation is concerned with the interaction - as far
as load-absorption is concerned - of a pair of identical and parallel elastic
filaments in a fiber-reinforced composite material. The filaments are
assumed to have uniform circular cross-sections, are taken to be
semi-infinite, and are supposed to be continuously bonded to an all
around infinite matrix of distinct elastic properties. At infinity the
matrix is subjected to uniaxial tension parallel to the filaments. Two
separate but related problems are treated. In the first both filaments
extend to infinity in the same direction and their terminal cross-sections
are coplanar. In the second problem the filaments extend to infinity in opposite
directions and their terminal cross-sections need no longer be coplanar,
the two filaments being permitted to overlap partly. An approximate scheme
based in part on three-dimensional linear elasticity and developed originally
by Muki and Sternberg is employed in the analysis. The problems are ultimately
reduced to Fredholm integral equations which characterize the distribution
of the axial filament force. The integral equations are analyzed asymptotically and
numerically. Results are presented which show the variation of
filament force with position and the effect on this variation of various relevant
geometrical and material properties.
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