Contact Analysis in Presence of Unidirectional Cylindrical Fibers Within a Matrix and Comparison With the Homogenized Anisotropic Solution

Abstract eng:
Depending on the size of the heterogeneities it could be interesting to explicitly account for the presence of inclusions, porosities or fibers in the contact problem [1,2]. Conversely when the size of this microstructure is very small in comparison to the contact area one may choose an homogenized method by assuming that the substrate behaves anisotropicaly [3,4]. The authors present here a comparison of the elastic problem solution when one of the bodies in contact contains unidirectional and cylindrical fibers, lying parallel to the surface, and with a diameter a few tenth of the contact radius. Figure 1a gives the pressure distribution of the frictionless contact problem of an homogeneous sphere pressed against a half-space, when the half-space contains 40% of unidirectional fibers of Young’s modulus then times higher than the matrix one. Since the cylindrical fibers are lying along the x-axis parallel to the surface, the contact problem could be also modeled as an anisotropic problem with a Young’s modulus depending on the orientation (E1≠ E2≠E3). The equivalent properties are obtained by the Mori-Tanaka homogenization method. A comparison of the subsequent contact patch obtained with both methods is given in Fig. 1b. One may conclude that the homogenized method provides only a very rough estimation of the real contact area and pressure distribution.

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