Homogenization method for discrete and periodic media: basic principle and specific asymptotic expansions.
Optical micrographies showing typical glass fiber-bundles used in industrial SMC: (a) top view of bundles, (b) cross-sections of bundles, (c) idealization of bundles geometry.
Modeling of bundle-bundle local interactions: side view of the interaction zone (b), top view of the interaction surface approximation for local moments evaluation (c).
Example of generated representative elementary volume , containing 437 bundles of length 25 mm . Open circles represent the connections location, lines represent the centerline of the bundles .
Approximation of the orientation distribution function given by the second-order orientation tensor in the case of a quasi-isotropic microstructure (, , ) (a), and of an oriented microstructure (, , ) (b).
Evolution of the relative orientation functions and with the major eigenvalue of the second order orientation tensor .
Typical experimental response of SMC of fiber content (Dumont et al., 2003): simple compression test (a) and a plane strain compression test (b), both performed at an axial strain rate -Comparison with the results of the micro-macro model.
Admissible range of values of parameters and determined from a unique simple compression test (Dumont et al., 2003; Le Corre et al., 2002).
Evolution of the normalized threshold viscosities with the volume fraction of bundles, comparison with experimental results obtained on an industrial SMC (Dumont et al., 2003): (a) axial component in simple compression (33sc), (b) axial component in plane strain compression (33ps), (c) lateral component in plane strain compression (22ps).
Influence of the axial strain-rate on the threshold stresses for a random suspension with various bundle content, comparison with experimental results of Dumont et al. (2003).
Influence of the orientation intensity , for fiber networks undergoing a plane strain deformation along , , and for : (a) components of , (b) components of .
Evolution of the fraction , where is the number of bundles such as and abscissa is a condition expressed in %—different bundle networks with and , submitted to four macroscopic strain rates: plane strain along , plane strain along , pure shear in direction 12, simple compression-(a) random orientation (, ), (b) rather oriented (, ), (c) very oriented (, ).
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