A Mixture Model for Unidirectionally Fiber-Reinforced Composites

Abstract

A binary mixture theory with microstructure is constructed for unidirectionally fiber-reinforced elastic composites. Model construction is based on an asymptotic scheme with multiple scales and the application of Reissner’s new mixed variational principle (1984). In order to assess the accuracy of the model, comparison of the mixture model predictions with available experimental data on dispersion of harmonic waves is made for boron/epoxy and tungsten/aluminum composites. Formulas for the effective moduli are also presented, and the results are compared with test data and other available predictions.

Computational multiple scattering analysis for shear wave propagation in unidirectional composites

“…Other theories so far formulated include the variational principles (Talbot and Willis, 1983), the differential (incremental) scheme (Beltzer and Brauner, 1987;Biwa et al, 2003), etc, for randomly arranged fiber composites. On the other hand, homogenization techniques based on asymptotic expansions or the Bloch theorem have been applied to wave propagation in composites with regular and periodic fiber arrangements (Nelson and Navi, 1975;Murakami and Hegemier, 1986;Naciri et al, 1994). Such periodic composites recently attract much attention regarding the phononic band gap structures and their acoustic applications (Kushwaha et al, 1993(Kushwaha et al, , 1994.…”

Wave dispersion and attenuation in fiber composites

“…In the ®rst category belong the works that consider the ®ber composite as a matrix containing periodically distributed inclusions and they predict its dynamic behaviour through homoginization techniques such those described e.g. in the effective stiffness theory of Achenbach and Herman (1968) and the mixture theory of Murakami and Hegemier (1972). The main problem with these theories is their restrictive applicability to cases where the microstructure (unit cell) of the periodic medium is much smaller than the wavelength of the wave propagating in the composite medium.…”

Characterization of heterogeneous solids via wave methods in computational microelasticity

“…Efforts towards modeling dispersion in fiber composites followed, from the work by Murakami and Hegemier (1986) to the more recent unit-cell based finite-element approach by Aberg and Gudmundson (1997). In addition, wave dispersion has been shown to be a common feature of geomaterials.…”