The effect of local and random fiber waviness on the microbuckling of composite materials

A methodology which is capable of predicting the microbuckling of various types of composite materials containing several randomly located fiber waviness of spatially varying amplitudes is presented. This methodology forms a more realistic modeling over standard micromechanical analyses of composites based on the periodic microstructure assumption, implying that the waviness is necessarily periodic of the same amplitude. The proposed approach is based on the combined applications of a perturbation expansion on the nonlinear governing equations, the representative cell method and the high-fidelity generalized method of cell (HFGMC) micromechanics. The application of perturbation expansion on the nonlinear equations yields a zero-order linear problem, which is solved by the standard HFGMC analysis, and a first-order linear problem which is coupled to the former. In the framework of the representative cell method the composite is divided into numerous cells and the application of the discrete Fourier transform reduces the first-order problem to the problem of a single cell in the transform domain. The resulting governing equations, formulated in the transform domain, are solved by the extended HFGMC approach. The inversion of the transform yields, in particular, the waviness growth (which depends on the number of wavy fibers and their amplitude distribution) with the increase of externally applied compressive loading on the composite. The proposed analysis provides an estimate of the actual failure stress of the composite with respect to its ideal bifurcation buckling stress and the detailed stress distribution. The offered analysis is applied on bi-layered, continuous and short-fiber composites, as well as on two and three-dimensional lattice blocks.