Analysis of bifurcation buckling and imperfections effect on the microbuckling of viscoelastic composites by HFGMC micromechanics

Two different approaches are presented for the prediction of the microbuckling of various types of viscoelastic composites under compression. In the first one, an incremental procedure in time is employed to establish, in conjunction with the Laplace's transform and its inversion, a determinant whose first complex root indicates the occurrence of the failure stress and strain of the composite (with no imperfections) at the critical time. In the second approach, the viscoelastic composite is assumed to possess, due to faulty manufacturing, imperfections. A perturbation expansion of the field in terms of a small parameter establishes a series of problems of various order. It is shown that the solutions of the zero and first-order problems yield, in conjunction with the Laplace's transform and its inversion, the imperfection growth with applied loading, which asymptotically approaches the bifurcation buckling stress of the viscoelastic composite. In both approaches a repeated application of the high-fidelity generalized method of cells (HFGMC) micromechanics is employed to obtain the solutions. The offered two analyses are verified and applied on bi-layered, continuous and short fiber viscoelastic composites, as well as on viscoelastic woven composites and lattice blocks. The latter two applications necessitate the employment of multiscale HFGMC micromechanical analyses since the yarns in the weaves and the elements of the lattices are themselves unidirectional viscoelastic composites.