Bifurcation buckling and the effect of imperfections on the microbuckling of soft materials with periodic microstructure by the finite strain HFGMC micromechanics

Abstract

Two approaches are presented for the prediction of the microbuckling of composites subjected to compressive loading and undergoing large deformations. In the first one, the finite strain high-fidelity generalized method of cells (HFGMC) micromechanical analysis is successively implemented for the prediction of the ideal bifurcation buckling stress of the composite. In the second approach which considers composites which possesses imperfections (e.g. wavy fibers), a perturbation expansion is adopted. The resulting zero and first-order problems are solved by employing the finite strain HFGMC micromechanics. Here, the ideal critical stress can be readily predicted, and from the form of the waviness growth with applied loading it is possible to estimate the actual bifurcation stress. In addition, in the particular case of a multilayered periodic composites, an exact solution is derived for the prediction of the bifurcation buckling stress. This exact solution is employed to verify the micromechanically predicted critical stresses of bi-layered composites. For fiber-reinforced composites, a comparison with available finite element solution is utilized to verify the micromechanical predictions. Applications of the offered approaches are given for periodically bi-layered composites that consist of five types of hyperelastic materials, and two types for fiber-reinforced composites. The present methods are also implemented to predict the microbuckling stresses of a porous hyperelastic material and lattice blocks whose elements consist of a hyperelastic material.