Microbuckling of viscoplastic composites by the high-fidelity generalized method of cells micromechanics

The high-fidelity generalized method of cells (HFGMC) micromechanical analysis is employed for the prediction of microbuckling stresses of composite materials which are composed of elastic–viscoplastic constituents. The inelastic material behavior is represented by a unified viscoplasticity theory which can model non-proportional loading paths, namely it is capable of providing the effect of axial loading on the reduction of shear modulus which dominates the microbuckling. By applying an incremental procedure and in conjunction with the instantaneous stiffnesses of the viscoplastic material, an eigenvalue problem at each time step is established by the HFGMC micromechanical method, which is modified to include the buckling terms arising from the linearization of the nonlinear equations of equilibrium. These buckling terms are provided by HFGMC analysis which predicts the local stress field and the effective current tangent properties of the composite. The present approach is verified by comparison of its predictions with an exact solution that can be established in the special case of composites that consist of periodic viscoplastic layers. Applications are given for the prediction of the microbuckling stresses of bi-layered, continuously reinforced and aligned short-fiber viscoplastic composites. In addition, the microbuckling stresses of viscoplastic lattices and layered plates are presented.