Onset of failure in a fiber reinforced elastomer under constrained bending

Fiber reinforced elastomers subjected to compressive loads are prone to failure initiated by fiber buckling, a phenomenon of great technological importance. A 2D bifurcation analysis for an infinite ply-reinforced elastomer, subjected to constrained bending, is hereby presented for determining the composite's critical (i.e. lowest) curvature and associated eigenmode. The study is complemented by a full 3D analysis of the same composite. More specifically, the onset of bifurcation analysis is based on the Bloch wave representation of the 3D eigenmode and the periodic, over a 2D unit cell, principal solution of the infinite, perfect composite subjected to constrained (i.e. its top layer is bonded to an inextensible metallic plate) bending. The critical curvature and corresponding eigenmode are found by minimizing the lowest bifurcation curvature as a function of the eigenmode's wavelengths. These semi-analytical results, based on a 2D Finite Element Method (F.E.M) representation of the unit cell, are found to be in remarkable agreement with the full 3D calculations of the corresponding imperfect composite, thus establishing the usefulness of the proposed analysis. A comparison of the numerical simulation results to some limited experimental data is also discussed.