Bending instability of a stiff lamella embedded in soft matrix

Sandwiched composite structures consisting of stiff lamella embedded in soft matrix are ubiquitous in nature and engineering, in which the instability of lamella is generally observed. Instead of the previously well-explored in-plane compression, a novel bending-induced instability in such sandwiched structure is investigated theoretically, numerically and experimentally in this manuscript. The theoretical model considers the non-linearity of both geometry and material to describe the finite bending of the sandwiched structure and makes use of the linear incremental theory to investigate the triggered instability. The high consistency among theoretical predictions, numerical simulations and experimental measurements of the wrinkling characteristics provides quantitative verification for the theoretical model. On this basis, the effects of the film position in the whole structure on the critical bending curvature and wrinkling characteristics are researched systemically. And finally, a phase diagram is established, enabling simple and intuitionistic prediction of bending instability characteristics from the geometric parameters of the system. These results might shed light on the underlying physical mechanisms of bending instability and provide design guidelines in some practical applications.