Conformability of laminated beams with shear-lag effects on slightly corrugated elastic substrates

Conformability, defined as the ability of a device to maintain intimate contact with a substrate with a curvilinear surface, is crucial for bio-interfacing devices and more. Existing conformability theories typically treat devices as homogeneous beams, neglecting the multi-material laminated structures commonly used in practice. Such material heterogeneity can induce shear-lag effects when there is a large interlayer modulus mismatch, modifying stress transfer and bending behavior and rendering classical conformability predictions inaccurate. In this work, we develop a conformability theory that explicitly incorporates shear-lag mechanisms in multilayer laminated beams and validate the theory through finite-element analysis. A systematic parametric study is conducted to quantify the dependence of conformability on the material and geometric properties of the multilayer beam. In particular, we demonstrate that introducing a compliant intermediate layer can significantly enhance conformability under appropriate combinations of elastic mismatch and layer thickness.