Shear-lag model of laminated films with alternating stiff and soft layers wrinkling on soft substrates

Abstract

Multilayer laminated films, consisting of alternating stiff and soft layers, are widely used in flexible electronics and photonics. The extreme modulus mismatch between these layers can induce shear-lag effects, leading to mechanical behavior distinct from conventional Euler–Bernoulli beam theory. Compared to three-point bending, wrinkling on a soft substrate is an easier-to-implement approach for probing the elasticity of ultrathin films. In this work, we introduce a wrinkle-based metrology for directly measuring the equivalent flexural rigidity of laminated beams with shear-lag. An analytical framework is developed, demonstrating good agreement with experimental results. We systematically investigate the effects of the number of layers and layer properties within the film, and substrate modulus. Additionally, we propose a criterion to determine when the wrinkle-based metrology is more suitable than the traditional three-point bending test.