A new family of finite elements for wrinkling analysis of thin films on compliant substrates

This paper presents a new one-dimensional finite elements’ family for the analysis of wrinkling in stiff thin films resting on a thick elastic substrate. Euler–Bernoulli’s theory is used for the thin film, whereas the substrate is ideally divided into two parts: 1. a core layer in the neighbourhood of the film where the displacement field presents high gradients (where an higher-order approximation is required) and 2. the remaining part of the substrate or bottom layer where displacements change very slowly. Low-order models allow an accurate yet efficient description of this latter part. Due to its versatility and generality, Carrera’s Unified Formulation is used to develop the proposed elements’ family. Governing equations’ weak form is derived by means of the principle of virtual displacements and discretised in a finite element sense. The asymptotic numerical method is used to solve the resulting non-linear equations’ system. Numerical investigations show that the proposed one-dimensional elements are able to capture the instability phenomena in film-substrate systems. In order to validate the proposed finite element models, the critical loads and half-wave numbers predicted by the one-dimensional elements are compared with those obtained via two-dimensional finite element analyses and a very good agreement is found.