Abstract
A comprehensive numerical study of three-dimensional surface instability patterns is presented. The formation of wrinkles is a consequence of deformation instability when a thin film, bonded to a compliant substrate, is subject to in-plane compressive loading. We apply a recently developed computational approach to directly simulate complex surface wrinkling from pre-instability to post-instability in a straightforward manner, covering the entire biaxial loading spectrum from pure uniaxial to pure equi-biaxial compression. The simulations use embedded imperfections with perturbed material properties at the film-substrate interface. This approach not only triggers the first bifurcation mode but also activates subsequent post-buckling states, thus capable of predicting the temporal evolution of wrinkle patterns in one simulation run. The state of biaxiality is found to influence the surface pattern significantly, and each bifurcation mode can be traced back to certain abrupt changes in the overall load–displacement response. Our systematic study reveals how the loading condition dictates the formation of various instability modes including one-dimensional (1D) sinusoidal wrinkles, herringbone, labyrinth, and checkerboard.
Highlights
A comprehensive numerical study of three-dimensional surface instability patterns is presented
When a thin film is bonded to a thick compliant substrate, parallel or more complex forms of wrinkles may develop if the thin film is under compression beyond a critical level
It is worth mentioning that the terms “direct numerical simulations” and “instability” used in this paper should not be mistaken as similar terminologies in the fluid mechanics literature
Summary
A comprehensive numerical study of three-dimensional surface instability patterns is presented. We apply a recently developed computational approach to directly simulate complex surface wrinkling from pre-instability to post-instability in a straightforward manner, covering the entire biaxial loading spectrum from pure uniaxial to pure equi-biaxial compression. The simulations use embedded imperfections with perturbed material properties at the film-substrate interface This approach triggers the first bifurcation mode and activates subsequent post-buckling states, capable of predicting the temporal evolution of wrinkle patterns in one simulation run. A common practice is to undertake a pre-instability linear modal analysis, followed by a separate post-instability analysis involving perturbations in geometry, boundary condition or mesh[15,24,25,26,27,28] In these approaches, the simulation process frequently involved prescribing a small wave pattern in the model, dictating subsequent evolution of wrinkle morphologies. Apparent similarities exist and one may draw analogies between the present surface instability analysis in solid materials and the studies of receptivity[39] or non-modal disturbance growth[40] in fluid mechanics
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