Computing wrinkling and restabilization of stretched sheets based on a consistent finite-strain plate theory

Mechanics of tension-induced film wrinkling and restabilization: a review

“…Differing from conventional buckling analysis usually based on the Föppl-von Kármán framework, models characterizing the large deformations of soft films should cover the post-buckling regime upon excess stretching. Here, we discuss an extended Föppl-von Kármán plate model proposed by Healey et al [33,34], a finite-strain thin sheet model presented by Taylor et al [71], and a consistent finite-strain plate model developed by Fu et al [70] in the prediction of wrinkling behaviour of highly stretched films.…”

“…They pointed out that the nonlinear in-plane terms in the geometric equations play a crucial role in the disappearance of wrinkles, since both SVK and FvK models follow the same Hooke’s material law. Furthermore, Fu et al [70] compared the computational results based on the consistent plate theory (CPT) in §4iii with EFvK model and shell models (S4R, S4R5 and S8R) in Abaqus for nHk and SVK materials, showing that the EFvK model may provide unreliable results in the post-buckling regime in some situations, as illustrated in figure 2 c . Fu et al [70] explained that the conventional thin plate models are almost based on some ad hoc kinematic and/or scaling assumptions, and as a result they are not consistent with the three-dimensional field equations.…”

“…Furthermore, Fu et al [70] compared the computational results based on the consistent plate theory (CPT) in §4iii with EFvK model and shell models (S4R, S4R5 and S8R) in Abaqus for nHk and SVK materials, showing that the EFvK model may provide unreliable results in the post-buckling regime in some situations, as illustrated in figure 2 c . Fu et al [70] explained that the conventional thin plate models are almost based on some ad hoc kinematic and/or scaling assumptions, and as a result they are not consistent with the three-dimensional field equations. For example, the deformation gradient of these FvK-type plate models is not a 3×3 matrix, and some plane stress assumptions (e.g.…”

“…To consider large deformations of soft films, some plate/shell theories accounting for finite in-plane strain [62][63][64][65] and advanced numerical methods [32,[66][67][68][69][70] for capturing multiple bifurcations in nonlinear post-buckling paths were developed. General mechanics models to characterize large deformations of thin films can be placed into three categories: extended Föppl-von Kármán plate model (EFvK) [32][33][34], finite-strain plate model derived from three-dimensional nonlinear elasticity [71][72][73][74], and consistent finite-strain plate model [64,65,70,75]. Besides, an analytical method based on Koiter stability theory to predict the isola-centre bifurcation points [43], and numerical analyses via the finite-element method to investigate wrinkling evolution in thin sheets [37], were conducted.…”

An asymptotic modeling and resolution framework for morphology evolutions of multiple-period post-buckling modes in bilayers

“…Inspired by Dai and Song [26]; Fu et al [30]; Wang et al [31,32], we develop an efficient and robust asymptotic modeling framework to solve complex instability problems in a neo-Hookean film-substrate system, and to predict non-linear morphology evolution with multiple mode transitions. With the expansion from the bottom surface in through-thickness direction based on 3D non-linear elasticity, our asymptotic model is consistent with the 3D energy principle for hyperelastic materials.…”