Geometrically Nonlinear Shell Analysis of Wrinkled Thin-Film Membranes with Stress Concentrations

Abstract

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling.Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns.

Localized Wrinkle Behavior near Fixed Boundaries in Flat and Cylindrical Membranes

“…Membrane wrinkling studies have focused mostly on certain effects on characteristics (i.e., gravity [7], creases [8], stress concentrations [9], etc). In general, wrinkling is analyzed as a membrane behavior event, and wrinkled geometry is computed for specific loads.…”

Modelling wrinkling interactions produced by patterned defects in metal thin films

“…Wrinkling patterns are commonly encountered in thin film structures and membranes subjected to local compressive stresses, either in loaded freestanding conditions [1,2] or via mechanical mismatches with substrates [3][4][5][6][7]. The pattern and its evolution can be controlled through different means of stress generation, e.g., applied lateral displacements [8,9], temperature variation [10], surface tension via liquid-solid interaction [11], and controllable residual stresses [12][13][14][15]. Specific wrinkling patterns can be designed to achieve desired functions in thin film systems, via changing surface morphology and roughness [16][17][18], wetting and adhesive properties [11,18], tuneable mechanical properties [19], and generating micro-fluidic channels [20].…”

“…Specific wrinkling patterns can be designed to achieve desired functions in thin film systems, via changing surface morphology and roughness [16][17][18], wetting and adhesive properties [11,18], tuneable mechanical properties [19], and generating micro-fluidic channels [20]. These wrinkling patterns manifest in structural [14,21], biological [6,22], electronic (e.g., 2D materials) [23], and metrology applications [3,9], but most modelling efforts treat materials as defect-free. Defects in such 2D and layered materials are common and may control the nucleation and propagation of wrinkling patterns [24][25][26][27][28].…”

Wrinkle-crease interaction behavior simulation of a rectangular membrane under shearing

“…The wrinkle is defined as the elastic response of a membrane due to localized buckling in compressed areas. The wrinkling of membrane structures has been well studied by using the membrane method [3][4][5][6][7][8] based on the tension field theory (TFT), the thin shell method [9][10][11][12][13][14] based on the buckling theory, and the explicit time integrate method [15,16].…”