Browsing by Author "Nayyar, Vishal"
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Item Stretch-induced compressive stress and wrinkling in elastic thin sheets(2010-08) Nayyar, Vishal; Huang, Rui, doctor of civil and environmental engineering; Chandar, Krishnaswamy R.A finite element analysis approach is used to determine the susceptibility to wrinkles for thin sheets with clamped ends when subjected to tensile loading. The model problem chosen to do this analysis is the stretching of a thin sheet with clamped-ends. In the preliminary analysis, a stress analysis of thin sheets is done to study the stresses that develop under these boundary conditions. The analysis shows that there is a stretch-induced compressive stress in the transverse direction to the applied load that causes wrinkles. Then, the parametric study is conducted to determine the effect of aspect ratio and strain on the compressive stress. Based on the results of the parametric study, a critical strain value for each aspect ratio is determined for which the corresponding compressive stress is zero. Further buckling analysis is performed to find the buckling modes of the model problem that shows a limit of aspect ratio below which buckling is not possible under given conditions. Finally, post-buckling analysis shows the nature of wrinkles observed in the model problem for different aspect ratios.Item Stretch-induced wrinkling of thin sheets(2013-08) Nayyar, Vishal; Huang, Rui, doctor of civil and environmental engineering; Ravi-Chandar, K.Thin sheets and membrane structures are widely used in space applications such as solar sails, sunshields and membrane optics. Surface flatness over a large area is one of the key requirements for many applications using the flexible thin structures. However, wrinkles are commonly observed in thin sheets. It is thus important to understand the mechanics of thin sheets for practical applications that require reliable control of surface wrinkles. In this study, a model problem of stretch-induced wrinkling of thin sheets is considered. First, a two-dimensional (2-D) finite element model was developed to determine stretch-induced stress distribution patterns in hyperelastic thin sheets, assuming no wrinkles. As a prerequisite for wrinkling, development of compressive stresses in the transverse direction was found to depend on both the length-to-width aspect ratio of the sheet and the applied tensile strain. Next, an eigenvalue analysis was performed to predict the critical conditions for buckling of the elastic sheet under the prescribed boundary conditions, followed by a nonlinear post-buckling analysis to simulate evolution of stretch-induced wrinkles. Experiments were conducted to measure stretch-induced wrinkling of polyethylene thin sheets, using the three-dimensional digital image correlation (3D-DIC) technique. It was observed that the wrinkle amplitude first increased and then decreased with increasing nominal strain, in agreement with finite element simulations for a hyperelastic thin sheet. However, unlike the hyperelastic model, the stretch-induced wrinkles in the polyethylene sheet were not fully flattened at high strains (> 30%), with the residual wrinkle amplitude depending on the loading rate. The hyper-viscoelastic and the parallel network nonlinear viscoelastic material models were adopted for finite element simulations to improve the agreement with the experiments, including the wrinkle amplitude, residual wrinkles and rate dependence. Finally it is noted that wrinkling is sensitive to defects and material inhomogeneity in thin sheets. By varying the elastic stiffness in a narrow region, numerical simulations show drastically different wrinkling behavior, including the critical strain and evolution of wrinkle amplitude and wavelength. In conclusion, a comprehensive understanding of stretch-induced wrinkling is established, where geometry, material, and boundary conditions all play important roles.