Post-buckling evolution of wavy patterns in trapezoidal film/substrate bilayers |
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| Institution: | 1. Institute of Mechanics and Computational Engineering, Department of Aeronautics and Astronautics, Fudan University, 220 Handan Road, Shanghai 200433, PR China;2. ESI Group, R&D, 99 Rue des Solets, 94513 Rungis, France;3. Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, LEM3, UMR CNRS 7239, Université de Lorraine, 7 Rue Félix Savart, BP 15082, 57073 Metz Cedex 03, France;1. Key Laboratory of Industrial Internet of Things & Networked Control, Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China;2. Department of Mathematics, Cornell University, Ithaca, NY, USA;1. Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA;2. Institute of Biomechanics and Medical Engineering, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;3. Department of Bioengineering, Stanford University, Stanford, CA 94305, USA |
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| Abstract: | This paper investigates quantitatively the post-buckling response of irregular wrinkles in a trapezoidal film/substrate bilayer. The geometric gradient can change the wrinkling profile to create ribbed and graded structural patterns with variations of wave direction, amplitude and wavelength. The tapered angle and edge dimension are examined numerically using a nonlinear shell/solid coupled finite element model that incorporates a path-following continuation technique, which explores their influences on secondary bifurcations, localization and surface mode transition. For instance, the competition between plate-like and beam-like post-buckling behavior is discussed. An analysis of graded amplitude is also provided based on Fourier envelope equations of beam/foundation models, which gives an insightful understanding of these fading wrinkles that differ from the ones usually observed in rectangular geometric cases. The results of this work can be used to guide the design of geometrically gradient film/substrate systems to achieve desired wavy instability patterns. |
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| Keywords: | Graded wrinkling Trapezoidal film/substrate Post-buckling Bifurcation |
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