A comparative analysis of numerical approaches to the mechanics of elastic sheets |
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Institution: | 1. School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, United States;2. Physics Department, University of Massachusetts Amherst, MA, United States;3. Kavli Institute for Bionano Science and Technology, Harvard University, Cambridge, MA, United States;1. Department of Mechanical Engineering, University of Tehran, Tehran, Iran;2. Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA;1. Centre de Recherche Public Henri Tudor, 29 Avenue John F. Kennedy, L-1855 Luxembourg-Kirchberg, Luxembourg;2. Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, LEM3, UMR CNRS 7239, Université de Lorraine, Ile du Saulcy, 57045 Metz Cedex 01, France;1. Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;2. Institute of Applied Physics and Computational Mathematics, Beijing 10094, China;3. Department of Aerospace Engineering, Iowa State University, Ames, IA 50011, USA;1. School of Civil Engineering, Wuhan University, 8 South Road of East Lake, Wuchang, 430072 Wuhan, PR China;2. Laboratoire d’Etude des Microstructures et de Mécanique des Matériaux, LEM3, UMR CNRS 7239, Université de Lorraine, Ile du Saulcy, 57045 Metz Cedex 01, France;3. Centre de Recherche Public Henri Tudor, 29, avenue John F. Kennedy, L-1855 Luxembourg-Kirchberg, Luxembourg;4. Laboratoire d’Ingénierie et Matériaux, LIMAT, Faculté des Sciences Ben M’Sik, Université Hassan II de Casablanca, Sidi Othman, Casablanca, Morocco |
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Abstract: | Numerically simulating deformations in thin elastic sheets is a challenging problem in computational mechanics due to destabilizing compressive stresses that result in wrinkling. Determining the location, structure, and evolution of wrinkles in these problems has important implications in design and is an area of increasing interest in the fields of physics and engineering. In this work, several numerical approaches previously proposed to model equilibrium deformations in thin elastic sheets are compared. These include standard finite element-based static post-buckling approaches as well as a recently proposed method based on dynamic relaxation, which are applied to the problem of an annular sheet with opposed tractions where wrinkling is a key feature. Numerical solutions are compared to analytic predictions of the ground state, enabling a quantitative evaluation of the predictive power of the various methods. Results indicate that static finite element approaches produce local minima that are highly sensitive to initial imperfections, relying on a priori knowledge of the equilibrium wrinkling pattern to generate optimal results. In contrast, dynamic relaxation is much less sensitive to initial imperfections and can generate low-energy solutions for a wide variety of loading conditions without requiring knowledge of the equilibrium solution beforehand. |
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Keywords: | Thin elastic sheets Wrinkling Finite element method Dynamic relaxation |
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