From period-doubling to folding in stiff film/soft substrate system: The role of substrate nonlinearity |
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| Affiliation: | 1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;2. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;3. Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;1. Institut za fiziku, Bijenička 46, 10000 Zagreb, Croatia;2. Center for Functional Nanomaterials, Brookhaven National Lab, Upton, NY 11973, USA;3. Center of Excellence for Advanced Materials and Sensing Devices, Institut za fiziku, Bijenička 46, 10000 Zagreb, Croatia;1. Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA;2. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305, USA;3. Department of Bioengineering, Stanford University, Stanford, CA 94305, USA;4. Department of Cardiothoracic Surgery, Stanford University, Stanford, CA 94305, USA;1. Laboratoire de Mécanique des Solides, C.N.R.S. UMR7649 & Département de Mécanique, École Polytechnique, ParisTech, 91128 Palaiseau Cedex, France;2. Aerospace Engineering Department & Mechanical Engineering Department (emeritus), The University of Michigan, Ann Arbor, MI 48109-2140, USA;1. Institute of Biomechanics and Medical Engineering, AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China;2. Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China |
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| Abstract: | Uniaxial compressed stiff films on soft substrates can evolve into the period-doubling and folding instabilities, beyond the onset of sinusoidal wrinkling. The substrate is modeled as a neo-Hookean solid with a pre-stretch prior to film attachment, and its nonlinearity is obtained. Both the pre-stretch and the external nominal strain imposed on the film/substrate system can induce different substrate nonlinearity, and thus have different effects on the post-buckling mode evolution of the system. This study shows that the critical strain of period-doubling instability is linear to the pre-stretch. As the compressive nominal strain increases, the folding mode occurs beyond the onset of period-doubling in both the pre-tension and the pre-compression case, due to the softening/hardening effects for the inward/outward displacements generated by the positive substrate nonlinearity. |
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| Keywords: | Period-doubling Folding neo-Hookean Substrate nonlinearity Pre-stretch |
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