Study of bifurcation in a pressurized hyperelastic membrane tube enclosed by a soft substrate |
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| Institution: | 1. Centre for Theoretical Studies, Indian Institute of Technology Kharagpur, 721302, India;2. Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, 721302, India;1. Luxembourg Institute of Science and Technology, L-4362 Esch-sur-Alzette, Luxembourg;2. Department of Continuum Mechanics and Structural Analysis. University Carlos III of Madrid, 28911 Leganés, Spain;3. Faculty of Mechanical Engineering, Technion—Israel Institute of Technology, 32000 Haifa, Israel;1. UC Santa Barbara, USA;2. University of Liverpool, UK;1. KTH Mechanics, Royal Institute of Technology, SE-10044 Stockholm, Sweden;2. Department of Mechanical Engineering, and Center for Theoretical Studies, IIT Kharagpur, 721302, India;1. Czech Technical University in Prague, Faculty of Mechanical Engineering, Technická 4, 166 07, Prague, Czech Republic;2. Charles University in Prague, Faculty of Mathematics and Physics, Ke Karlovu 3, Prague, 121 16, Czech Republic;3. The College of Polytechnics Jihlava, Tolstého 16, Jihlava, 586 01, Czech Republic |
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| Abstract: | We model a perivascular supported arterial tube as a uniform cylindrical membrane tube enclosed by a soft substrate, and derive the solution bifurcation criterion. We assume the surrounding soft substrate as an elastic foundation with distributed stiffness. We consider the tube to be a neo-Hookean material with isotropic and anisotropic (orthotropic) properties, and study solution bifurcation at a constant axial stretch. In the isotropic case, the surrounding soft substrate can substantially delay the onset of bifurcation through a subcritical jump in circular distension at bifurcation with increasing substrate stiffness. Introduction of anisotropy can significantly change the jump behavior from subcritical to supercritical. |
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| Keywords: | Bifurcation Aneurysms Hyperelastic membrane tube Neo-Hookean material |
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