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On Microstructure Evolution in Fiber-reinforced Elastomers and Implications for Their Mechanical Response and Stability

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dc.contributor.advisor Goldman, Vladimir J. en_US
dc.contributor.author Li, Zhiyun en_US
dc.contributor.other Department of Mechanical Engineering en_US
dc.date.accessioned 2012-05-15T18:04:54Z
dc.date.available 2012-05-15T18:04:54Z
dc.date.issued 1-May-10 en_US
dc.date.submitted May-10 en_US
dc.identifier Li_grad.sunysb_0771M_10117.pdf en_US
dc.identifier.uri http://hdl.handle.net/1951/55525
dc.description.abstract Lopez-Pamies and Idiart [Lopez-Pamies, O., Idiart, M.I., 2010, Fiber-reinforced hyperelastic solids: A realizable homogenization constitutive theory. Journal of Engineering Mathematics, doi:10.1007/s10665-009-9359-y.] have recently put forward a homogenization theory with the capability to generate exact results not only for the macroscopic response and stability, but also for the evolution of the microstructure in fiber-reinforced hyperelastic solids subjected to finite deformations. In this thesis, we make use of this new theory to construct exact, closed-form solutions for the change in size, shape, and orientation undergone by the underlying fibers in a model class of fiber-reinforced hyperelastic solids along arbitrary 3D loading conditions. Making use of these results we then establish connections between the evolution of the microstructure and the overall stress-strain relation and macroscopic stability in fiber-reinforced elastomers. In particular, we show that the rotation of the fibers may lead to the softening of the overall stiffness of fiber-reinforced elastomers under certain loading conditions. Furthermore, we show that this geometric mechanism is intimately related to the development of long-wavelength instabilities. These findings are discussed in light of comparisons with recent results for related material systems. en_US
dc.description.sponsorship Stony Brook University Libraries. SBU Graduate School in Department of Mechanical Engineering. Lawrence Martin (Dean of Graduate School). en_US
dc.format Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Engineering, Mechanical en_US
dc.subject.other Finite Strain, Hamilton-Jacobi Equation, Homogenization, Instabilities, Microstructures en_US
dc.title On Microstructure Evolution in Fiber-reinforced Elastomers and Implications for Their Mechanical Response and Stability en_US
dc.type Thesis en_US
dc.description.advisor Advisor(s): Oscar Lopez-Pamies. Committee Member(s): Robert Kukta; Chad Korach. en_US
dc.mimetype Application/PDF en_US

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