Type
Text
Type
Thesis
Advisor
Robert Kukta | Goldman, Vladimir J. | Chad Korach.
Date
2010-05-01
Keywords
Engineering, Mechanical | Finite Strain, Hamilton-Jacobi Equation, Homogenization, Instabilities, Microstructures
Department
Department of Mechanical Engineering
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/72583
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
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.
Recommended Citation
Li, Zhiyun, "On Microstructure Evolution in Fiber-reinforced Elastomers and Implications for Their Mechanical Response and Stability" (2010). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 1787.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/1787