Iterative and variational homogenization methods for filled elastomers

Goudarzi, Taha

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https://hdl.handle.net/2142/50629 Copy

Description

Title

Iterative and variational homogenization methods for filled elastomers

Author(s)

Goudarzi, Taha

Issue Date

2014-09-16

Director of Research (if dissertation) or Advisor (if thesis)

Lopez-Pamies, Oscar

Doctoral Committee Chair(s)

Lopez-Pamies, Oscar

Committee Member(s)

• Paulino, Glaucio H.
• Chasiotis, Ioannis
• Masud, Arif
• Johnson, Harley T.

Department of Study

Civil & Environmental Eng

Discipline

Civil Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Iterative Homogenization methods
• comparison medium methods
• finite deformation
• filled elastomers
• hydrodynamic effect
• interphasial effects
• homogenization with body charges

Abstract

Elastomeric composites have increasingly proved invaluable in commercial technological applications due to their unique mechanical properties, especially their ability to undergo large reversible deformation in response to a variety of stimuli (e.g., mechanical forces, electric and magnetic fields, changes in temperature). Modern advances in organic materials science have revealed that elastomeric composites hold also tremendous potential to enable new high-end technologies, especially as the next generation of sensors and actuators featured by their low cost together with their biocompatibility, and processability into arbitrary shapes. This potential calls for an in-depth investigation of the macroscopic mechanical/physical behavior of elastomeric composites directly in terms of their microscopic behavior with the objective of creating the knowledge base needed to guide their bottom-up design. The purpose of this thesis is to generate a mathematical framework to describe, explain, and predict the macroscopic nonlinear elastic behavior of filled elastomers, arguably the most prominent class of elastomeric composites, directly in terms of the behavior of their constituents — i.e., the elastomeric matrix and the filler particles — and their microstructure — i.e., the content, size, shape, and spatial distribution of the filler particles. This will be accomplished via a combination of novel iterative and variational homogenization techniques capable of accounting for interphasial phenomena and finite deformations. Exact and approximate analytical solutions for the fundamental nonlinear elastic response of dilute suspensions of rigid spherical particles (either firmly bonded or bonded through finite size interphases) in Gaussian rubber are first generated. These results are in turn utilized to construct approximate solutions for the nonlinear elastic response of non-Gaussian elastomers filled with a random distribution of rigid particles (again, either firmly bonded or bonded through finite size interphases) at finite concentrations. Three-dimensional finite element simulations are also carried out to gain further insight into the proposed theoretical solutions. Inter alia, we make use of these solutions to examine the effects of particle concentration, mono- and poly-dispersity of the filler particle size, and the presence of finite size interphases on the macroscopic response of filled elastomers. The solutions are found able to explain and describe experimental results that to date have been understood only in part. More generally, the solutions provide a robust tool to efficiently guide the design of filled elastomers with desired macroscopic properties. The homogenization techniques developed in this work are not limited to nonlinear elasticity, but can be readily utilized to study multi-functional properties as well. For demonstration purposes, we work out a novel exact solution for the macroscopic dielectric response of filled elastomers with interphasial space charges.

Graduation Semester

2014-08

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http://hdl.handle.net/2142/50629

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Copyright 2014 Taha Goudarzi

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