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Title:Nucleation and propagation of fracture and healing in elastomers
Author(s):Kumar, Aditya
Director of Research:Lopez-Pamies, Oscar
Doctoral Committee Chair(s):Lopez-Pamies, Oscar
Doctoral Committee Member(s):Duarte, C. Armando; Francfort, Gilles A; Geubelle, Philippe H
Department / Program:Civil & Environmental Eng
Discipline:Civil Engineering
Degree Granting Institution:University of Illinois at Urbana-Champaign
Fracture nucleation
Self-healing polymers
Non-conforming elements
Finite deformations
Configurational forces
Abstract:The main objective of this dissertation work is to introduce a macroscopic theory capable of describing, explaining, and predicting the nucleation and propagation of fracture and healing in elastomers undergoing arbitrarily large quasistatic deformations. Elastomers are assumed to behave as purely elastic isotropic solids. The proposed theory, which can be viewed as a generalization of the phase-field approximation of the variational theory of brittle fracture of Francfort and Marigo (1998) to account for physical attributes innate to elastomers that have been recently unveiled by experiments at high spatiotemporal resolution, rests on two central ideas. The first one is to view elastomers as solids capable to phase transition to another solid of vanishingly small stiffness: the forward phase transition serves to model the nucleation and propagation of fracture while the reverse phase transition models the possible healing. The second central idea is to take those phase-transitions to be driven by the competition of the elasticity, the strength, and the critical energy release rate of the elastomer under investigation. Two models based on the general formulation are presented which account for the strength of elastomers in different manners. The first and simpler model accounts only for the hydrostatic strength of elastomers. The second and more elaborate model accounts for a generic strength surface in the entire stress space and as a result is capable of describing fracture nucleation at large, be it within the bulk (under arbitrary states of stress, not just hydrostatic), from large pre-existing cracks, small pre-existing cracks, or from smooth and non-smooth boundary points. The descriptive and predictive capabilities of both models are examined by confronting their predictions with a wide range of famed --- but hitherto unexplained --- and new experimental results. From an applications point of view, the proposed theory amounts to solving a system of two coupled and nonlinear PDEs for the deformation field and a phase field. A numerical scheme is presented to generate solutions for these PDEs in $N=2$ and 3 space dimensions. This is based on an efficient non-conforming finite-element discretization, which remains stable for large deformations and elastomers of any compressibility, together with an implicit gradient flow solver, which is able to deal with the large changes in the deformation field that can ensue locally in space and time from the nucleation of fracture. Beyond its pertinence to elastomers, the proposed theory seems to provide a complete framework for the description of fracture nucleation and propagation in elastic brittle materials at large. Evidence of this remarkable generality is provided by direct comparisons with experiments on fracture nucleation and propagation in a broad spectrum of materials, including numerous ceramics and hard polymers.
Issue Date:2020-09-17
Rights Information:Copyright 2020 Aditya Kumar
Date Available in IDEALS:2021-03-05
Date Deposited:2020-12

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