On The Mechanics of Deformation and Fracture of Elastomers and Porous Elastomers
Advisor: Prof. Oscar Lopez-Pamies
ABSTRACT
Ever since Charles Goodyear discovered the vulcanization of natural rubber in 1839, the use of elastomers in
technological applications has increased pervasively at a remarkable pace. This technological growth has been driven
more so by empirical (trial and error) evidence than by fundamental quantitative understanding of the fascinating
mechanical and physical properties of elastomers. This is because elastomers typically exhibit complex heterogeneities
at the relatively large length scale of microns (e.g., they often contain fillers and pores), undergo large deformations,
and these deformations often incur significant energy dissipation, aspects that have proven difficult to handle from
both theoretical and computational points of view.
Motivated by this lacuna in knowledge, the overarching goal of this dissertation is to advance the theoretical and
computational description of the mechanics of elastomers. The focus is on porous elastomers. Specifically, the first
part of the dissertation is devoted to the mechanics of deformation of four different classes of porous elastomers. The
second part addresses a fundamental question in the mechanics of fracture: when and how does fracture nucleate
and subsequently propagate from large pre-existing cracks in elastomers?. Throughout, attention is restricted to finite
elastic or viscoelastic quasistatic deformations; in particular, strain-induced crystallization and inertia are assumed
absent.
In the first part of this dissertation, the four different classes of porous elastomers that are studied are those of:
i) isotropic porous elastomers comprised of an incompressible isotropic elastic matrix embedding equiaxed closedcell
vacuous pores, ii) elastomeric syntactic foams made of a nonlinear elastic matrix filled with a random isotropic
distribution of hollow thin-walled spherical shells, iii) thin perforated Kirchhoff plates made of a homogeneous elastic
plate (with thickness h) that is perforated with periodic distributions (with unit-cell sizes ε ≫ h and ε ≪ h) of
monodisperse cylindrical holes, and iv) isotropic porous elastomers comprised of an incompressible isotropic viscoelastic
matrix embedding initially spherical vacuous bubbles. For all of these four classes, computational homogenization
solutions, as well as analytical approximations, are worked out that make use of either novel or recently developed
algorithms and techniques. Direct comparisons with experiments are presented when available.
In the second part of this dissertation, it is shown that fracture from large pre-existing cracks in elastomers is
governed by a fundamental Griffith criticality condition that involves exclusively the intrinsic fracture energy Gc of
the elastomer. Inter alia, this result brings resolution to the complete description of the historically elusive notion of
critical tearing energy Tc. After its derivation, which is based on two elementary — yet overlooked — observations,
this new Griffith criticality condition is deployed to explain the three types of fracture tests commonly used in the
literature to probe the growth of cracks in elastomers: the“pure-shear” fracture test, the delayed fracture test, and
the trousers fracture test. Direct comparisons with experiments are also presented when available.