  In a recent study, Kumar and Lopez-Pamies (J. Mech. Phys. Solids 150: 104359,
2021) have provided a complete quantitative explanation of the famed poker-chip
experiments of Gent and Lindley (Proc. R. Soc. Lond. Ser. A 249: 195--205,
1959) on natural rubber. In a nutshell, making use of the fracture theory of
Kumar, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 112: 523--551, 2018),
they have shown that the nucleation of cracks in poker-chip experiments in
natural rubber is governed by the strength -- in particular, the hydrostatic
strength -- of the rubber, while the propagation of the nucleated cracks is
governed by the Griffith competition between the bulk elastic energy of the
rubber and its intrinsic fracture energy. The main objective of this paper is
to extend the theoretical study of the poker-chip experiment by Kumar and
Lopez-Pamies to synthetic elastomers that, as opposed to natural rubber: ($i$)
may feature a hydrostatic strength that is larger than their uniaxial and
biaxial tensile strengths and ($ii$) do not exhibit strain-induced
crystallization. A parametric study, together with direct comparisons with
recent poker-chip experiments on a silicone elastomer, show that these two
different material characteristics have a profound impact on where and when
cracks nucleate, as well as on where and when they propagate. In conjunction
with the results put forth earlier for natural rubber, the results presented in
this paper provide a complete description and explanation of the poker-chip
experiments of elastomers at large. As a second objective, this paper also
introduces a new fully explicit constitutive prescription for the driving force
that describes the material strength in the fracture theory of Kumar,
Francfort, and Lopez-Pamies.
