The systems encountered in biophysics typically straddle the line between solidand fluid, and are thus subject to large deformations even at modest stress val-
ues. This, along with the presence of material properties such as visco-elasticity
and strain hardening, necessitate the use of non-linear elasticity when describ-
ing the physics of these systems. In this dissertation, we explore the use of
non-linear elasticity theory in describing soft matter physics, with a focus on
the specific example of cavitation in polymer gels and similar systems.
We first look at cavitation in the context of equilibrium mechanics. In sim-
ple materials that obey neo-Hookean elasticity, we show that compressibility
effects strongly enhance cavitation. On the other hand, cavitation phenom-
ena in gels of flexible polymers in a binary solvent that phase separates are
surprisingly similar to those of incompressible materials. We find that, as a
function of the interfacial energy between the two solvent components, there is
a sharp transition between cavitation and classical nucleation-and-growth. Fi-
nally, biopolymer gels are characterized by strain hardening, and even very low
levels of strain hardening are shown to suppress cavitation in polymer gel that
obey Flory-Huggins theory in the absence of strain hardening.
Next, we explore the dynamics of cavitation in non-linear incompressible mate-
rials. We find that, while purely elastic systems can be described entirely within
either a Lagrangian or Eulerian frame of reference, and viscous fluids with no
elasticity can be described entirely within an Eulerian frame, visco-elastic ma-
terials such a Maxwell materials cannot be fully described without making use
both frames, translating between the two using a known deformation mapping.