Solvent-coupled deformation in polymers near free surfaces

Polymeric gels are biphasic materials consisting of a crosslinked polymer network permeated by an interstitial solvent. Their macroscopic behavior is governed by the poroelastic coupling between the elastic deformation of the solid skeleton and the transport of the fluid phase. Despite the ubiquity and importance of poroelasticity in describing phenomena across natural systems and engineered applications, local characterization of solvent transport under controlled stress and transport boundary conditions remains scarce. Such characterization is experimentally challenging, yet essentialâ conventional bulk tests provide only spatial averages, whereas transport is inherently local. This limitation becomes especially pronounced under large deformations. In this thesis, we develop an experimental framework to obtain high-resolution 3D kinematic fields, combining particle tracking with a deformation gradient tensor (F) estimator. This estimator uses local least-squares to quantify F from particle trajectories, enabling subsequent calculation of various fields and volumetric changes. We analyze the estimator's error and experimentally demonstrate its superior accuracy over conventional Digital Image Correlation (DIC) in handling large deformations and displacement discontinuities.

Using this tool, we quantify silicone-oil transport with controlled viscosities in polydimethylsiloxane (PDMS) networks during free swelling and bending. In free swelling, through-thickness profiles reveal a flux-limited transport boundary condition, contradicting the commonly assumed fully drained limit and implying diffusivities ~10Ã larger than canonical bulk-uptake fits. Under bending, Under bending, we resolve tensile-side dilation and compressive-side contraction, extracting diffusivities consistent with global force-relaxation. Together, these experiments benchmark diffusivity $\simeq10^{-12}$â $10^{-10}$ m$^2$/s, decreasing with increasing solvent viscosity. Furthermore, the free swelling equilibrium is captured by a Flory--Rehner theory that requires modification to include effective finite extensibility.

We then extend this approach to Mode I fracture of brittle hydrogels. In the fast, non-poroelastic regime, near-tip kinematics and a J-integral evaluation reveal a characteristic process zone (100ÎŒm) with a "horizontal droplet" shape, where energy dissipation partitions into two contributionsâ a distributed process-zone dissipation and a tip-localized dissipation below our resolution. In the slow, poroelastic regime, we resolve the full 3D near-tip kinematic fields and directly quantify solvent migration via the determinant of F. These measurements, departing from classic linear elastic fracture mechanics predictions, reveal strong multiaxial stretch state at the tip and substantial rigid-body rotation in the wake. Pronounced swelling is observed surrounding the crack tip and intensifies towards the tip; this swelling correlates with the local stretch state