Description
Hydrogels are crosslinked polymer networks saturated in a liquid solvent and can be modeled as
a two-phase system employing the phase field approach. During swelling and squeezing, they un-
dergo enormous volume changes, which requires finite strain models for realistic considerations. We
analytically investigate the two-phase model for phase separation in a geometrically nonlinear elas-
tic material. The coupled system of PDEs consists of a Cahn-Hilliard equation and a quasi-static
mechanical force balance of the deforming gel. The phase field and the mechanics are coupled by a
multiplicative decomposition of the deformation gradient, and time-dependent Dirichlet boundary
conditions are imposed on the deformation field. Based on a time-incremental scheme, we derive
existence theory of solutions in a suitable weak formulation. Using techniques from the calculus of
variations and nonlinear PDE theory, we obtain further an existence result for the time-continuous
problem under suitable assumptions.
This is a joint work with Marita Thomas within the DFG priority program SPP 2171 Dynamic
wetting of flexible, adaptive and switchable substrates, project # 422786086 and within the MATH+
project AA2-9.