Polymeric structures forming via phase separation - such as microporous membranes, thin films, hydrogels, and electrospun fibers - often undergo large changes in volume and shape. These deformations arise not only from external stimuli but also from internal mechanisms associated with the accommodation of evolving phases. To investigate and track the evolution of such microstructures in silico, a fully coupled chemomechanical phase-field model was developed within a Lagrangian framework to describe phase separation in deforming biphasic polymeric media [1]. The model extends the classical Cahn-Hilliard (CH) and Flory-Huggins formulations by accounting for finite deformations into both the interfacial and mixing energy contributions. Particular emphasis is placed on the consistent reformulation of the interfacial energy in the Lagrangian configuration (cf. [2]), recognizing that the CH equation is originally posed in the Eulerian framework. In contrast to previous studies [3, 4], the resulting formulation entails a strong nonlinear dependence of the interfacial energy on deformation. Simulations of phase separation under large volume loss due to solvent evaporation, across various parameter regimes, reveal that the choice of interfacial energy representation significantly affects the interface morphology in geometrically nonlinear settings. Furthermore, the interplay between chemical and elastic driving forces is investigated through case studies involving applied mechanical loading and thermal quenching. These findings underscore the critical role of elasticity in modulating phase separation dynamics [5], and ultimately, in shaping the resulting microstructures.