Curvature-Driven Rigidity Transitions and Rheological Response of Confluent Epithelial Tissues

Epithelial tissues often adopt curved geometries that can strongly influence their collective mechanical behavior and organization. However, the role of curvature in governing rigidity and viscoelastic response remains poorly understood. In this work, we investigate how surface geometry affects the mechanical properties and collective dynamics of confluent epithelial layers. Using a dissipative vertex model, we explore how variations in curvature modify tissue rigidity, relaxation behavior, and the transition between solid-like and fluid-like states. The model provides a computational framework for connecting geometric constraints to emergent viscoelastic behavior. The results show that curvature modulates rheological response through stress propagation and relaxation, altering the collective motion of vertices across the tissue. These findings highlight curvature as a key physical factor regulating viscoelastic dynamics and may inform future studies of tissue morphogenesis and mechanobiology.