Damage localization as a bifurcation phenomenon and the resulting fracture patterns in soft materials

Symmetry breaking phenomena are central to the morphogenesis of natural structures and can also be harnessed in engineered soft materials subjected to external loads. While traditionally viewed as elastic instabilities, these phenomena may involve irreversible processes such as damage and fracture, significantly influencing the morphology of resultant patterns. Here, we investigate instabilities arising during radial expansion of soft, incompressible cylindrical bodies, employing a gradient damage framework coupled with hyperelastic constitutive modeling. Our analytical bifurcation analysis identifies the critical thresholds at which symmetric cavity growth transitions into localized, multi-lobed fracture modes, explicitly delineating how geometry, toughness, and intrinsic damage length scales govern the selection and morphology of these fracture patterns. Comparison with finite element simulations reveals a notable delay in the numerically predicted bifurcation threshold, highlighting limitations in existing finite element based methods, and underscoring the necessity of analytical benchmarks for accurate fracture initiation predictions. Ultimately, this work provides a road map for accurate prediction of damage induced bifurcations and sheds light on the role of geometry and constitutive properties in determining the failure modes of expanding tubular structures.