Crack front ligament as elastic energy reservoir in fracture of brittle hydrogels

Cracks in brittle solids often break planar symmetry and develop complex three-dimensional structures, with segmented fronts bridged by thin material ligaments. These ligaments are not just geometric irregularities; they are topological features that may hold the key to understanding brittle failures in 3D. To probe the mechanics inside the ligament, we perform in-situ 3D measurements of the deformation field around complex cracks in brittle hydrogels. The gels are fluorescently dyed and embedded with small tracer particles. Using light sheet microscopy, the 3D crack front geometries are reconstructed from the fluorescent signals, and the kinematics fields around the complex crack front are characterized by tracking the particle displacements. We find that both the maximum stretch and the strain energy density are highly localized within the material ligament, which acts as a mechanical bottleneck that must extend and fail before the crack can advance. Moreover, the critical strain energy release rate Gc increases proportionally with the energy stored in the ligament region, making it an "energy reservoir" for the segmented cracks. These insights bridge local field structure with global fracture outcomes, and call for a fully 3D energetic framework when analyzing crack dynamics.