  The structural complexity of soft gels is at the origin of a versatile
mechanical response that allows for large deformations, controlled elastic
recovery and toughness in the same material. A limit to exploiting the
potential of such materials is the insufficient fundamental understanding of
the microstructural origin of the bulk mechanical properties. Here we
investigate the role of the network topology in a model gel through 3D
numerical simulations. Our study links the topology of the network organization
in space to its non-linear rheological response preceding yielding and damage:
our analysis elucidates how the network connectivity alone could be used to
modify the gel mechanics at large strains, from strain-softening to hardening
and even to a brittle response. These findings provide new insight for smart
material design and for understanding the non-trivial mechanical response of a
potentially wide range of technologically relevant materials.
