Abstract :
A variety of heterogeneous materials such as concrete, wood or fiberglass exhibit a quasi-brittle failure behavior : their sudden breakage is preceded by a complex damage process with rich spatio-temporal organization. During the first part of the talk, I will present the toy-model we propose to capture the characteristic failure behavior of such material. It relies on the introduction of heterogeneities and elastic interactions, while damage evolution is determined from energy conservation arguments. The simplicity of the model allows for the theoretical prediction of the onset of damage localization and catastrophic failure, which I will show controlled by the interaction function.

In the second part of the talk, I will focus on the failure behavior of geometrically disordered networks. These structures are inherent to many systems, such as rigid foams, biological networks or granular materials. We experimentally study the uniaxial response of networks of beams with geometry derived from the force chains observed in granular experiments. We find that the mean degree of the network is a control parameter of the failure behavior, which ranges from ductile to brittle. Performing a rigidity analysis, we identify that the failure transition corresponds to the emergence of a percolating rigid cluster. Moreover, for networks close to the transition point, failure events predominantly occur within the floppy regions between rigid clusters. We also build a simple test using a measure taken from network-science tools and able to identify likely failure locations in the samples.