Statistical Physics of (Quasi)-Brittle Fracture: Theory and Applications to Construction Materials

In this presentation, we introduce a novel fracture model for quasi-brittle materials that is grounded in statistical principles. This approach redefines the treatment of the underlying discretization, by conceptualizing it as interacting atoms within a semi-grand ensemble, drawing parallels to binary mixtures in experimental physics. This unique perspective allows us to characterize fracture as a phase transition and assess its evolution statistically, employing the concept of heat of adsorption. The model's validity is demonstrated through comprehensive benchmark examples, with a particular emphasis on 2D bending tests and shear tests on (un)notched beams. We discuss the predicted fracture patterns, peak loads, and the incorporation of size-effect. We also present a phase-diagram of beam fracture. Finally, a first approach of softening is discussed on a 1D example.