Localization and stability in damageable amorphous solids

In the present article, based on a recently proposed model (De Tommasi et al. in J Rheol 50:495–512, 2006; Phys Rev Lett 100:085502, 2008), we analyze the influence of the microstructure properties on the damage behavior of amorphous materials. In accordance with the experimental observations, different scenarios of damage nucleation and evolution are associated to different material distributions at the microscale. In particular, we observe the possibilities of uniform or localized damage and strain geometries with a macroscopic behavior that may range from brittle to ductile or rubber-like. To describe the possibility of extending our stability analysis to three-dimensional damageable amorphous bodies we consider a simple boundary value problem of engineering interest.