Mean field theories for the aging and yielding of athermal amorphous solids

Abstract

In this thesis we study mean field elastoplastic models to understand athermal amorphous solids, which show complex slow relaxation (aging) phenomena and intricate mechanical responses under deformation. These models consider the dynamics of mesoscopic blocks of material, which alternate between elastic and plastic deformation. In mean field, the interactions mediated by the elastic stress propagator are treated as a mechanical noise. The main contribution of this thesis is to extend these models in two important directions, concerning the nature of the mechanical noise and the inclusion of a disordered local energy landscape. Although the groundwork for such extensions was already laid out in the literature, previous studies were limited to the case of steady shear. Here we develop these ideas further to study two important phenomena: the aging of athermal systems, and their yielding behaviour, particularly (but not only) under oscillatory shear.