Modeling nonclassical nonlinearity, conditioning, and slow dynamics effects in mesoscopic elastic materials

Several materials with mesoscopic characteristics (e.g., defects or intergrain regions) have been shown to share several nonclassical nonlinear features, which distinguish them from classical nonlinear media. Most striking among them is the log-time recovery of the material properties after they have been conditioned by the action of an external perturbation. A simple model based on the description of the mesoscopic features as bond regions between elastic portions is presented here. The implementation of the model is illustrated by the application of a special bi-state protocol, which, by considering also thermally induced transitions between the two basic states, allows to explain all experimentally observed nonclassical nonlinear effects.