Power Laws Behavior and Nonlinearity Mechanisms in Mesoscopic Elastic Materials

Nonlinear mesoscopic elastic (NME) materials present an anomalous nonlinear elastic behavior, which could not be explained by classical theories. New physical mechanisms should be individuated to explain NMEs response. Dislocations in damaged metals, fluids in rocks and adhesion (in composites) could be plausible. In this thesis I have searched for differences in the macroscopic elastic response of materials which could be ascribed to different physical processes. I have found that the nonlinear indicators follow a power law behavior as a function of the excitation energy, with exponent ranging from 1 to 3 (this is not completely new). This allowed to classify materials into well-defined classes, each characterized by a value of the exponent and specific microstructural properties. To link the measured power law exponent to plausible physical mechanisms, I have extended the Preisach-Mayergoyz formalism for hysteresis to multi-state models. Specific multi-state discrete models have been derived from continuous microscopic physical processes, such as adhesion-clapping, adhesion-capillary forces, dislocations motion and hysteresis. In each model, the microscopic behavior is described by a multistate equation of state, with parameters which are statistically distributed. Averaging over many microscopic elements the so-called mesoscopic equation of state is derived and, from wave propagation simulations in a sample composed by many mesoscopic elements, the experimental results could be reproduced. In the work of the thesis, I have shown that model predictions of the exponent b ( the exponent b has not been introduced before) are linked in a ‘a priori’ predictable way to the number of states and the properties of the statistical distribution adopted. We have classified models into classes defined by a different exponent b and comparing with experimental results we have suggested plausible mechanisms for the nonlinearity generation.