Adhesion and plasticity in the dynamic response of rough surfaces in contact

Several phenomenological models have been proposed in the last decades to understand and describe the phenomenology of elastic hysteresis observed in dynamic experiments, i.e. the combination of nonlinear phenomena, usually referred to as “fast” and “slow” dynamics, including harmonic generation, resonance frequency shift, time variation of elastic properties when large conditioning strain is applied. These models correctly reproduce various experimental observations for repeated loading–unloading cycles in quasi-static conditions, but they lack a convincing interpretation in terms of possible physical mechanisms. The aim of this work is to provide a model for the description of the dynamic behavior of a material with an internal microcrack, which attempts to link measurable macroscopic observables to physical crack features at the microscale (e.g. crack concentration, roughness, adhesion, elasticity and plasticity). The existence of adhesive/continuous phases, of crack activation thresholds, of harmonic generation and of the presence of metastable equilibrium states are emerging features of the model and are proposed herein as a possible source of slow dynamics effects. The proposed model can serve as a basis for the extension to a more macroscopic view, i.e. a material containing a network of microcracks.