Alexander M. Sutin
Veniamin E. Nazarov
Inst. of Appl. Phys., Russian Acad. Sci., 46 Ulyanov str., Nizhny Novgorod 603600, Russia
There are many experimental data showing that third-order elastic constants of solids with cracks can be anomalously high and can exceed these parameters for homogeneous solids more than a thousand times. Here a physical model of a medium with cracks is suggested to explain such high nonlinearity. The model is based on the assumption that the stress applied to a single crack is the same as that applied to the whole body, that is valid for a low concentration of cracks. The crack behavior was described using the model in which a crack can be presented as an elastic contact of two rough surfaces, pressed one to another under the action of internal stresses in the surrounding solid. The nonlinear behavior of a crack is due to the contact area changing when the crack is undergoing stress or extension. Linear and nonlinear elastic constants of the medium with cracks are calculated; it is shown that in this medium negative values of Poisson's ratio and anomalously high values of the third-order constants are possible.