Generation of nonlinear oscillations at weak perturbations and generalization of cracks at fracture

The paper studies properties of a continuum with structure. The characteristic size of the structure governs the fact that difference relations do not automatically transform into differential ones. It is impossible to distinguish an infinitesimal volume of a body to which we could apply the major conservation laws, because the minimum representative volume of the body should contain at least a few elementary microstructures. This gives motion equations of infinite order. Solutions for such equations include, along with sound waves, perturbations propagating with abnormally low velocities not bounded below. It is shown that in such media weak perturbations can increase or decrease without limit. Weak dispersion of structure sizes reduces the intensity of such increase and therefore stabilizes the medium, whereas unlimited growth of dispersion destabilizes it. The nonlinearity of the stress-strain curve is shown to cause a reduction of the specific surface of a cracked medium, i.e. the medium undergoes fracture with the formation of a system of a small number of large cracks as though it ignores a large number of small cracks.