Solitons in a damaged medium
V.I. Erofeyev
Nizhny Novgorod Branch of Mechanical Engineering
Research Institute of Russian Academy of Sciences,
Nizhny Novgorod, Russia
The propagation of longitudinal and shear waves in a damaged medium with microstructure is investigated [1,2]. In order to describe the behavior of an elastic medium with microfractures, the internal energy is specified in the form of a Myasnikov-Luakhovskii potential, the presence of microstructure is taken into account with the aid of the Le Roux hypothesis:
where 
and 
are invariants of the strain tensor, 
is the microdistortion gradient. the resulting mathematical model is
strongly nonlinear and can describe stationary waves. Dependencies
relating the primary wave parameters to the extent of material fracturing
are determined. It is shown that these dependencies may be used as basis
for developing an acoustic technique to test the fracturing of materials.