ABSTRACT

The nonlinear elasticity of solids is based, on a model of elastic potential of atomic interactions, while the second definition seems not to be rigorously applicable to amorphous, porous or granular solids. There are several sources of nonlinearity that affect the elastic wave propagation. J. Engelbrecht provided the examples of kinematical nonlinearity which occurred in the compound motion of solids or in rotation dynamics of rigid body. Combined and complex nonlinearities should be mentioned, also, provided, e.g., by thermal processes influencing the mechanical stress field, or by pre-stressing of a material, or by viscous liquidsolid interface interaction. The nonlinear stress-strain dependence, e.g., according to the Hodgkinson law, can be caused by internal sliding of either long molecule, in polymers, or of thin layers in polycrystalline solids. Nonlinear wave problems with energy influx are typical for many applications.