WAVES, SOLIDS, AND NONLINEARITIES

In this article nonlinearity is taken as a basic property of continua or any other wave-bearing system. The analysis includes the convention al wave propagation problems and also the wave phenomena that are not described by traditional hyperbolic mathematical models. The basic con cepts of continuum mechanics and the possible sources of nonlinearitie s are briefly discussed. It is shown that the technique of evaluation equations leads to physically well-explained results provided the basi c models are hyperbolic. Complicated constitutive behavior and complic ated geometry lead to mathematical models of different character and, as shown by numerous examples, other methods are then used for the ana lysis. It is also shown that propagating instabilities possess wave pr operties and in this case the modeling of energy redistribution has a great importance. Finally, some new directions in the theory and appli cations are indicated. (C) 1995 John Wiley & Sons, Inc.