Post instability in continuous systems. II - Post-instability models of continua

Abstract

New models simulating postinstability behavior of continuous systems are discussed. Multivalued velocity fields of the motion of a medium are analyzed, deriving concepts which are applied to a new model of turbulence. Postinstability models of solids are examined, emphasizing the multivaluedness of the parameters. The consequences are addressed of the simplifying assumption that in solids the rate of dissipation of energy of the pulsations is much higher than in fluids. The principal stress formulation of postinstability models is considered, including the geometry, kinematics, and dynamics of the principal stress coordinates. The fundamental properties of enlarged models of a solid are illustrated by the theory of wrinkling films. Results are presented for the statics of such films, the effects of shocks and shock waves, and the behavior of singular effects and singular thick wrinkles.