On Anticipatory Systems at Continua

In case of classical continuum mechanics the set of basic equations consists of the equation of motion, the kinematic equation and the constitutive equations. The paper concentrates on the stability problems and the effects of discretization on material modeling. The method of investigation is analytic, the monodromy operator of the discrete system is studied. We study how discretization, stability and anticipation act on one another. As results we show cases, when the anticipatory nature of a material model leads to instability.