Energy bounds for a mixture of two linear elastic solids occupying a semi-infinite cylinder

The aim of this paper is to establish some forms of the Saint-Venant principle for a mixture of two linear elastic solids occupying a semi-infinite prismatic cylinder. We examine the behaviour of the energy for both static and dynamical problems. Under mild assumptions on the asymptotic behaviour of the unknown fields at infinity, we show that in the static case the elastic energy of the portion of the cylinder beyond a distance x3 from the loaded region decays exponentially with x3. For the dynamical problem we estimate through the data the total energy stored in that part of the cylinder whose minimum distance from the loaded end is x3; these estimates, which are based on the assumption that the initial total energy is finite, depend upon x3 but do not depend upon the time t. © 1995 Springer-Verlag.