Differential Growth and Instability in Elastic Shells

Abstract

Differential growth in elastic materials can produce stress either through incompatibility of growth or by interaction with the surrounding medium. In many situations, this stress can be sufficient to induce shape instability in the growing medium. To gain better insight in growth-induced instabilities, the growth of an elastic shell loaded with hydrostatic pressure or embedded in an elastic medium is studied. The residual stress arising from the incompatibility of growth and the contact stress arising from the interaction with the surrounding medium are computed with respect to growth and geometric parameters and critical values for instability are obtained. Depending on these parameters, different modes of instability can be obtained.