The shrink-fit problem for aeolotropic nonlinearly elastic bodies

In the classical shrink-fit problem of linear elasticity (cf. Timoshenko [4, Sec. 31]) an annulus of natural inner radius a and natural outer radius (scaled to be) 1 is expanded (e.g., by heating) and then allowed to shrink down upon a disk of natural radius b, which is greater than a. See Fig. 1.1. Here we solve generalizations of this axisymmetric problem for aeolotropic, nonlinearly elastic bodies of different constitution subject to arbitrary axisymmetric boundary conditions on the outer edge of the annulus. We show that these problems exhibit a remarkable richness of physical phenomena and we show how easy it is to determine the detailed qualitative properties, the existence or nonexistence, and the uniqueness or multiplicity of all equilibrium states. We also show how to construct solutions for problems in which there are several annular layers