Alexey Stepanov, alex314@umd.edu
Co-authors: Stuart S. Antman
Equilibrium States of Nonlinearly Elastic Annuli and Spherical Shells
Within the linear theory of elasticity, the problems for the equilibria of circular annuli and spherical shells
composed of homogeneous, transversely isotropic materials were solved by Gabriel Lamé. The radially symmetric equilibria of an isotropic nonlinearly elastic disk or ball is elementary. If, however, the disk or ball is
aeolotropic, even for a homogeneous linearly elastic material, the solution can exhibit a rich range of singular
behavior at the origin. We show that BVPs for the equilibria of circular annuli and spherical shells composed of
transversely isotropic nonlinearly elastic materials are far from elementary within the framework of geometrically exact theories. We employ a variety of mathematical approaches, discussing the virtues and idiosyncracies
of each.