Coexistent phases in nonlinear thermoelasticity: radially symmetric equilibrium states of aeolotropic bodies

We determine the detailed qualitative behavior of radially symmetric equilibrium states having coexistent phases for general classes of aeotropic nonlinearly thermoelastic materials. We treat both structured and non-structured interfaces. The aeolotropy is responsible for many novel effects. We show that linearly elastic materials cannot sustain coexistent radially symmetric phases unless the interfaces are structured. Our analysis is largely elementary, being based on a combination of geometric constructions with phase-plane methods. A few results, however, depend on our development of appropriate versions of the theory of asymptotically autonomous ordinary differential equations.