Symmetry and bifurcation in three-dimensional elasticity, III

Marsden, J. E. and Y. H. Wan

Arch. Ration. Mech. Anal., 84, (1983), 203-233

Abstract:

Consider a hyperelastic material, with a region $\mathcal {B}$ in $\mathbb {R}$³ as its reference configuration. Suppose that the reference configuration is in equilibrium under some initial system of forces (not necessarily zero).
The general problem: Describe the equilibrium solutions of this elastic material subject to a system of forces close to the initial one. Specifically, we want
(a) to count the number of solutions,
(b) to determine their stabilities.