The flip side of buckling

Buckling of slender structures under compressive loading is a failure of infinitesimal stability due to a confluence of two factors: the energy density non-convexity and the smallness of Korn’s constant. The problem has been well understood only for bodies with simple geometries when the slenderness parameter is well defined. In this paper we present the first rigorous analysis of buckling for bodies with complex geometry. By limiting our analysis to the ”near-flip” instability we address the universal features of the buckling phenomenon that depend on neither the shape of the domain nor the degree of constitutive nonlinearity of the elastic material.