General approach to near-flip buckling of bodies with complex geometry

Buckling of beams and plates is reasonably well-understood. In my talk I will emphasize the universality of buckling, opening the possibility of the common approach to buckling of bodies with complex geometry. Buckling is exhibited as a failure of non-negativity of second variation in non-linear elasticity. The universality of the frame indifference of energy densities for all hyper-elastic materials is seen to be the common cause of both flip and buckling instabilities under compressive loading. The constitutive linearization procedure is introduced, that takes into account both linear material response and the geometric non-linearity associated with frame indifference. Finally, the critical buckling load is understood mathematically as a generalized Korn constant in the Korn-type inequality.