Internal buckling under initial stress in finite elasticity

Abstract

Abstract It is shown that elastic instability may occur in the interior of a medium which is of infinite extent or confined by rigid boundaries. This type of buckling is the mathematical analogue of body waves in dynamics. The analysis is based on the writer’s theory of elasticity under initial stress. Significant incremental coefficients are derived for a medium in an initial state of finite strain. The existence of internal buckling is shown to be a consequence of the mixed hyperbolic-elliptic nature of the equations. Additional insight is provided by a variational analysis. The phenomenon may also be derived from earlier results of the writer for acoustic propagation under initial stress. In general, internal buckling requires the material to be anisotropic. However, it may occur in a medium of finite isotropy under exceptional conditions which recall the appearance of slip line in plasticity.