On the bifurcations of the Lame solutions in plane-strain elasticity

摘要

We consider the in-plane bifurcations experienced by the Lame solutions corresponding to an elastic annulus subjected to radial tension on the curved boundaries. Numerical investigations of the relevant incremental problem reveal two main bifurcation modes: a long-wave local deformation around the central hole of the domain, or a material wrinkling-type instability along the same boundary. Strictly speaking, the latter scenario is related to the violation of the Shapiro-Lopatinskij condition in an appropriate traction boundary-value problem. It is further shown that the main features of this material instability mode can be found by using a singular-perturbation strategy.