On failure of the complementing condition and nonuniqueness in linear elastostatics (Q1064806)

A homogeneous isotropic body composed of a compressible linearly elastic material is considered. It is assumed that the body is at equilibrium in a state of plane strain. It is well known that the traction problem for such a body has a unique solution, modulo an infinitesimal rigid deformation, provided that \(\mu\) \(\neq 0\), \(\mu +\lambda \neq 0\) and \(2\mu +\lambda \neq 0\), where \(\mu\) and \(\lambda\) are the Lamé moduli. The authors in the paper under review show that the above mentioned uniqueness result fails when \(\mu =-\lambda\).