Stability of homogeneous deformation of an incompressible elastic body under dead-load surface tractions (Q1097077)

In this interesting paper the author discusses the problem of stability of a given homogeneous deformation for isotropic, incompressible materials. First he considers locally stable and locally neutrally stable deformations and derives necessary and sufficient conditions for the two types of stability using two different approaches. In both cases the dead-load surface tractions are assumed. In particular two examples are investigated, i.e., unaxial and biaxial dead-load. Moreover, a global stability of pure homogeneous deformation under biaxial dead-load surface tractions is studied. The author establishes the corresponding necessary and suffcient conditions of global stability. Toward this purpose the results of \textit{J. M. Ball} and \textit{D. G. Schaeffer} are employed [Math. Proc. Camb. Philos. Soc. 94, 315-339 (1983; Zbl 0568.73057)].