Material instabilities of an incompressible elastic cube under triaxial tension

Abstract

Besides purely geometrical non-linearity, unstable solutions in finite elasticity may arise due to non-linear material behaviour. In this paper, a stability criterion is developed with which these so-called material instabilities can be distinguished from geometrical or structural instabilities like the buckling of shells and plates. Finally, the value of this criterion is demonstrated analytically by examining the case of a cube under triaxial tension. To obtain realistic results, the stability investigation is based on the material model of Ogden, which is characterized by excellent agreement with experimental results.