On the second order scalar component of pressure in incompressible materials (Q805352)

In the second order theory which is one of the analytical methods of three-dimensional elastic problems in finite deformations, the induced second-order scalar components of hydrostatic pressure in the stress- strain relationship for incompressible materials has two kinds of expressions. One expression [e.g.: \textit{A. J. M. Spencer}, J. Inst. Math. Appl. 6, 164-200 (1970; Zbl 0211.276)] is to absorb the induced invariant into the second order term of hydrostatic pressure. The other expression [\textit{A. E. Green} and \textit{J. E. Adkins}, Large elastic deformations (1970; Zbl 0227.73067)] is to determine the two second order scalar components by a limit process. However - derived by two kinds of methods - these components are not equal, as they should be. In order to solve certain unnatural contents, we propose a new way of expressing the second order hydrostatic components and deriving the second order scalar terms. Further, the effectiveness of this approach for the axisymmetrical elastic problems in incompressible materials is examined by a simple example.