Abstract
Conditions are obtained for the incremental shear modulus to be positive for small simple shear superposed on a pure homogeneous deformation of an elastic material, the direction and plane of shear being parallel to a principal direction and principal plane respectively. Results are obtained for an isotropic elastic material and for a transversely isotropic elastic material in which the axis of rotational symmetry is in a principal direction of the pure homogeneous deformation. For an isotropic material, it is shown that the Baker-Ericksen condition on the strain-energy function follows from the assumption that the incremental shear modulus is positive. A number of further conditions that have been proposed are shown to be unacceptable.