The uniaxial exponential law, , has been applied to experimental results for steady-state creep, including that of wet and dry olivine, pyroxenite and carbonates, at a deviatoric stress greater than ∼100 MPa. Such stress levels likely occur in the upper-mantle lithosphere and middle crust. In a layered rock, in layer-parallel extension or shortening, high deviatoric stress can occur in the stiffest layers, for example, a dolomite layer in fine-grained marble. Under assumptions of isotropy and incompressibility, the uniaxial law yields where J2 = sijsij/2 is an invariant of the deviatoric stress tensor, sij. Linearization about a homogeneous basic-state of flow yields equations identical in form to those obtained for the familiar power law. This establishes expressions for an effective viscosity, and stress exponent, , where is an invariant of the basic-state deformation rate, . These results allow application of existing analytical folding and necking solutions for a rock layer of power-law fluid to a rock layer with an exponential flow law. The effective stress exponent for the exponential flow law increases with decreasing temperature, through the dependence of C on the latter and, weakly, with increasing deformation rate. For dry olivine, effective stress exponents are between 10 and 30 for temperatures between 400 and 600°C with little dependence on deformation rate. Finite element simulations employing full non-linear forms of the flow laws show that large strain necking is nearly identical for power law and exponential flow laws. The results suggest that the instability in necking and folding in ductile rock layers can be considerably stronger than inferred from results based on flow laws representing diffusion and dislocation creep. The large values of the effective stress exponent, ne > ∼15, that may be attained for exponential flow laws can account for observed outcrop-scale ductile neckin
