Constitutive relations for an isotropic pore-power-law fluid are propo
sed in which the effective viscosities in both shear and dilation have
the same power-law dependence on the second invariant of the deviator
ic stress alone, but the viscosity in dilation is 1/v times the viscos
ity in shear. The shear rate is otherwise proportional to the deviator
ic stress and the dilation rate to an effective mean stress. The behav
ior may either involve Darcy Bow of a pore fluid whose viscosity is mu
ch less than that of the solid matrix, or involve dissolution, diffusi
ve transport, and precipitation of a soluble phase, as in pressure-sol
ution. Linearized relations for small additional rate-of-deformation a
nd stress superposed on a basic-state flow are obtained. These are use
d to treat the deformation due to a shallow, narrow indentation at the
interface between a layer and an adjacent medium when both undergo bu
lk uniform layer-parallel shortening or extension. If the layer, the m
edium, or both, are nonlinear fluids with large stress exponent, shear
-band like structures, extending from the indentation, and 'reflecting
' from any weak, slipping interface, occur in both the instantaneous v
elocity field and in the strain field. Since the materials considered
have constant and uniform properties - e.g., they do not exhibit strai
n-softening - these features leave no imprint in the medium. They pers
ist over mean strains of 10-20%, but are, like the indentation, epheme
ral. It is hypothesized that localization due to an interfacial irregu
larity of this sort would produce bona fide shear bands if the materia
l were strain-softening. The development of shear bands is enhanced if
the adjacent medium has a large stress exponent, or if it is a porovi
scous fluid with low resistance to dilation. In a poroviscous medium,
dilation is concentrated in paired positive and negative lobes at the
terminations of shear bands in the adjacent layer. The development of
shear bands in a poroplastic layer is mildly suppressed, relative to t
hat in an incompressible layer. Dilation is concentrated in paired loc
i at shear band terminations, with weaker, paired bands of positive an
d negative dilation on either side of the shear zone. (C) 1998 Elsevie
r Science B.V. All rights reserved.