A sponge subjected to an increase of the outside fluid pressure expands its
volume but nearly mantains its true density and thus gives way to an incre
ase of the interstitial volume. This behaviour, not yet properly described
by solid-fluid mixture theories, is studied here by using the Principle of
Virtual Power with the most simple dependence of the free energy as a funct
ion of the partial apparent densities of the solid and the fluid. The model
is capable of accounting for the above mentioned dilatational behaviour, b
ut in order to isolate its essential features more clearly we compromise on
the other aspects of deformation. Specifically, the following questions ar
e addressed: (i) The boundary pressure is divided between the solid and flu
id pressures with a dividing coefficient which depends on the constituent a
pparent densities regarded as state parameters. The work performed by these
tractions should vanish in any cyclic process over this parameter space. T
his condition severely restricts the permissible constitutive relations for
the dividing coefficient, which results to be characterized by a single ma
terial parameter. (ii) A stability analysis is performed for homogeneous, p
ressurized reference states of the mixture by postulating a quadratic form
for the free energy and using the afore mentioned permissible constitutive
relations. It is shown that such reference states become always unstable if
only the external pressure is sufficiently large, but the exact value depe
nds on the interaction terms in the free energy. The larger this interactio
n is, the smaller will be the critical (smallest unstable) external pressur
e. (iii) It will be shown that within the stable regime of behaviour an inc
rease of the external pressure will lead to a decrease of the solid density
and correspondingly an increase of the specific volume, thus proving the w
anted dilatation effects. (iv) We close by presenting a formulation of mixt
ure theory involving second gradients of the displacement as a further defo
rmation measure (Germain 1973); this allows for the regularization of the o
therwise singular boundary effects (dell'Isola and Hutter 1998, dell'Isola,
Hutter and Guarascio 1999).