  The consolidation of suspended particulate matter under external forces such
as pressure or gravity is of widespread interest. In this work, we derive a
constitutive relation to describe the deformation of a {\it two-dimensional}
strongly aggregated colloidal system by incorporating the inter-particle
colloidal forces and contact dynamics. The theory accounts for the plastic
events that occur in the form of rolling/sliding during the deformation along
with elastic deformation. The theory predicts a yield stress that is a function
of area fraction of the colloidal packing, the coordination number, the
inter-particle potential, coefficient of friction and the normal and tangential
stiffness coefficients. The predicted yield stress scales linearly with area
fraction for low area fractions, and diverges at random close packing.
Increasing the normal stiffness coefficient or the friction coefficient
increases the yield stress. For stresses greater than the yield stress, both
elastic and plastic deformations contribute to the overall stress.
