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

A theory for the compression of two dimensional strongly aggregated colloidal networks