  A semi-empirical mechanistic contact law for micro-crystalline cellulose
(Avicel PH-200) particles is proposed and characterized experimentally using
force-displacement curves obtained from diametrical compression of single
particles. The concepts of a shape factor and a master contact law are
introduced first for elastic ellipsoidal particles, and subsequently
generalized to plastic irregular particles. The proposed loading-unloading
contact law is a function of three characteristic diameters (lengths of the
principal axes of an approximated ellipsoid), a geometric parameter associated
with the loading condition, three plastic and one elastic material properties.
The force-displacement curves obtained using a micro-compression tester exhibit
an apparent strain-hardening at distinctly different strain values, which is
captured by the shape factor function and its geometric parameter. The three
plastic material properties are log-normal distributions estimated from the
loading experimental curves, while the elastic property is estimated from the
unloading experimental curves. The study shows a very good agreement between
predictions of the calibrated loading-unloading contact law and the
experimental values.
