In this research, we are modeling the behavior of spherical and non-spherical particle aggregates by a combination of numerical methods including finite element and discrete-element approximations. Our primary objective is to study the mechanical behavior of these particle aggregates via their constitutive law and yield surface characteristics.

Our current models include three-dimensional studies of spherical particle aggregates using a network model and a two-dimensional model of viscoplastic spherical particle aggregate compaction using an iterative finite element procedure. A typical particle packing is shown on the left along with the basic behavior of the yield surface for isostatic precompaction, where our network model is compared with results from a statistical random particle aggregate. Results from our two-dimensional aggregate are shown in the sequence of figures at the bottom of the page, with the viscoplastic particles gradually eliminating the void space through the enforcing of incompressibility.

This work is currently being funded by the National Science Foundation and the Alexander von Humboldt Research Foundation. Members of the research team include Mr. Yu-Ching Wu (CSU), Professor Erik Thompson (CSU), Professor Robert McMeeking (UCSB), Dr. Karsten Thompson (LSU), and Professor Paul Heyliger (CSU).

A typical
sphere packing of 2100 particles used to study yield surfaces for perfectly
plastic particle aggregates.

Typical
yield surface for isostatic precompaction of the aggregate shown above using
a network model for cohesive and cohesionless aggregates.

In this sequence of images,
we show the viscoplastic compaction of non-spherical particle aggregates as
modeled using an iterative penalty method finite element representation. The
particles are incompressible, and are therefore sequentially compacted into
a fixed-volume (images courtesy of Mr. Yu-Ching Wu).

The
two images above show the results from a new family of Ritz finite element
particle models that treat each particle as a finite continuum rather than
as a representation of line forces. On the left, the steady-state heat transfer
of a cold (blue) particle is demonstrated in a packing of ``chips'' formed
by the four quadrants of minor ellipses. The color contours represent temperature
within the packing of insulated particles. On the right, we show the formation
of force chains in a stacking of elliptical elastic particles where the
dots denote particles with stiffness 20 orders of magnitude higher than
the others. The force of gravity follows the blue line of higher stress
through the packing.