Abstract: Geometric modeling is one of the main factors affecting the accuracy of material properties
calculation by finite element method. Using simple geometric entities, such as circles, to simulate
discrete objects is demonstrated well. Beyond the great simplifications in the geometrical calculation,
it can provide an approximate model within acceptable error. Material properties not only depend on
the average grain size, but also are influenced by the grain size distribution significantly. Random
circles packing algorithm designed in this paper ensured these circles′ radius following a certain
probability distribution. Normal circles generation method and generating new circle based on the
interference types were analyzed. This algorithm not only avoided the interference completely, but
reduced the separation greatly. Compared with existing filling algorithms, the filling density of this
algorithm was improved obviously.

Key words: random radius, material simulation, sphere packing, finite element method