In recent years, dense packings of two-and three-dimensional objects have been studied intensely in the context of computational Physical properties of composite materials have been physics and material sciences. For example, computer simulations studied recently by using discrete computational models of disordered solids usually employ a two-dimensional model which related to packings of equal-sized disks in the plane. The is based on hexagonal networks of elastic and rigid bonds or arapproach is closely related to theoretical and numerical rangements of mixed soft and hard disks, respectively. Both types studies on two-dimensional random networks of rigid and of bonds/disks are distributed randomly. Large systems of equations have to be solved at any simulation step for the calculation of local nonrigid bonds. The basic methodology of the work dealing displacements or particle velocities. The simulations start from equiwith random rigid-nonrigid networks comes from percoladistant nodes of the hexagonal network or centers of disks, respection theory [33]. An important parameter in percolation tively, which, in general, may not be in an equilibrium state. We theory is the percolation threshold p c , defining whether or suggest an extension of the model where first a near-equilibrium not arbitrarily large clusters affected by percolation may packing of randomly distributed bonds/disks is calculated. Then, we can compute the displacement caused by external forces from appear. Obviously, p c depends on the underlying network this near-equilibrium initial packing of the elementary units. To this that represents the connection of elementary cells of the end, we propose a stochastic simulation of the external impact by medium. In some cases, p c can be calculated exactly, e.g., incorporating the computation of near-equilibrium states as well as for hexagonal interconnections, where p c Ο 1 Οͺ 2 ΠΈ sin specific boundary conditions. Our methodology is based on a two-(Θ/18). Networks representing elastic, granular materials step approach consisting of a preprocessing stage, where physical properties of different types of particles are analyzed by numerical are studied in particular for a fraction of rigid bonds that methods, and a second stage of stochastic (annealing-based) simu-1 Research partially supported by the Strategic Research Program at replicated in the vertical direction with periodic boundary The Chinese University of Hong Kong under Grant SRP 9505. conditions [17]. Thus, by solving systems of linear equa-2 On leave from BerCom GmbH, Bruno-Taut-Str. 4-6, D-12527 Bertions, relative displacements can be calculated, keeping the lin, Germany.