Model for behavior of granular materials with pseudo particle-potentials

We consider the overall mechanical behavior of materials with granular microstructure, which may be viewed as collection of particles that interact with their nearest neighbors via pseudo particle potentials. For random granular materials, the nearest neighbors are expected to be randomly oriented in a 3-dimensional space. The orientations of nearest neighbors are modeled using a 3-dimensional statistical distribution density function represented by spherical harmonic expansions. The pseudo particle-potential functions are formulated in terms of both normal and tangential interaction energies. These particle potentials are used to obtain the incremental stiffness at the particle-level. The derived incremental stiffness is utilized to obtain the incremental stress-strain behavior of a representative volume element under monotonic uniaxial, biaxial and triaxial tension and compression. These calculations are compared with the phenomena exhibited by brittle materials, such as Portland cement concrete. Closed form solutions are also derived to obtain material properties.