Two-dimensional disordered granular assemblies composed of 2048 polydispersed frictionless disks are simulated using the discrete element method. The height of the first peak of the pair correlation function, gl, the local and global bond orientational parameters ψ6^1 and ψ6^g, and the fluctuations of these parameters decrease with increasing polydispersity s, implying the transition from a polycrystalline state to an amorphous state in the system. As s increases, the peak position of the boson peak aJBp shifts towards a lower frequency and the intensity of the boson peak D（ωBP）/ωBp increases, indicating that the position and the strength of the boson peak are controlled by the polydispersity of the system. Moreover, the inverse of the boson peak intensity ωBP/D（ωBP）, the shear modulus G, and the basin curvature SIS all have a similar dependence on s, implying that the s dependence of the vibrational density of states at low frequencies likely originates from the s dependence of the basin curvature.
We study the effect of size polydispersity on the stress distributions and structural properties of static frictionless packings under isotropic compressions.More than 50 isostatic packings with constant mean stress of 1 kPa are generated for each size polydispersity s with a uniform distribution of diameter between(d_(0-s)/2)and(d_(0+s)/2).In order to vary the degree of positional order,the size polydispersity s ranges from 0 to 0.5.Several typical structural characterizations,(i.e.,the height of the first pair correlation peak,the global and the local order parameters),the probability distribution of the normalized mean stress and the stress-stress correlation are calculated.The result shows that(i)the stress distribution scales as a power law in the limit of small stresses,and the distribution displays a Gaussian tail in the limit of large stresses;(ii)s has no evident influence on the structural and mechanical properties when s>0.2.
Granular materials are omnipresent in industries and in nature. For small strains, elastic-plastic and hypoplastic constitutive relations are widely used in engineering practice, but they are not a significant reflection of the underlying physics. Under a unified thermodynamics framework explaining the physics of materials, granular solid hydrodynamics （GSH） was an ex- tension towards describing granular materials, not only solid-like, but also fluid-like behaviors. In this paper, the fundamentals of GSH are briefly treated and then simplified to analyze quasi- static deformations in triaxial compressions. The calculated stress-strain relations and volumetric strain are compared with experimental results. The influences of the major parameters in GSH, especially their cross coupling influences, are analyzed and their physical meanings are further clarified. After parameters were calibrated, the calculated stress values in the characteristic stress state are found to be within 22% of tested values. Meanwhile, the energy dissipation during triaxial compression is analyzed. The above results support and partially quantify GSH.
