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.
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.
Fresh cement mortar is a type of workable paste,which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering.In this paper,Papanastasiou’s model for Bingham fluids is solved by using the multiplerelaxation-time lattice Boltzmann model(MRT-LB).Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou’s model provides a good approximation of realistic Bingham plastics for values of m>108.For lower values of m,Papanastasiou’s model is valid for fluids between Bingham and Newtonian fluids.The MRT-LB model is validated by two benchmark problems:2D steady Poiseuille flows and lid-driven cavity flows.Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability.We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle.Besides the rich flow structures obtained in this work,the dynamics fluid force on the round particle is calculated.Results show that both the Reynolds number Re and the Bingham number Bn afect the drag coefcients CD,and a drag coefcient with Re and Bn being taken into account is proposed.The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed.Finally,the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields.These results help simulation of fresh concrete flowing in porous media.
A granular material is a conglomeration of discrete solid particles.It is intrinsically athermal because its dynamics always occur far from equilibrium.In highly excited gaseous states,it can safely be assumed that only binary interactions occur and a number of kinetic theories have been successfully applied.However,for granular flows and solidlike states,the theory is still poorly understood because of the internally correlated structures,such as particle clusters and force networks.The current theory is that the mesoscale characteristics define the key differences between granular materials and homogeneous solid materials.Widespread interest in granular materials has arisen among physicists,and significant progress has been made,especially in understanding the jamming phase diagram and the characteristics of the jammed phase.In this paper,the underlying physics of the mesoscale structure is discussed in detail.A multiscale framework is then proposed for dense granular materials.
