Research Of The Buckling Deformation Of Force Chain And Constitutive Model Of Granular Materials

The study of granular materials institutes multiscale mechanics involving several physical hierachical structure and mechanism, which shows that inside granular materials the internal cause of bearing external load is the energy storage and consumption induced by buckling deformation and relative displacement of structural grains in the force chain of the shear zone. Therefore, the key of studying the constitutive model of granular materials is to establish a mechanism centering on deformation and destruction of the force chain.First two types of constitutive models are discussed according to different modeling ideas:constitutive model based upon dualistic exposition theory and constitutive model based upon deformation properties of clusters of grains. The former one whose dependent variable is continuous, essentially referring to the theory of continuous media, links the displacement of microcosmic grains and macroscopic deformation of continuous media by using affine mechanism. The latter one adopts separable variables and essentially avoids affine. The formula of plastic evolution is deduced from boundary conditions provided by buckling deformation analysis model of the force chain.Secondly, it comes up with the mechanic mechanism of deformation and destruction of the force chain in granular materials of density and cohesionlessness and under standard static loading effect without taking granular damage into account. With displacement model between grains, establish buckling deformation analysis model of the force chain regarding changing radiuses of grains. Given same radiuses of grains, this model is similar to Tordesillas' model which can match the experimental results obtained by DEM with definite parameters; the loading and deformation properties of the force chain have closer relationship with changing radiuses of grains after being analyzed in that case in changing positions.Thirdly, a constitutive model of granular materials of density and cohesionlessness comes after the buckling deformation analysis model of the force chain, whose variables are microcosmic and, different from empirical variables, have explicit physical significance. Variables in this model together with its evolving formula are merely related with loading deformation of the force chain. Strain softening in the process of shearing in granular materials can be depicted inn view of the meso-mechanism with this model.Fourthly, it is analyzed that the loading and deformation properties of the force chain are also concerned with the original shape of the force chain, the size and assignment of lateral bracing grains beside the granular radius. The original buckling deformation the force chain reduces the chain's carrying capacity and the lateral bracing force cannot pass the center of the middle grains horizontally due to different size and asymmetric assignment of lateral bracing grains. For this reason, the model with original deformation and asymmetric lateral bracing is ultimately studied and compared with the original model the fitted accuracy of the loading deformation curve calculated in the new model is greatly improved.