Modeling of Discrete Granulates as Micropolar Continua

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Abstract
Granular material perceived as a collection of particles is modeled as a macrocontinuum. The model takes into account the effects of microdiscreteness and the interparticle contact properties in the system. With consideration of particle rotation, the continuum model for granular solid is found to be of micropolar type. The derived constitutive law of the material includes variables of Cauchy stress, polar stress, deformation strain, and polar strain. Considering the effect of particle interaction, the stresses are defined in terms of interparticle contact forces and contact couples. The constitutive coefficients are derived explicitly in terms of the interparticle contact stiffness. Using the derived stress‐strain relationships, a solution procedure based on variational principle is applied to obtain solutions for boundary value problems. Examples of boundary value problems are shown for particle assemblies with elastic contact interaction. The results are compared with those obtained from a discrete element method to demonstrate the applicability of this method.

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