Development of the Particle-Scale Definition of Stress and Strain for the Discrete Element Method
ENGINEER RESEARCH AND DEVELOPMENT CENTER VICKSBURG MS VICKSBURG
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The discrete element method DEM provides a realistic approach to modeling materials at fundamental length scales. Materials at the discrete scale can be the particle size in granular materials, micrometer sizes when dealing with polycrystalline materials, or nanometer sizes when dealing with biologic materials. Complex material behavior can be simulated as relatively simple interactions between discrete entities, obviating the need for sophisticated constitutive models. The ultimate goal is to obtain the engineering behavior at the prototype scale at which problems are formulated in terms of continuum mechanics. The simple concepts of kinematics for the discrete entities are tied to continuum quantities using affine projections and thermodynamic conjugates. The continuum quantities such as force and displacement are equated to their continuum counterparts, stress and strain, using the method of virtual power. The kinematics at the fundamental scale include the rotations of the discrete elements, which in contrast to those of material points in a continuum are independent of the translational motion. To accommodate the rotations as independent variables, the Cosserat continuum theory is used. The procedures are implemented in a Fortran subroutine, which can be used in the post-processing phase of DEM simulations. Example computations for three test cases are included.
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