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INTRODUCTION
The behavior of granular media is complex and surprising. Small changes in individual particle shape or material properties can result in large changes in aggregate response. The mechanics of granular media is important to many fields of application, such as powder processing, avalanche mechanics, soil consolidation, food processing, bitumen technology, and sintering. Yet many aspects of the fundamental mechanical behavior of granular aggregates are not well understood. RESEARCH The purpose of this research is to develop a two-dimensional particle based model for the investigation of the effect of particle size, shape, orientation, distribution, and compaction history on the macro behavior of visco-plastic powders, during and after compaction. The Finite Element Simulation The method for the numerical simulation of the aggregate of particles is the finite element method where each particle is represented by a single particle-element. Various methods for creating these particle-elements are being investigated, including (1) a new polygonal element (2) a cluster of standard elements and (3) an assumed stress hybrid finite element of Pian (1964). Micro Constitutive Theory The elements are modeled as purely visco-plastic materials. A bi-linear formulation is being considered to simulate a yield stress below which plastic flow is small and above which, large plastic strain rates will be possible. Strain hardening will be incorporated into the yield stress, thus creating history dependent constitutive behavior. Also, a general nonlinear constitutive model is being considered for which plastic flow occurs at any level of stress, but becomes much more pronounced with increased stress. Incremental Solution Algorithm The initial configuration and density of the elements is created using a program to randomly generate distribution, size, shape, and orientation, but with certain prevailing characteristics including, for example, the percent of particles of certain size, or oriented in a particular direction. In this initial investigation, the mesh of particles is confined to rectangular regions with either periodic boundaries to simulate an infinite medium or fixed boundaries to simulate a specific packing. |
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Once an initial particle configuration is established, an incremental transient analysis is conducted using various loading conditions for the compaction. For each time increment, the nodal point velocities are calculated based on the current stress, strain, and strain rate within the elements. Once determined, each element's position and configuration is updated using a quasi-Lagrangian algorithm. Techniques for conducting these updates is an important aspect of the research. The proposed model will track the deformation of the particle aggregate from its initial stage of particle contacts through the state that appears to be (except for the tangential slip between elements) a continuum. During the compaction, it is possible that either global or local instabilities will occur, manifested by the singularity, or near singularity, of the stiffness matrix. Global instabilities will occur when mechanisms develop that allow global motion with no, or very little, increase in external forces. |