L. Anand
Massachusetts Institute of Technology
Department of Mechanical Engineering
Under certain conditions many solids appear in a disordered form; such solids are referred to as amorphous or glassy. Important examples of amorphous solids are the current generation of bulk metallic glasses. When a metallic glass is deformed at ambient temperatures the inelastic deformation is characterized by the formation of intense localized shear bands; fracture typically occurs after very small inelastic strain in tension, but substantial inelastic strain levels can be achieved under states of confined compression, such as in indentation experiments. The plastic deformation of amorphous metallic glasses is fundamentally different from that in crystalline solids because of the lack of long-range order in the atomic structure of these materials. Molecular-dynamic computer simulations in the literature show that at a micromechanical level inelastic deformation in metallic glasses occurs by local shear transformations in clusters of atoms (≈ 30 to 50 atoms), and topologically such shear transformations require a local inelastic dilatation that produces an elastic strain field in the surrounding material that autocatalytically then initiates similar shear transformations in neighbouring volume elements, leading to the formation of shear bands. These simulations also suggest that a pressure-sensitive Coulomb-Mohr yield criterion describes the data pertaining to the onset of inelastic deformations in the numerical simulations quite well.
The Coulomb-Mohr yield condition is widely used in soil mechanics to determine the stress required for flow of a granular material; however, the flow-rule, that is, the equation which governs the flow behavior for this class materials is generally not agreed upon. In this talk we will present a complete three-dimensional elastic-viscoplastic constitutive model for the large deformation response of cohesive granular materials. The model is a generalization of the classical two-dimensional (plane-strain) .double-shearing. constitutive model to three-dimensions, includes the effects of elastic deformation, and the typical pressure-sensitive and dilatant, hardening/softening response observed in granular materials. We apply the new constitutive equations to model the inelastic deformation of a representative amorphous metallic glass under isothermal conditions.