Abstract
The primary mode of failure in disordered solids results from the formation and persistence of highly localized regions of large plastic strains known as shear bands. Continuum-level field theories capable of predicting this mechanical response rely upon an accurate representation of the initial and evolving states of the amorphous structure. We perform molecular dynamics simulations of a metallic glass and propose a methodology for coarse graining discrete, atomistic quantities, such as the potential energies of the elemental constituents. A strain criterion is established and used to distinguish the coarse-grained degrees-of-freedom inside the emerging shear band from those of the surrounding material. A signal-to-noise ratio provides a means of evaluating the strength of the signal of the shear band as a function of the coarse graining. Finally, we investigate the effect of different coarse graining length scales by comparing a two-dimensional, numerical implementation of the effective-temperature description in the shear transformation zone (STZ) theory with direct molecular dynamics simulations. These comparisons indicate the coarse graining length scale has a lower bound, above which there is a high level of agreement between the atomistics and the STZ theory, and below which the concept of effective temperature breaks down.
Highlights
Amorphous solids are characterized by a complex, random arrangement of their atomic or molecular constituents [1,2,3]
In this paper we propose a methodology for coarse-graining discrete, atomistic data pertaining to an amorphous solid, and use the coarse-grained representations to initialize and validate the effective-temperature dynamics of the shear transformation zone (STZ) theory
We have presented a study of shear banding using non-equilibrium molecular dynamics (NEMD) simulations and a two-dimensional numerical implementation of the continuum STZ effectivetemperature theory
Summary
Amorphous solids are characterized by a complex, random arrangement of their atomic or molecular constituents [1,2,3]. A mathematical field theory of this kind has significant advantages as it essentially reduces the particle-level complexity of amorphous plasticity to a boundary-value problem in solid mechanics, but with the challenge of generating appropriate initial conditions, determining values of the theory’s physical parameters, and establishing an accurate method of validation Related to these considerations is the notion that a well-formulated continuum theory must have far fewer degrees-of-freedom (DOF) than, for example, detailed atomistic simulations, and should provide a computationally efficient description of the mechanical response. In most mesoscale models the RVE is merely taken to be the size of an individual STZ or slip event, and so the fundamental question regarding how to correctly average over experimental or atomistic data of the amorphous microstructure has not been addressed These approaches have no connection to fundamental thermodynamic considerations, which are known to be essential in describing the shear-induced disordering of the material’s structure during plastic deformation [52]. V with a discussion of how this preliminary work can inform future efforts to develop continuum theories of amorphous plasticity where coarse-grained representations of atomistic data are used to parametrize and validate the material models
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