Connecting discrete to the continuum: continuum-level simulation of shear-banding in metallic glasses on transforming grids with Lees-Edwards boundary conditons

We simulate a three-dimensional continuum-level elasto-plastic model of a bulk metallic glass based on the shear transformation zone (STZ) theory of amorphous plasticity. The simulation utilizes a new projection method valid in the quasi-static limit based on a mathematical correspondence between the Navier-Stokes equations for incompressible fluid flow and the equations of quasi-static hypoelastoplasticity. We emphasize a variation of the method based on a coordinate transformation that permits the use of Lees-Edwards boundary conditions at the continuum scale, enabling direct comparisons between continuum and discrete simulation. We consider several interesting numerical examples, including simple and pure shear boundary conditions imposed in the transformed frame.