Three-Dimensional Continuum-Level Simulation of Shear Banding in Metallic Glasses*

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 test the method by simulating three-dimensional shear band nucleation and growth in materials undergoing simple shear. We also present a variation of the method based on a coordinate transformation that enables direct mapping between continuum-level boundary conditions and the Lees-Edwards boundary conditions that are frequently imposed in molecular dynamics simulations, enabling direct comparisons between continuum and discrete simulation.