Hypo-elastoplasticity is a flexible framework for modeling the mechanics of
many hard materials under small elastic deformation and large plastic
deformation. Under typical loading rates, most laboratory tests of these
materials happen in the quasi-static limit, but there are few existing
numerical methods tailor-made for this physical regime. In this work, we extend
to three dimensions a recent projection method for simulating quasi-static
hypo-elastoplastic materials. The method is based on a mathematical
correspondence to the incompressible Navier-Stokes equations, where the
projection method of Chorin (1968) is an established numerical technique. We
develop and utilize a three-dimensional parallel geometric multigrid solver
employed to solve a linear system for the quasi-static projection. Our method
is tested through simulation of three-dimensional shear band nucleation and
growth, a precursor to failure in many materials. As an example system, we
employ a physical model of a bulk metallic glass based on the shear
transformation zone theory, but the method can be applied to any
elastoplasticity model. We consider several examples of three-dimensional shear
banding, and examine shear band formation in physically realistic materials
with heterogeneous initial conditions under both simple shear deformation and
boundary conditions inspired by friction welding.Comment: Final version. Accepted for publication in Computer Physics
Communication
