  Molecular dynamics simulations frequently employ periodic boundary conditions
where the positions of the periodic images are manipulated in order to apply
deformation to the material sample. For example, Lees-Edwards conditions use
moving periodic images to apply simple shear. Here, we examine the problem of
precisely comparing this type of simulation to continuum solid mechanics. We
employ a hypoelastoplastic mechanical model, and develop a projection method to
enforce quasistatic equilibrium. We introduce a simulation framework that uses
a fixed Cartesian computational grid on a reference domain, and which imposes
deformation via a time-dependent coordinate transformation to the physical
domain. As a test case for our method, we consider the evolution of shear bands
in a bulk metallic glass using the shear transformation zone theory of
amorphous plasticity. We examine the growth of shear bands in simple shear and
pure shear conditions as a function of the initial preparation of the bulk
metallic glass.
