  Shear transformations (i.e., localised rearrangements of particles resulting
in the shear deformation of a small region of the sample) are the building
blocks of mesoscale models for the flow of disordered solids. In order to
compute the time-dependent response of the solid material to such a shear
transformation, with a proper account of elastic heterogeneity and shear wave
propagation, we propose and implement a very simple Finite-Element (FE) -based
method. Molecular Dynamics (MD) simulations of a binary Lennard-Jones glass are
used as a benchmark for comparison, and information about the microscopic
viscosity and the local elastic constants is directly extracted from the MD
system and used as input in FE. We find very good agreement between FE and MD
regarding the temporal evolution of the disorder-averaged displacement field
induced by a shear transformation, which turns out to coincide with the
response of a uniform elastic medium. However, fluctuations are relatively
large, and their magnitude is satisfactorily captured by the FE simulations of
an elastically heterogeneous system. Besides, accounting for elastic anisotropy
on the mesoscale is not crucial in this respect. The proposed method thus paves
the way for models of the rheology of amorphous solids which are both
computationally efficient and realistic, in that structural disorder and
inertial effects are accounted for.
