  We propose a new second-order accurate lattice Boltzmann formulation for
linear elastodynamics that is stable for arbitrary combinations of material
parameters under a CFL-like condition. The construction of the numerical scheme
uses an equivalent first-order hyperbolic system of equations as an
intermediate step, for which a vectorial lattice Boltzmann formulation is
introduced. The only difference to conventional lattice Boltzmann formulations
is the usage of vector-valued populations, so that all computational benefits
of the algorithm are preserved. Using the asymptotic expansion technique and
the notion of pre-stability structures we further establish second-order
consistency as well as analytical stability estimates. Lastly, we introduce a
second-order consistent initialization of the populations as well as a boundary
formulation for Dirichlet boundary conditions on 2D rectangular domains. All
theoretical derivations are numerically verified by convergence studies using
manufactured solutions and long-term stability tests.
