  We present the second set of benchmark problems for phase field models that
are being jointly developed by the Center for Hierarchical Materials Design
(CHiMaD) and the National Institute of Standards and Technology (NIST) along
with input from other members in the phase field community. As the integrated
computational materials engineering (ICME) approach to materials design has
gained traction, there is an increasing need for quantitative phase field
results. New algorithms and numerical implementations increase computational
capabilities, necessitating standard problems to evaluate their impact on
simulated microstructure evolution as well as their computational performance.
We propose one benchmark problem for solidification and dendritic growth in a
single-component system, and one problem for linear elasticity via the shape
evolution of an elastically constrained precipitate. We demonstrate the utility
and sensitivity of the benchmark problems by comparing the results of 1)
dendritic growth simulations performed with different time integrators and 2)
elastically constrained precipitate simulations with different precipitate
sizes, initial conditions, and elastic moduli. These numerical benchmark
problems will provide a consistent basis for evaluating different algorithms,
both existing and those to be developed in the future, for accuracy and
computational efficiency when applied to simulate physics often incorporated in
phase field models.
