  This paper concerns anisotropic two-dimensional and planar elasticity models
within the frameworks of classical linear elasticity and the bond-based
peridynamic theory of solid mechanics. We begin by reviewing corresponding
models from the classical theory of linear elasticity. This review includes a
new elementary and self-contained proof that there are exactly four material
symmetry classes of the elasticity tensor in two dimensions. We also summarize
classical plane strain and plane stress linear elastic models and explore their
connections to the pure two-dimensional linear elastic model, relying on the
definitions of the engineering constants. We then provide a novel formulation
for pure two-dimensional anisotropic bond-based linear peridynamic models,
which accommodates all four material symmetry classes. We further present
innovative formulations for peridynamic plane strain and plane stress, which
are obtained using direct analogies of the classical planar elasticity
assumptions, and we specialize these formulations to a variety of material
symmetry classes. The presented anisotropic peridynamic models are constrained
by Cauchy's relations, which are an intrinsic property of bond-based
peridynamic models. The uniqueness of the presented peridynamic plane strain
and plane stress formulations in this work is that we directly reduce
three-dimensional models to two-dimensional formulations, as opposed to
matching two-dimensional peridynamic models to classical plane strain and plane
stress formulations. This results in significant computational savings, while
retaining the dynamics of the original three-dimensional bond-based peridynamic
problems under suitable assumptions.

Classical Physics;Soft Condensed Matter