  State-based peridynamic models provide an important extension of bond-based
models that allow the description of general linearly elastic materials.
Meshfree discretizations of these nonlocal models are attractive due to their
ability to naturally handle fracture. However, singularities in the integral
operators have historically proven problematic when seeking convergent
discretizations. We utilize a recently introduced optimization-based quadrature
framework to obtain an asymptotically compatible scheme able to discretely
recover local linear elasticity as the nonlocal interaction is reduced at the
same rate as the grid spacing. By introducing a correction to the definition of
nonlocal dilitation, surface effects for problems involving bond-breaking and
free surfaces are avoided without the need to modify the material model. We use
a series of analytic benchmarks to validate the consistency of this approach,
illustrating second-order convergence for the Dirichlet problem, and
first-order convergence for problems involving curvilinear free surfaces and
composite materials. We additionally illustrate that these results hold for
material parameters chosen in the near-incompressible limit.
