  We present a meshfree quadrature rule for compactly supported non-local
integro-differential equations (IDEs) with radial kernels. We apply this rule
to develop a strong-form meshfree discretization of a peridynamic solid
mechanics model that requires no background mesh. Existing discretizations of
peridynamic models have been shown to exhibit a lack of asymptotic
compatibility to the corresponding linearly elastic local solution. By posing
the quadrature rule as an equality constrained least squares problem, we obtain
asymptotically compatible convergence via reproducability constraints. Our
approach naturally handles traction-free conditions, surface effects, and
damage modeling for both static and dynamic problems. We demonstrate high-order
convergence to the local theory by comparing to manufactured solutions and to
cases with crack singularities for which an analytic solution is available.
Finally, we verify the applicability of the approach to realistic problems by
reproducing high-velocity impact results from the Kalthoff-Winkler experiments.
