  Meshfree discretizations of state-based peridynamic models are attractive due
to their ability to naturally describe fracture of general materials. However,
two factors conspire to prevent meshfree discretizations of state-based
peridynamics from converging to corresponding local solutions as resolution is
increased: quadrature error prevents an accurate prediction of bulk mechanics,
and the lack of an explicit boundary representation presents challenges when
applying traction loads. In this paper, we develop a reformulation of the
linear peridynamic solid (LPS) model to address these shortcomings, using
improved meshfree quadrature, a reformulation of the nonlocal dilitation, and a
consistent handling of the nonlocal traction condition to construct a model
with rigorous accuracy guarantees. In particular, these improvements are
designed to enforce discrete consistency in the presence of evolving fractures,
whose {\it a priori} unknown location render consistent treatment difficult. In
the absence of fracture, when a corresponding classical continuum mechanics
model exists, our improvements provide asymptotically compatible convergence to
corresponding local solutions, eliminating surface effects and issues with
traction loading which have historically plagued peridynamic discretizations.
When fracture occurs, our formulation automatically provides a sharp
representation of the fracture surface by breaking bonds, avoiding the loss of
mass. We provide rigorous error analysis and demonstrate convergence for a
number of benchmarks, including manufactured solutions, free-surface,
nonhomogeneous traction loading, and composite material problems. Finally, we
validate simulations of brittle fracture against a recent experiment of dynamic
crack branching in soda-lime glass, providing evidence that the scheme yields
accurate predictions for practical engineering problems.
