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State-based peridynamic models provide an important extension of bond-basedmodels that allow the description of general linearly elastic materials.Meshfree discretizations of these nonlocal models are attractive due to theirability to naturally handle fracture. However, singularities in the integraloperators have historically proven problematic when seeking convergentdiscretizations. We utilize a recently introduced optimization-based quadratureframework to obtain an asymptotically compatible scheme able to discretelyrecover local linear elasticity as the nonlocal interaction is reduced at thesame rate as the grid spacing. By introducing a correction to the definition ofnonlocal dilitation, surface effects for problems involving bond-breaking andfree surfaces are avoided without the need to modify the material model. We usea series of analytic benchmarks to validate the consistency of this approach,illustrating second-order convergence for the Dirichlet problem, andfirst-order convergence for problems involving curvilinear free surfaces andcomposite materials. We additionally illustrate that these results hold formaterial parameters chosen in the near-incompressible limit.

Asymptotically compatible meshfree discretization of state-based peridynamics for linearly elastic composite materials