2018/01/13 by Nathaniel Trask, Trask, Nathaniel, Huaiqian You +5 · 1 citation
Engineering · #Computational Physics (physics.comp-ph) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Geotechnical Engineering and Underground Structures #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.1801.04488
openalex publication_date 2018/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a meshfree quadrature rule for compactly supported non-local\nintegro-differential equations (IDEs) with radial kernels. We apply this rule\nto develop a strong-form meshfree discretization of a peridynamic solid\nmechanics model that requires no background mesh. Existing discretizations of\nperidynamic models have been shown to exhibit a lack of asymptotic\ncompatibility to the corresponding linearly elastic local solution. By posing\nthe quadrature rule as an equality constrained least squares problem, we obtain\nasymptotically compatible convergence via reproducability constraints. Our\napproach naturally handles traction-free conditions, surface effects, and\ndamage modeling for both static and dynamic problems. We demonstrate high-order\nconvergence to the local theory by comparing to manufactured solutions and to\ncases with crack singularities for which an analytic solution is available.\nFinally, we verify the applicability of the approach to realistic problems by\nreproducing high-velocity impact results from the Kalthoff-Winkler experiments.\n