Geometry-aware Nodal Influence Factors for Mitigating Boundary Effects in Bond-based Peridynamics
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Peridynamic formulations are attractive for fracture because they regularize displacement discontinuities with nonlocal interactions, as in bond-based peridynamics. In bounded domains, however, the interaction neighbourhoods of points close to free surfaces, cracks or pores are truncated, which breaks horizon symmetry. The resulting loss of neighbours leads to artificial surface compliance and inconsistencies in the discrete peridynamic derivative and energy operators that do not vanish with grid refinement, thereby limiting the predictive capability of bond-based peridynamics. In this work we first quantify these effects by comparing the spectral response of full- and truncated-horizon operators in one and two dimensions. We then introduce a geometry-aware surface correction for bond-based peridynamics that restores, as far as possible, the behaviour of a full horizon while keeping the original horizon radius and bond topology. The correction is expressed through scalar influence factors attached to every node; each bond contribution is scaled by the average of the two endpoint factors, preserving pairwise reciprocity and the symmetry of the global stiffness matrix. The nodal factors are obtained in a single, load-independent preprocessing step by solving local least-squares problems that enforce agreement between truncated-horizon and analytically evaluated full-horizon derivative and energy operators on a polynomial test space. The resulting scheme requires neither ghost particles nor coupling to classical continuum models, and it improves not only the near-surface response but also the accuracy of interior volume integration. Numerical examples in one and two dimensions, including quasi-static benchmarks and a Kalthoff--Winkler-type dynamic fracture test, show that the optimized influence factors markedly reduce boundary-induced softening, yield more consistent energy measures and significantly accelerate convergence of bond-based peridynamic solutions.
