Surface and boundary corrections in peridynamics using optimized nodal influence weights

Peridynamics (PD), similarly to some other nonlocal continuum theories, exhibits truncated interaction horizons near free surfaces, cracks, and voids in bounded domains. This loss of neighbors causes artificial surface effects and inconsistencies in the derivative and energy operators that persist under discretization refinement, limiting PD accuracy and robustness. First, the analysis and numerical isolation of the effects of horizon truncation on these operators are carried out, showing how it induces surface softening in bond‐based and stiffening/softening in state‐based PD formulations. Then, a purely PD‐based surface correction is proposed to restore full‐horizon behavior while preserving the original horizon radius and bond topology. Each node is assigned a scalar influence weight, and every bond is scaled by the average of the endpoint weights to maintain symmetry. The nodal influence weights are computed in a preprocessing optimization step enforcing agreement between truncated‐ and full‐horizon derivative and energy operators. Unlike existing approaches, the proposed method does not rely on ghost particles, variable horizons, or reference solutions from classical continuum mechanics (CCM). Benchmarks in one, two, and three dimensions, including a dynamic brittle fracture test, show that the optimized nodal influence weights reduce boundary‐induced surface effects, improve energy consistency, and accelerate convergence of PD solutions. Analytical evaluation of the calibration targets over full‐horizons also improves interior volume integration accuracy. The proposed scheme is simple to implement in existing PD codes, incurs only a modest preprocessing cost, performs robustly for flat and curved boundaries on both regular and irregular point sets, produces reliable crack paths, and applies to both bond‐based and ordinary state‐based PD formulations. An open‐source Python implementation, perifit, is provided.

Content

Subjects

horizon truncation

nodal influence weights

open-source software

peridynamics

surface correction

DDC Class

620.1: Engineering Mechanics and Materials Science

Funding References

Funding(s)

EXC 3120 - BlueMat - Wassergesteuerte Materialien

EXC 3120 BlueMat - Cross Area Modeling

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https://creativecommons.org/licenses/by/4.0/

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Numerical Meth Engineering - 2026 - Shojaei - Surface and Boundary Corrections in Peridynamics Using Optimized Nodal.pdf

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