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Item type:Publication, Access status: with files , Surface and boundary corrections in peridynamics using optimized nodal influence weights(Wiley, 2026-07-14); ; ; ; 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.Publicationtype: Journal Article41 61 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , On efficient simulation of self-assembling diblock copolymers using a peridynamic-enhanced Fourier spectral method(Elsevier, 2025-05-01); ; ; ; This study introduces a computational framework for simulating the self-assembly of diblock copolymers using a novel peridynamic (PD)-enhanced Fourier spectral method (FSM). Diblock copolymers, composed of two distinct polymer blocks, are capable of forming nanostructured domains with applications in nanoelectronics, photonics, and advanced membranes. Current simulation techniques face challenges in capturing the multiscale dynamics of polymer systems and are often limited by computational inefficiencies. Our approach combines a phase-field model with FSM for spatial discretization and leverages a PD-based diffusion operator to overcome the stability restrictions of explicit time-stepping schemes. This integration allows for larger time steps, ensuring both stability and computational efficiency. The method's scalability is enhanced through parallel implementation using C++ and OpenMP, optimized for multi-core CPUs. Validation through phase diagrams of copolymer melts and simulations of evaporation-induced self-assembly (EISA) processes demonstrates the capability of the proposed method to accurately capture large-scale, dynamic morphologies. Our approach provides a versatile framework and was found in certain examples to improve computational efficiency by more than a factor of 6 compared to forward-Euler FSM approach.Publicationtype: Journal Article24 20 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: with files , Dirichlet-type absorbing boundary conditions for peridynamic scalar waves in two-dimensional viscous media(Wiley, 2023-08-30); ; ; ; Construction of absorbing boundary conditions (ABCs) for nonlocal models is generally challenging, primarily due to the fact that nonlocal operators are commonly associated with volume constrained boundary conditions. Moreover, application of Fourier and Laplace transforms, which are essential for the majority of available methods for ABCs, to nonlocal models is complicated. In this paper, we propose a simple method to construct accurate ABCs for peridynamic scalar wave-type problems in viscous media. The proposed ABCs are constructed in the time and space domains and are of Dirichlet type. Consequently, their implementation is relatively simple, since no derivatives of the wave field are required. The proposed ABCs are derived at the continuum level, from a semi-analytical solution of the exterior domain using harmonic exponential basis functions in space and time (plane-wave modes). The numerical implementation is done using a meshfree collocation approach employed within a boundary layer adjacent to the interior domain boundary. The modes satisfy the peridynamic numerical dispersion relation, resulting in a compatible solution of the interior region (near-field) with that of the exterior region (far-field). The accuracy and stability of the proposed ABCs are demonstrated with several numerical examples in two-dimensional unbounded domains.Publicationtype: Journal ArticleScopus© Citations 4 74 74 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , Peridynamic elastic waves in two-dimensional unbounded domains: construction of nonlocal Dirichlet-type absorbing boundary conditions(Elsevier, 2023-02-17); ; ; ; The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. Our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.Publicationtype: Journal Article38 - Some of the metrics are blocked by yourconsent settings
Item type:Publication, Access status: without files , A hybrid meshfree discretization to improve the numerical performance of peridynamic models(2022-03-01); ; ; ; Efficient and accurate calculation of spatial integrals is of major interest in the numerical implementation of peridynamics (PD). The standard way to perform this calculation is a particle-based approach that discretizes the strong form of the PD governing equation. This approach has rapidly been adopted by the PD community since it offers some advantages. It is computationally cheaper than other available schemes, can conveniently handle material separation, and effectively deals with nonlinear PD models. Nevertheless, PD models are still computationally very expensive compared with those based on the classical continuum mechanics theory, particularly for large-scale problems in three dimensions. This results from the nonlocal nature of the PD theory which leads to interactions of each node of a discretized body with multiple surrounding nodes. Here, we propose a new approach to significantly boost the numerical efficiency of PD models. We propose a discretization scheme that employs a simple collocation procedure and is truly meshfree; i.e., it does not depend on any background integration cells. In contrast to the standard scheme, the proposed scheme requires a much smaller set of neighboring nodes (keeping the same physical length scale) to achieve a specific accuracy and is thus computationally more efficient. Our new scheme is applicable to the case of linear PD models and within neighborhoods where the solution can be approximated by smooth basis functions. Therefore, to fully exploit the advantages of both the standard and the proposed schemes, a hybrid discretization is presented that combines both approaches within an adaptive framework. The high performance of the developed framework is illustrated by several numerical examples, including brittle fracture and corrosion problems in two and three dimensions.Publicationtype: Journal Article63