A damage correspondence formulation that enables direct incorporation of damage models from local continuum damage mechanics theory into nonlocal peridynamics for modeling and simulating materials failure is presented. The model was developed based on the bond-associated concept using non-spherical influence functions. It not only inherently removes the material instability in the conventional material correspondence formulation, but also significantly improves the accuracy of bond-level continuum-like measures such as deformation gradient. As a result, the correspondence is established at bond level instead of material point level. By directly using damage models from local continuum theory in the peridynamics, the developed correspondence model provides a consistent and inherently nonlocal approach to model material failure as progressive material mechanical property degradation following the local continuum damage mechanics approach. The numerical study demonstrated that the proposed model can accurately predict damage initiation and growth for various practical problems. In addition, it was found that a small horizon of δ =2Δ x can be used in the proposed model to greatly improve computational efficiency while maintaining the same level of prediction accuracy.
This study presents a computational framework for implementing bond-based peridynamics (PD) within LS-DYNA using truss elements. A MATLAB pre-processor provides a parametric environment where users define domain dimensions, material properties, discretization, and initial crack configurations. The algorithm features automated discontinuity handling to generate intact or pre-cracked models. It utilizes a node-duplication logic that introduces physical cracks while maintaining mass conservation. Furthermore, the framework automatically manages node generation, interaction list construction, cross-sectional area calculations, and yield stress-based failure calibration. A comprehensive set of benchmark scenarios validates the proposed framework. First, the investigation began with a systematic evaluation of mesh sensitivity and horizon radius effects. Second, implicit static analyses evaluated intact beam geometries under axial and bending loads. By systematically increasing the macroscopic structural dimensions under a fixed horizon-to-grid ratio, the PD results demonstrated convergence toward classical analytical solutions. Third, an explicit transient analysis evaluated the dynamic transverse response of an intact cantilever beam. The PD tip displacement history showed consistent alignment when compared directly against standard solid finite element formulations. Third, the framework simulated dynamic crack propagation in a pre-cracked specimen under plane stress conditions. The numerical model captured the failure process, including crack initiation, progressive branching, and total fracture. Finally, a simulated quasi-static three-point bending test on a concrete specimen verified the framework’s capability for quasi-brittle materials. The numerical outcomes showed comparable trends with experimental Load-Crack Mouth Opening Displacement (Load-CMOD) curves, capturing both the peak load and post-peak softening behavior. Ultimately, the developed framework offers a practical approach for simulating static deformations and complex fracture behaviors in structural materials.
This study develops an analytical framework for examining the transverse vibration behavior of bi-directional functionally graded (B-FG) nanobeams, whose material characteristics vary through both the width and height of the cross-section. The nanobeam is modelled within the context of the nonlocal Euler–Bernoulli beam theory and is supported by simple supports at both ends, while also being constrained by rotational springs. Under the presence of an axial compressive force, the governing relations for the beam with spatially varying material properties and the corresponding nonlocal vibration equations are first formulated. Subsequently, an analytical solution strategy combining the Fourier sine series with Stokes’ transform is employed. Enforcing the force and moment boundary conditions leads to an eigenvalue system explicitly incorporating the rotational spring stiffnesses. Setting the determinant of the resulting characteristic equation equal to zero provides the natural frequencies, which are evaluated for varying material gradation parameters, spring stiffnesses, nonlocal effects, and axial load compression levels. The principal novelty of this work lies in presenting an analytical solution for B-FG nanobeams with deformable rotational end restraints under axial compression.
Fracture resistance is a critical consideration in engineering structures, particularly in applications where material failure can have catastrophic consequences. Traditional topology optimization methods often struggle to account for fracture propagation due to the inherently nonlocal nature of crack formation and growth. This work presents a framework for topology optimization that integrates bond-based peridynamics, a nonlocal continuum theory capable of modeling fracture without external failure criteria, with differentiable programming via JAX to enable gradient-based optimization of fracture-resistant designs. The peridynamic damage variable, defined as the volume-averaged fraction of broken bonds at each material point, is adopted as the optimization objective, providing a more direct indicator of discrete fracture than strain energy density or total fracture energy. Using this framework, optimized geometries are identified that provide highly localized reinforcement, forming impedance mismatches that reflect shock waves and suppress fracture. In one-dimensional examples, damage-based optimization produced fracture-resistant structures using substantially less material than strain energy density minimization and converged in less than 0.5
An accurate model for simulating shear deformation and model II crack propagation is essential for investigating the failure mechanism underlying material fracture behavior. In this paper, the traditional ordinary state-based peridynamic model is refined by introducing a rotation angle term to accurately capture shear-related behaviors, including shear deformation and mode II fracture. Furthermore, the proposed model eliminates the influence of rigid body rotation and overcomes the limitations of the traditional bond-based peridynamic theory regarding material’s Poisson ratio. Subsequently, a failure criterion based on a skew angle is incorporated to enable the simulation of mode II crack propagation. To validate the model, several benchmark cases are conducted, including an intact plate under in-plane bending loads, a plate with an initial crack subject to shear loading, and a plate with a hole under compressive loading. The high degree of consistency between the deformation predicted by the proposed model and the finite element method confirms the present peridynamic model’s accuracy. Finally, the model’s ability in predicting mode II crack propagation is demonstrated through the agreement between the simulated propagation path and existing results for a plate under shear loading.
