Abstract
Peridynamics (PD) is a novel nonlocal theory of continuum mechanics capable of describing crack formation and propagation without defining any fracture rules in advance. In this study, a multi-grid bond-based dual-horizon peridynamics (DH-PD) model is presented, which includes varying horizon sizes and can avoid spurious wave reflections. This model incorporates the volume correction, surface correction, and a technique of nonuniformity discretization to improve calculation accuracy and efficiency. Two benchmark problems are simulated to verify the reliability of the proposed model with the effect of the volume correction and surface correction on the computational accuracy confirmed. Two numerical examples, the fracture of an L-shaped concrete specimen and the mixed damage of a double-edged notched specimen, are simulated and analyzed. The simulation results are compared against experimental data, the numerical solution of a traditional PD model, and the output from a finite element model. The comparisons verify the calculation accuracy of the corrected DH-PD model and its advantages over some other models like the traditional PD model.
Highlights
Material fracture is a classical problem in solid mechanics [1]
Volume Correction and Surface Correction In PD theory, the problem domain is discretized into a series of particles, and each particle interacts with the neighboring particles in its horizon
The parameters are set k Errork = u − uanalytic, and the analysis shows that the introduction of the volume correction and surface correction reduces the error to 0.01 mm
Summary
Material fracture is a classical problem in solid mechanics [1]. In contrast to experimental research, numerical simulations provide a more efficient approach to understanding material fractures since they eliminate the limitations of complex specimen preparation, test environment conditions, and loading systems. The element erosion technique [9,10] and the phase field method [11,12] were proposed to simulate the problems of crack propagation with different levels of success. Silling et al [19,20] proposed a new nonlocal theory of continuum mechanics called peridynamics (PD) for solving material fracture problems It describes such a phenomenon by means of the failure of bonds linking material points. Shojaei et al [35] proposed an adaptive refinement strategy to use a variable grid size in a peridynamic model, which was verified to be effective and efficient This approach was successfully applied to simulate the fracture of a ceramic disk under central thermal shock [36]. This model is applied to analyze two numerical examples to validate the model’s reliability and applicability
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