A novel and effective way to impose boundary conditions and to mitigate the surface effect in state‑based Peridynamics

AbstractPeridynamics is a nonlocal continuum theory capable of modeling effectively crack initiation and propagation in solid bodies. However, the nonlocal nature of this theory is the cause of two main problems near the boundary of the body: an undesired stiffness fluctuation, the so‐called surface effect, and the difficulty of defining a rational method to properly impose the boundary conditions. The surface effect is analyzed analytically and numerically in the present paper in a state‐based peridynamic model. The authors propose a modified fictitious node method based on an extrapolation with a truncated Taylor series expansion. Furthermore, a rational procedure to impose the boundary conditions is defined with the aid of the fictitious nodes. In particular, Neumann boundary conditions are implemented via the peridynamic concept of force flux. The accuracy of the proposed method is assessed by means of several numerical examples for a state‐based peridynamic model: with respect to the peridynamic model adopting no corrections, the results are significantly improved even if low values of the truncation order for the Taylor expansion are chosen

Aeroelastic behaviour of the inverted jet spoilers

Aerodynamic and structural analyses on the inverted jet spoiler highlighted not only the low possibility of damaging or fracturing the material, but also the high probability of aeroelastic vibration occurrence because of the device large deformation due to the low stiffness of the spoiler panel. It was demonstrated that spoiler stiffness increases by implementing stiffer materials, shortening the chord-wise length, thickening the panel and lengthening the span-wise dimension

Peridynamic simulation of elastic wave propagation by applying the boundary conditions with the surface node method

Peridynamics is a novel nonlocal theory able to deal with discontinuities, such as crack initiation and propagation. Near the boundaries, due to the incomplete nonlocal region, the peridynamic surface effect is present, and its reduction relies on using a very small horizon, which ends up being expensive computationally. Furthermore, the imposition of nonlocal boundary conditions in a local way is often required. The surface node method has been proposed to solve both the aforementioned issues, providing enhanced accuracy near the boundaries of the body. This method has been verified in the cases of quasi-static elastic problems and diffusion problems evolving over time, but it has never been applied to a elastodynamic problems. In this work, we show the capabilities of the surface node method to solve a peridynamic problem of elastic wave propagation in a homogeneous body. The numerical results converge to the corresponding peridynamic analytical solution under grid refinement and exhibit no unphysical fluctuations near the boundaries throughout the whole timespan of the simulation