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

impact force reconstruction in composite panels

Abstract Passive sensing is a branch of structural health monitoring which aims at detecting positions and intensities of impacts occurring on aeronautical structures. Impacts are one of the main causes of damage in composite panels, limiting the application of these modern components on aircraft. In particular, impacts can cause the so called barely visible impact damage which, if not detected rapidly, can grow and lead to catastrophic failure. The determination of the impact location and the reconstruction of impact force is necessary to evaluate the health of the structure. These data may be measured indirectly from the measurements of responses of sensors located on the system subjected to the impact. The impact force reconstruction is a complex inverse problem, where the cause is to be inferred from its consequences. Inverse problems are in general ill-posed and ill-conditioned. Therefore, several techniques have been employed in the last four decades and have proven to be effective within certain limitations. Among these methods, transfer function based methods have been mainly validated for low-energy impact where the linear assumption should be valid. Nonlinearities may affect the accuracy in the reconstruction process and thus in the evaluation of damage other techniques have been adopted, such as artificial neural networks (ANN) or genetic algorithms (GA). In this study, a stiffened panel model developed in Abaqus/CAE is first validated, then numerical simulations are used to obtain data for several impacts, characterized by different impact locations and different energy (by changing the impactor mass and/or velocity). Geometrical nonlinearities of the dynamic system are considered in order to represent accurately the mechanics of the composite panel. Then the complex nonlinear behavior will be modeled through a nonlinear system identification approach, such as ANN, and an intelligent algorithm with global search capabilities, such as GA, will be used in sequence to accurately recovery the impact force peak and, therefore, properly evaluate the health status of the structure

Matrix-based implementation and GPU acceleration of linearized ordinary state-based peridynamic models in MATLAB

Ordinary state-based peridynamic (OSB-PD) models have an unparalleled capability to simulate crack propagation phenomena in solids with arbitrary Poisson's ratio. However, their non-locality also leads to prohibitively high computational cost. In this paper, a fast solution scheme for OSB-PD models based on matrix operation is introduced, with which, the graphics processing units (GPUs) are used to accelerate the computation. For the purpose of comparison and verification, a commonly used solution scheme based on loop operation is also presented. An in-house software is developed in MATLAB. Firstly, the vibration of a cantilever beam is solved for validating the loop- and matrix-based schemes by comparing the numerical solutions to those produced by a FEM software. Subsequently, two typical dynamic crack propagation problems are simulated to illustrate the effectiveness of the proposed schemes in solving dynamic fracture problems. Finally, the simulation of the Brokenshire torsion experiment is carried out by using the matrix-based scheme, and the similarity in the shapes of the experimental and numerical broken specimens further demonstrates the ability of the proposed approach to deal with 3D non-planar fracture problems. In addition, the speed-up of the matrix-based scheme with respect to the loop-based scheme and the performance of the GPU acceleration are investigated. The results emphasize the high computational efficiency of the matrix-based implementation scheme.Comment: 32 pages, 16 figure

Numerical simulation of forerunning fracture in saturated porous solids with hybrid FEM/Peridynamic model

In this paper, a novel hybrid FEM and Peridynamic modeling approach proposed in Ni et al. (2020) is used to predict the dynamic solution of hydro-mechanical coupled problems. A modified staggered solution algorithm is adopted to solve the coupled system. A one-dimensional dynamic consolidation problem is solved first to validate the hybrid modeling approach, and both -convergence and -convergence studies are carried out to determine appropriate discretization parameters for the hybrid model. Thereafter, dynamic fracturing in a rectangular dry/fully saturated structure with a central initial crack is simulated both under mechanical loading and fluid-driven conditions. In the mechanical loading fracture case, fixed surface pressure is applied on the upper and lower surfaces of the initial crack near the central position to force its opening. In the fluid-driven fracture case, the fluid injection is operated at the centre of the initial crack with a fixed rate. Under the action of the applied external force and fluid injection, forerunning fracture behavior is observed both in the dry and saturated conditions.Comment: arXiv admin note: text overlap with arXiv:2307.1092

Hybrid FEM and peridynamic simulation of hydraulic fracture propagation in saturated porous media

This paper presents a hybrid modeling approach for simulating hydraulic fracture propagation in saturated porous media: ordinary state-based peridynamics is used to describe the behavior of the solid phase, including the deformation and crack propagation, while FEM is used to describe the fluid flow and to evaluate the pore pressure. Classical Biot poroelasticity theory is adopted. The proposed approach is first verified by comparing its results with the exact solutions of two examples. Subsequently, a series of pressure- and fluid-driven crack propagation examples are solved and presented. The phenomenon of fluid pressure oscillation is observed in the fluid-driven crack propagation examples, which is consistent with previous experimental and numerical evidences. All the presented examples demonstrate the capability of the proposed approach in solving problems of hydraulic fracture propagation in saturated porous media