Simulation of thermal shock cracking in ceramics using bond-based peridynamics and FEM

European Union FP7 project ‘Mechanics of refractory materials at high-temperature for advanced industrial technologies’ under contract number PIAPP-GA-2013-60975

Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

A peridynamics (PD)–extended finite element method (XFEM) coupling strategy for brittle fracture simulation is presented. The proposed methodology combines a small PD patch, restricted near the crack tip area, with the XFEM that captures the crack body geometry outside the domain of the localised PD grid. The feasibility and effectiveness of the proposed method on a Mode I crack opening problem is examined. The study focuses on comparisons of the J integral values between the new coupling strategy, full PD grids and the commercial software Abaqus. It is demonstrated that the proposed approach outperforms full PD grids in terms of computational resources required to obtain a certain degree of accuracy. This finding promises significant computational savings when crack propagation problems are considered, as the efficiency of FEM and XFEM is combined with the inherent ability of PD to simulate fracture

On the computational derivation of bond-based peridynamic stress tensor

The concept of ‘contact stress’, as introduced by Cauchy, is a special case of a nonlocal stress tensor. In this work, the nonlocal stress tensor is derived through implementation of the bond-based formulation of peridynamics that uses an idealised model of interaction between points as bonds. The method is sufficiently general and can be implemented to study stress states in problems containing stress concentration, singularity, or discontinuities. Two case studies are presented, to study stress concentration around a circular hole in a square plate and conventionally singular stress fields in the vicinity of a sharp crack tip. The peridynamic stress tensor is compared with finite element approximations and available analytical solutions. It is shown that peridynamics is capable of capturing both shear and direct stresses and the results obtained correlate well with those obtained using analytical solutions and finite element approximations. A built-in MATLAB code is developed and used to construct a 2D peridynamic grid and subsequently approximate the solution of the peridynamic equation of motion. The stress tensor is then obtained using the tensorial product of bond force projections for bonds that geometrically pass through the point. To evaluate the accuracy of the predicted stresses near a crack tip, the J-integral value is computed using both a direct contour approximation and the equivalent domain integral method. In the formulation of the contour approximation, bond forces are used directly while the proposed peridynamic stress tensor is used for the domain method. The J-integral values computed are compared with those obtained by the commercial finite element package Abaqus 2018. The comparison provides an indication on the accurate prediction of the state of stress near the crack tip

Digital clone testing platform for the assessment of SHM systems under uncertainty

The performance of a Structural Health Monitoring (SHM) system can be assessed using Probability of Detection (PoD) curves, which is a common tool for the evaluation of Non-Destructive Testing (NDT) methods. This study presents a novel digital clone platform to quantify and account for uncertainties that can be detrimental to the reliability of a SHM system. Uncertainties relating to experimental measurement noise and Environmental and Operational Conditions (EOC) are considered during the definition of a threshold value that aims at reliably distinguishing between pristine and damaged signals. At the same time, the variability of impact damage characteristics and uncertainties associated with Lamb waves interaction in composites are captured though the Bayesian calibration of a Finite Element (FE) model using experimental observations. The FE model is integrated within the digital clone testing platform to substitute the experimental testing and generate a statistical sample of distributed impact events at different locations on a composite plate and compute the Model Assisted Probability of Detection (MAPOD). This approach allows the estimation of the system’s performance under different EOC that can be used during the selection and operation of a specific SHM configuration

Assessment of the performance of different element types for guided wave simulations in abaqus

Accurate numerical tools for the simulation of wave propagation are essential for the development and optimization of guided wave based Structural Health Monitoring systems. This article aims in delivering a systematic comparison of the Finite Element simulation of Lamb wave propagation using different types of elements. The numerical simulations are all realized within the environment of the commercial software Abaqus. In total three different element types are considered: conventional shell, continuum shell and 3D solid elements. To evaluate the performance of each element type, the numerically simulated signals are compared with experimental measurements from two panels. The first panel is made of Aluminium while the second is a layered composite panel. When continuum or 3D solid elements are used, the numerical predictions are closely correlated to the experimental observations. Accurate predictions were also made using conventional shell elements to model wave propagation in the first panel however, the group velocity for the first symmetric wave mode is over-estimated for the second panel when the excitation frequency is fc = 250kHz