Fracture mechanics‐based progressive damage modelling of adhesively bonded fibre‐reinforced polymer joints

A quasi‐static progressive damage model for prediction of the fracture behaviour and strength of adhesively bonded fibre‐reinforced polymer joints is introduced in this paper. The model is based on the development of a mixed‐mode failure criterion as a function of a master R‐curve derived from the experimental results obtained from standard fracture mechanics joints. Consequently, the developed failure criterion is crack‐length and mode‐mixity dependent, and it takes into account the contribution of the fibre‐bridging effect. Energy release rate values for adhesively bonded double‐lap joints are obtained by using the virtual crack closure technique method in a finite element model, and the numerically obtained strain energy release rate is compared to the critical strain energy release rate given by the mixed‐mode failure criterion. The entire procedure is implemented in a numerical algorithm, which was successfully used for predicting the strength and R‐curve response of adhesively bonded double‐lap structural joints made of pultruded glass fibre‐reinforced polymers and epoxy adhesives.     

An investigation of T‐stresses in a plate with an inclined crack under biaxial loadings

For plates with an inclined crack of wide‐range aspect ratios under biaxial loadings, T‐stress values are calculated with three‐dimensional finite element method. The results show that the normalized T‐stress is crack length and orientation dependent. A linear equation for the relationship between normalized T‐stresses and biaxility factors is proposed to describe the normalized T‐stresses for different crack lengths and crack angles under different biaxial loadings, which is more convenient and involves wider biaxility ratios compared with the existing solutions. The plate thickness effect and the trend of normalized T‐stresses along the crack front thickness are also studied for mode I and I–II mixed‐mode cracks. Based on the analyses and comparisons, it is necessary to take the thickness effect into consideration when the crack length is long enough (a/W = 7/10). When the component of mode II is significant (β > 45°), and the biaxility ratios are negative, T‐stresses near the free surface are lower than those at other positions, which are the opposite of mode I crack and most of I–II mixed‐mode crack.     

The tetrahedral finite cell method: Higher‐order immersogeometric analysis on adaptive non‐boundary‐fitted meshes

The finite cell method (FCM) is an immersed domain finite element method that combines higher‐order non‐boundary‐fitted meshes, weak enforcement of Dirichlet boundary conditions, and adaptive quadrature based on recursive subdivision. Because of its ability to improve the geometric resolution of intersected elements, it can be characterized as an immersogeometric method. In this paper, we extend the FCM, so far only used with Cartesian hexahedral elements, to higher‐order non‐boundary‐fitted tetrahedral meshes, based on a reformulation of the octree‐based subdivision algorithm for tetrahedral elements. We show that the resulting TetFCM scheme is fully accurate in an immersogeometric sense, that is, the solution fields achieve optimal and exponential rates of convergence for h‐refinement and p‐refinement, if the immersed geometry is resolved with sufficient accuracy. TetFCM can leverage the natural ability of tetrahedral elements for local mesh refinement in three dimensions. Its suitability for problems with sharp gradients and highly localized features is illustrated by the immersogeometric phase‐field fracture analysis of a human femur bone. Copyright © 2016 John Wiley & Sons, Ltd.     

A monotone nonlinear finite volume method for approximating diffusion operators on general meshes

The basic principles of the discrete duality and nonlinear monotone finite volume methods are combined in order to obtain a new monotone nonlinear finite volume method for the approximation of diffusion operators on general meshes. Numerical results highlight both the second‐order accuracy of this method on general meshes and its capability to deal with challenging anisotropic diffusion problems on various computational domains. Copyright © 2016 John Wiley & Sons, Ltd.     

Vademecum‐based GFEM (V‐GFEM): optimal enrichment for transient problems

This paper proposes a generalized finite element method based on the use of parametric solutions as enrichment functions. These parametric solutions are precomputed off‐line and stored in memory in the form of a computational vademecum so that they can be used on‐line with negligible cost. This renders a more efficient computational method than traditional finite element methods at performing simulations of processes. One key issue of the proposed method is the efficient computation of the parametric enrichments. These are computed and efficiently stored in memory by employing proper generalized decompositions. Although the presented method can be broadly applied, it is particularly well suited in manufacturing processes involving localized physics that depend on many parameters, such as welding. After introducing the vademecum‐generalized finite element method formulation, we present some numerical examples related to the simulation of thermal models encountered in welding processes. Copyright © 2016 John Wiley & Sons, Ltd.     

Error estimation for the automated multi‐level substructuring method

In this study, we propose an effective method to estimate the reliability of finite element models reduced by the automated multi‐level substructuring (AMLS) method. The proposed error estimation method can accurately predict relative eigenvalue errors in reduced finite element models. A new, enhanced transformation matrix for the AMLS method is derived from the original transformation matrix by properly considering the contribution of residual substructural modes. The enhanced transformation matrix is an important prerequisite to develop the error estimation method. Adopting the basic concept of the error estimation method recently developed for the Craig–Bampton method, an error estimation method is developed for the AMLS method. Through various numerical examples, we demonstrate the accuracy of the proposed error estimation method and explore its computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

A distortion measure to validate and generate curved high‐order meshes on CAD surfaces with independence of parameterization

A framework to validate and generate curved nodal high‐order meshes on Computer‐Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin‐shell and 3D finite element analysis with unstructured high‐order methods. First, we define a distortion (quality) measure for high‐order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high‐order), and handles with low‐quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high‐order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process. Copyright © 2015 John Wiley & Sons, Ltd.     

Identification of Pivotal Causes and Spreaders in the Time‐Varying Fault Propagation Model to Improve the Decision Making under Abnormal Situation

Under abnormal conditions, timely and effective decisions of system recovery and protective measures are of great significance for safety‐critical systems. The knowledge of the roles that network nodes play in the spreading process is crucial for developing efficient maintenance decisions; for singling out and preferential control, the ‘pivotal spreaders’ may be a way to maximize the chances to timely hinder the fault pervasion. Inspired by the inhomogeneous topological nature of a complex fault propagation network, this study is devoted to exploring the spreading capabilities of nodes regarding both structural connectivity and causal influence strength, so as to provide decisions of preferential recovery actions under specific fault scenarios. Specifically, the dynamic betweenness centrality and nonsymmetrical entropy are incorporated to adaptively measure the system‐wide fault diffusion risk of a set of controllable fault events. In order to model the dynamics and uncertainties involved in the complex fault spreading process, we introduce the model of a dynamic uncertain causality graph, based on which solutions of time‐varying structure decomposition and causality reduction are adopted to improve the reasoning efficiency. Verification experiments consisting of simulated calculation cases and generator faults of a nuclear power plant show empirically the effectiveness and applicability of this method in large‐scale engineering practice. Copyright © 2014 John Wiley & Sons, Ltd.     

Reliability Estimation of Blu‐Ray Recordable Media with Effect of Initial Recording Performance

The lifetime and the reliability of Blu‐Ray Recordable media were estimated with an acceleration test varying the temperature and the relative humidity. Some brand of the media showed relatively long lifetime over 80 years, but another brand was immeasurable because the media was broken during the acceleration procedure. A strong dependence of the lifetime of the media on the brand was observed. Effect of the initial recording performance in terms of the random symbol error rate and the jitter on the reliability was analyzed. The random symbol error rate showed a strong correlation with the reliability of the Blu‐Ray Recordable media. Copyright © 2014 John Wiley & Sons, Ltd.